1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
1979 VERSION OF THE LINWOOD 40 VARIABLE, 1000 OBSERVATION PROGRAM
REFER TO FITTING EQUATIONS TO DATA BY DANIEL AND WOOD, SECOND EDITION, WILEY PUBLISHER,
FOR GLOSSARY OF TERMS, USER'S MANUAL, DETAILS OF CALCULATIONS AND INTERPRETATION OF RESULTS.
0FIRST BROWNLEE
0 CONTROL CARD INFORMATION ORDER OF CARDS
COL. INPUT MAX. ITEM (NOTE: BLANK ON CARD = 0) FIRST PROBLEM
1-18 PROBLEM IDENTIFICATION. 1 CONTROL CARD.
19-20 4 NUMBER OF INDEPENDENT VARIABLES READ IN 2 FORMAT CARD(S), IF ANY.
(ALLOW SPACE FOR TRANSFORMATIONS). 3 DELETE OBSERVATIONS CARD(S), IF ANY.
21-22 3 NUMBER OF DEPENDENT VARIABLES READ IN. 4 INDICATOR-VARIABLE-OBSERVATIONS CARD(S), IF ANY.
7 65 TOTAL NUMBER OF VARIABLES (BEFORE TRANSFORMATIONS, IF ANY). 5 TRANSFORMATION CARD(S), IF ANY.
24 E E CAUSES Y, FITTED Y AND RESIDUALS TO BE 6 INFORMATION CARD(S) FOR PRINTOUT, IF ANY.
LISTED WITH AN E RATHER THAN AN F FORMAT. 7 NAMES OF VARIABLES CARD(S) FOR PRINTOUT, IF ANY.
25 1 1 DO TRANSFORMATIONS. 8 CP FACTORIAL SEARCH CARD, IF ANY.
26 0 1 WEIGHT OBSERVATIONS. WEIGHT ENTERED IN LAST POSITION. 9 DATA CARDS (IF NOT READ FROM A FILE).
2 WEIGHT BY 1/VAR. OF OBSERVATION. VARIANCE ENTERED. 10 END CARD (END IN COLUMNS 1 - 3 OF IDENTIFICATION
27 0 1 LET B(0) = ZERO, OTHERWISE B(0) IS CALCULATED VALUE. FIELD). THE NUMBER OF END CARDS MUST EQUAL THE
28 0 1 CHECK OBSERVATION NUMBER SEQUENCE. NUMBER OF CARDS PER OBSERVATION. (END CARDS
29 0 1 CHECK SEQUENCE WITHIN OBSERVATION NUMBER. ARE NOT NEEDED IF DATA ARE READ FROM A FILE).
30 0 1 DO BACK TRANSFORMATION OF DEPENDENT VARIABLE. 11 ESTIMATE OF VARIANCE CARD, IF ANY.
31 0 1 PUNCH DATA FOR CONFIDENCE INTERVAL PROGRAM. 12 ADDITIONAL CP FACTORIAL SEARCH AND ESTIMATE OF
32 0 0 LIST ALL INPUT DATA. VARIANCE CARDS, IF ANY.
1 LIST ONLY 1ST OBSERVATION.
2 DO NOT LIST ANY INPUT DATA. SECOND PROBLEM
33 0 0 LIST TRANSFORMATIONS AND ALL TRANSFORMED DATA. IF DATA ARE REUSED FROM FIRST PROBLEM,
1 LIST TRANSFORMATIONS AND 1ST TRANSFORMED OBSERVATION. DELETE THE FORMAT, DATA AND END CARDS.
2 DO NOT LIST TRANSFORMATIONS OR TRANSFORMED DATA. IF NAMES ARE REUSED,
34 0 1 DO NOT LIST SUMS OF VARIABLES. DELETE THE NAME CARDS.
35 0 1 DO NOT LIST RAW SUMS AND CROSS PRODUCTS WHEN B(O)=O. IF DIFFERENT INPUT DATA AND NAMES,
36 0 1 DO NOT LIST RESIDUAL SUMS AND CROSS PRODUCTS. REPEAT 1 - 12 ABOVE.
37 0 1 DO NOT LIST MEANS AND ROOT MEAN SQUARES OF VARIABLES.
38 0 1 DO NOT LIST SIMPLE CORRELATION COEFFICIENTS.
39 0 1 DO NOT LIST INVERSE MATRIX.
40 0 1 DO NOT PRINT PLOTS OF RESIDUALS VS. FITTED Y.
2 PLOT (A) RESIDUALS AND (B) COMPONENT AND COMPONENT-
PLUS-RESIDUALS VS. EACH INDEPENDENT VARIABLE.
3 PLOT (A) RESIDUALS ONLY.
4 PLOT (B) COMPONENT AND COMPONENT-PLUS-RESIDUALS ONLY.
5 PLOT (B) BUT EXPAND SCALE TO FILL EACH PLOT.
41 1 0 READ DATA WITH STANDARD FORMAT (A6, I4, I2, 10F6.3).
1 READ DATA WITH FORMAT TO BE READ, 1 CARD (72COL) ASSUMED.
2 READ DATA WITH READ DATA (REDATA) SUBROUTINE.
42 0 0 DO NOT SAVE DATA FOR NEXT PROBLEM.
1 SAVE DATA FOR NEXT PROBLEM.
2 REUSE DATA FROM PREVIOUS PROBLEM.
43-44 0 18 NUMBER OF VARIABLES IN CP SEARCH IF GREATER THAN 12.
45 0 8 NUMBER OF FORMAT CARDS IF GREATER THAN 1.
46-47 12 12 NUMBER OF INFORMATION CARDS TO BE READ FOR DISPLAY ON
PRINTOUT IF DESIRED, 72 COL. EACH.
48 1 1 READ NAMES OF VARIABLES FOR DISPLAY ON PRINTOUT.
NAMES IN SAME POSITIONS AS VARIABLES ON TRANSFORMATION
CARDS - COLS. 1-6, 11-16, - - - , 61-66.
NAMES ARE NOT MOVED, ONLY LISTED OR DELETED.
2 REUSE NAMES OF VARIABLES FROM PREVIOUS PROBLEM.
49 3 SEARCH FOR CANDIDATE EQUATIONS VIA CP. USE ESTIMATE
OF VARIANCE (RMS) FROM:
1 FULL EQUATION,
2 SUBSET EQUATION WITH MINIMUM RMS VALUE, OR
3 ESTIMATE OF VARIANCE CARD, F16.8 FORMAT.
50 1 NUMBER OF CP FACTORIAL SEARCH CARDS TO BE READ PER
DEPENDENT VARIABLE. KEYPUNCH IN ASCENDING ORDER THE
IDENTIFING NUMBER OF THE VARIABLES (AFTER TRANSFOR-
MATIONS) TO BE USED IN THAT SEARCH, 18(2X,I2) FORMAT.
ALL OTHER VARIABLES WILL BE PLACED IN BASIC EQUATION.
51 0 1 LIST COMPONENT-EFFECT TABLE, REQUIRED X(I) PRECISION,
ESTIMATE OF STANDARD DEVIATION FROM NEAR NEIGHBORS,
AND FUNCTIONS OF FITTED Y.
2 LIST ONLY ESTIMATE OF STD. DEVIATION AND FUNCTIONS.
3 LIST ONLY FUNCTIONS OF FITTED Y.
52-53 0 NUMBER OF FILE IF DATA ARE READ FROM SEPARATE FILE,
NO END CARD IF ONLY ONE SET OF DATA IS ON EACH FILE.
54-55 0 NUMBER OF INDEPENDENT VARIABLES GREATER THAN THE 99
ALLOWED IN COLS 19-20.
56-58 3 TO REDUCE PRINTOUT WITH MANY OBSERVATIONS,
NUMBER OF CENTRAL OBSERVATIONS AND RESIDUALS NOT
TO BE PRINTED. THIS REQUIRES AN E IN COL 24.
59 1 CROSS VERIFICATION OF MODEL AND COEFFICIENTS WITH A
SECOND SAMPLE OF DATA:
1 WRITE B(0) AND B(I)S ON FILE IN ONE PROBLEM
(TRANSFORMATIONS ARE NOT SAVED).
2 READ B(0) AND B(I)S FROM FILE IN NEXT PROBLEM
WITH SECOND SET OF OBSERVATIONS.
60 1 5 NUMBER OF DELETE-OBSERVATIONS CARDS. KEYPUNCH
OBSERVATION NUMBER OF DATA TO BE DELETED IN ORDER READ
BY COMPUTER USING 7(I4,6X) FORMAT.
61 1 5 NUMBER OF INDICATOR-VARIABLE-OBSERVATIONS CARDS.
USING A 7(I4,2X,I3,1X) FORMAT, KEYPUNCH OBSERVATION
NUMBER (IN ORDER READ) AND VARIABLE NUMBER (BEFORE
TRANSFORMATIONS) INTO WHICH A 1 IS TO BE INSERTED.
0PROBLEM HAS ONE EQUATION
0DATA READ WITH SPECIAL FORMAT
0FORMAT CARD 1 ( A6, I4, I2, 2F6.3, F5.2, F1.0, F6.3, 2F1.0 )
0BZERO = CALCULATED VALUE
0OBSERVATIONS TO BE DELETED
22
0OBSERVATIONS AND INDICATOR VARIABLES INTO WHICH A 1 IS TO BE INSERTED
23 4
0INFORMATION CARDS
EXAMPLE OF SAVING COEFFICIENTS FOR CROSS VERIFICATION OF EQUATION,
REDUCING PRINTOUT (CENTRAL RESIDUALS AND OBSERVATIONS 10-12), E FORMAT,
DELETED OBSERVATION, INDICATOR-VARIABLE-OBSERVATION, AND CP FACTORIAL
SEARCH WITH GIVEN ESTIMATE OF VARIANCE.
OBSERVATION 22 DELETED FROM FIRST SET OF DATA, INCLUDED IN NEXT SET.
Y = B(0) + B(1)X1 + B(2)X2 + B(3)X3 + B(4)X4
Y = 100( LOG(NUMBER OF DEATHS FROM HEART DISEASE PER 100,000 FOR MALES
IN THE 55 TO 59 AGE GROUP) - 2 )
X1 = 1000(TELEPHONES PER PERSON)
X2 = FAT CALORIES AS PER CENT OF TOTAL CALORIES
X3 = ANIMAL PROTEIN CALORIES AS PER CENT TOTAL CALORIES
X4 = INDICATOR VARIABLE, 1 FOR OBSERVATION 23 (U.N.), 0 OTHERWISE.
0DATA TRANSFORMATIONS
POSITION CODE OPERATION CONSTANT LOCATION OMIT VARIABLE NAME
1 NONE 1 0 1 TELEPH
2 NONE 2 0 2 F. CAL
3 NONE 3 0 3 AP.CAL
4 NONE 4 0 4 UN IND
5 2 COMMON LOG 6 1
6 8 ADD CONSTANT -2. 7 1
7 6 MULTIPLY BY CONSTANT 100. 7 0 5 DEATHS
0VARIABLES ON FIRST CP FACTORIAL SEARCH CARD
1 2 3
0
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
FIRST BROWNLEE
0DATA INPUT 4 INDEPENDENT VARIABLES 3 DEPENDENT VARIABLE(S)
OBSV. SEQ. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 0 124.000 33.000 8.000 0.000 646.000 0.000 0.000
2 0 49.000 31.000 6.000 0.000 355.000 0.000 0.000
3 0 181.000 38.000 8.000 0.000 631.000 0.000 0.000
4 0 4.000 17.000 2.000 0.000 174.000 0.000 0.000
5 0 22.000 20.000 4.000 0.000 603.000 0.000 0.000
6 0 152.000 39.000 6.000 0.000 331.000 0.000 0.000
7 0 75.000 30.000 7.000 0.000 759.000 0.000 0.000
8 0 54.000 29.000 7.000 0.000 282.000 0.000 0.000
9 0 43.000 35.000 6.000 0.000 316.000 0.000 0.000
10 0 41.000 31.000 5.000 0.000 490.000 0.000 0.000
11 0 17.000 23.000 4.000 0.000 457.000 0.000 0.000
12 0 22.000 21.000 3.000 0.000 282.000 0.000 0.000
13 0 16.000 8.000 3.000 0.000 174.000 0.000 0.000
14 0 10.000 23.000 3.000 0.000 269.000 0.000 0.000
15 0 63.000 37.000 6.000 0.000 240.000 0.000 0.000
16 0 170.000 40.000 8.000 0.000 525.000 0.000 0.000
17 0 125.000 38.000 6.000 0.000 257.000 0.000 0.000
18 0 15.000 25.000 4.000 0.000 240.000 0.000 0.000
19 0 221.000 39.000 7.000 0.000 331.000 0.000 0.000
20 0 171.000 33.000 7.000 0.000 331.000 0.000 0.000
21 0 97.000 38.000 6.000 0.000 457.000 0.000 0.000
A VALUE OF 1.0 HAS BEEN PLACED IN VARIABLE 4 OF OBSERVATION 23
23 0 87.000 30.000 5.000 1.000 776.000 0.000 0.000
0DATA TRANSFORMATIONS
POSITION CODE OPERATION CONSTANT LOCATION OMIT VARIABLE NAME
1 NONE 1 0 1 TELEPH
2 NONE 2 0 2 F. CAL
3 NONE 3 0 3 AP.CAL
4 NONE 4 0 4 UN IND
5 2 COMMON LOG 6 1
6 8 ADD CONSTANT -2. 7 1
7 6 MULTIPLY BY CONSTANT 100. 7 0 5 DEATHS
0DATA AFTER TRANSFORMATIONS THE FITTED EQUATION HAS 4 INDEPENDENT VARIABLES, 1 DEPENDENT VARIABLE(S)
TELEPH F. CAL AP.CAL UN IND DEATHS
OBSV. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 1.24000E+02 3.30000E+01 8.00000E+00 0.00000E+00 8.10233E+01
2 4.90000E+01 3.10000E+01 6.00000E+00 0.00000E+00 5.50228E+01
3 1.81000E+02 3.80000E+01 8.00000E+00 0.00000E+00 8.00029E+01
4 4.00000E+00 1.70000E+01 2.00000E+00 0.00000E+00 2.40549E+01
5 2.20000E+01 2.00000E+01 4.00000E+00 0.00000E+00 7.80317E+01
6 1.52000E+02 3.90000E+01 6.00000E+00 0.00000E+00 5.19828E+01
7 7.50000E+01 3.00000E+01 7.00000E+00 0.00000E+00 8.80242E+01
8 5.40000E+01 2.90000E+01 7.00000E+00 0.00000E+00 4.50249E+01
9 4.30000E+01 3.50000E+01 6.00000E+00 0.00000E+00 4.99687E+01
10 4.10000E+01 3.10000E+01 5.00000E+00 0.00000E+00 6.90196E+01
11 1.70000E+01 2.30000E+01 4.00000E+00 0.00000E+00 6.59916E+01
12 2.20000E+01 2.10000E+01 3.00000E+00 0.00000E+00 4.50249E+01
13 1.60000E+01 8.00000E+00 3.00000E+00 0.00000E+00 2.40549E+01
14 1.00000E+01 2.30000E+01 3.00000E+00 0.00000E+00 4.29752E+01
15 6.30000E+01 3.70000E+01 6.00000E+00 0.00000E+00 3.80211E+01
16 1.70000E+02 4.00000E+01 8.00000E+00 0.00000E+00 7.20159E+01
17 1.25000E+02 3.80000E+01 6.00000E+00 0.00000E+00 4.09933E+01
18 1.50000E+01 2.50000E+01 4.00000E+00 0.00000E+00 3.80211E+01
19 2.21000E+02 3.90000E+01 7.00000E+00 0.00000E+00 5.19828E+01
20 1.71000E+02 3.30000E+01 7.00000E+00 0.00000E+00 5.19828E+01
21 9.70000E+01 3.80000E+01 6.00000E+00 0.00000E+00 6.59916E+01
23 8.70000E+01 3.00000E+01 5.00000E+00 1.00000E+00 8.89862E+01
0SUMS OF VARIABLES
1.75900E+03 6.58000E+02 1.21000E+02 1.00000E+00 1.24820E+03
0RESIDUAL SUMS OF SQUARES + CROSS PRODUCTS
1 9.04810E+04
2 8.93191E+03 1.50582E+03
3 1.95450E+03 2.61000E+02 6.75000E+01
4 7.04545E+00 9.09091E-02-5.00000E-01 9.54545E-01
5 8.93019E+03 1.27891E+03 3.72718E+02 3.22499E+01 7.82405E+03
0OBSERVATIONS DELETED
22
0MEANS OF VARIABLES
7.99545E+01 2.99091E+01 5.50000E+00 4.54545E-02 5.67362E+01
0ROOT MEAN SQUARES OF VARIABLES
6.56401E+01 8.46792E+00 1.79284E+00 2.13201E-01 1.93022E+01
0SIMPLE CORRELATION COEFFICIENTS, R(I,I PRIME)
1 1.000
2 0.765 1.000
3 0.791 0.819 1.000
4 0.024 0.002 -0.062 1.000
5 0.336 0.373 0.513 0.373 1.000
0INVERSE, C(I,I PRIME)
1 3.035
2 -1.057 3.427
3 -1.546 -1.976 3.858
4 -0.166 -0.106 0.282 1.022
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
FIRST BROWNLEE DEP VAR 1: DEATHS MIN Y = 2.405E+01 MAX Y = 8.899E+01 RANGE Y = 6.493E+01
EXAMPLE OF SAVING COEFFICIENTS FOR CROSS VERIFICATION OF EQUATION,
REDUCING PRINTOUT (CENTRAL RESIDUALS AND OBSERVATIONS 10-12), E FORMAT,
DELETED OBSERVATION, INDICATOR-VARIABLE-OBSERVATION, AND CP FACTORIAL
SEARCH WITH GIVEN ESTIMATE OF VARIANCE.
OBSERVATION 22 DELETED FROM FIRST SET OF DATA, INCLUDED IN NEXT SET.
Y = B(0) + B(1)X1 + B(2)X2 + B(3)X3 + B(4)X4
Y = 100( LOG(NUMBER OF DEATHS FROM HEART DISEASE PER 100,000 FOR MALES
IN THE 55 TO 59 AGE GROUP) - 2 )
X1 = 1000(TELEPHONES PER PERSON)
X2 = FAT CALORIES AS PER CENT OF TOTAL CALORIES
X3 = ANIMAL PROTEIN CALORIES AS PER CENT TOTAL CALORIES
X4 = INDICATOR VARIABLE, 1 FOR OBSERVATION 23 (U.N.), 0 OTHERWISE.
OBSERVATIONS DELETED: 22
0IND.VAR(I) NAME COEF.B(I) S.E. COEF. T-VALUE R(I)SQRD MIN X(I) MAX X(I) RANGE X(I) REL.INF.X(I)
0 2.02254E+01
1 TELEPH -6.76016E-02 9.13E-02 0.7 0.6705 4.000E+00 2.210E+02 2.170E+02 0.23
2 F. CAL -2.98541E-01 7.52E-01 0.4 0.7082 8.000E+00 4.000E+01 3.200E+01 0.15
3 AP.CAL 8.92234E+00 3.77E+00 2.4 0.7408 2.000E+00 8.000E+00 6.000E+00 0.82
4 UN IND 3.89866E+01 1.63E+01 2.4 0.0214 0.000E+00 1.000E+00 1.000E+00 0.60
0NO. OF OBSERVATIONS 22
NO. OF IND. VARIABLES 4
RESIDUAL DEGREES OF FREEDOM 17
F-VALUE 3.6
RESIDUAL ROOT MEAN SQUARE 15.76802212
RESIDUAL MEAN SQUARE 248.63052149
RESIDUAL SUM OF SQUARES 4226.71886529
TOTAL SUM OF SQUARES 7824.04773566
MULT. CORREL. COEF. SQUARED .4598
ADJ. MULT. CORR. COEF. SQUARED .3327
0*** COEFFICIENTS SAVED AS REQUESTED ***
0--------------ORDERED BY COMPUTER INPUT--------------- ----------------------ORDERED BY RESIDUALS-----------------------
IDENT. OBS. NO. OBS. Y FITTED Y RESIDUAL OBS. NO. OBS. Y FITTED Y ORDERED RESID. STUD.RESID. SEQ
AUSTRL 1 8.1023E+01 7.3370E+01 7.6536E+00 5 7.8032E+01 4.8457E+01 2.9575E+01 2.0 1
ASTRIA 2 5.5023E+01 6.1192E+01 -6.1694E+00 7 8.8024E+01 6.8655E+01 1.9369E+01 1.4 2
CANADA 3 8.0003E+01 6.8024E+01 1.1979E+01 11 6.5992E+01 4.7899E+01 1.8093E+01 1.2 3
CEYLON 4 2.4055E+01 3.2724E+01 -8.6696E+00 10 6.9020E+01 5.2811E+01 1.6209E+01 1.1 4
CHILE 5 7.8032E+01 4.8457E+01 2.9575E+01 3 8.0003E+01 6.8024E+01 1.1979E+01 0.8 5
DENMK 6 5.1983E+01 5.1841E+01 1.4190E-01 21 6.5992E+01 5.5858E+01 1.0134E+01 0.7 6
FINLND 7 8.8024E+01 6.8655E+01 1.9369E+01 1 8.1023E+01 7.3370E+01 7.6536E+00 0.6 7
FRANCE 8 4.5025E+01 7.0374E+01 -2.5349E+01 12 4.5025E+01 3.9236E+01 5.7891E+00 0.4 8
GMANY 9 4.9969E+01 6.0404E+01 -1.0435E+01 16 7.2016E+01 6.8170E+01 3.8457E+00 0.3 9
JAPAN 13 2.4055E+01 4.3522E+01 -1.9468E+01 19 5.1983E+01 5.6099E+01 -4.1159E+00 -0.3 13
MEXICO 14 4.2975E+01 3.9450E+01 3.5253E+00 2 5.5023E+01 6.1192E+01 -6.1694E+00 -0.4 14
NTHLDS 15 3.8021E+01 5.8455E+01 -2.0433E+01 4 2.4055E+01 3.2724E+01 -8.6696E+00 -0.6 15
NWZEAL 16 7.2016E+01 6.8170E+01 3.8457E+00 20 5.1983E+01 6.1270E+01 -9.2873E+00 -0.7 16
NORWAY 17 4.0993E+01 5.3965E+01 -1.2971E+01 18 3.8021E+01 4.7437E+01 -9.4161E+00 -0.6 17
PORTGL 18 3.8021E+01 4.7437E+01 -9.4161E+00 9 4.9969E+01 6.0404E+01 -1.0435E+01 -0.7 18
SWEDEN 19 5.1983E+01 5.6099E+01 -4.1159E+00 17 4.0993E+01 5.3965E+01 -1.2971E+01 -0.9 19
SWITZD 20 5.1983E+01 6.1270E+01 -9.2873E+00 13 2.4055E+01 4.3522E+01 -1.9468E+01 -1.7 20
UNKING 21 6.5992E+01 5.5858E+01 1.0134E+01 15 3.8021E+01 5.8455E+01 -2.0433E+01 -1.4 21
U.N. 23 8.8986E+01 8.8986E+01 0.0000E+00 8 4.5025E+01 7.0374E+01 -2.5349E+01 -1.9 22
1 FIRST BROWNLEE DEP VAR 1: DEATHS CUMULATIVE DISTRIBUTION OF RESIDUALS
.0002 .001 .005 .01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8 .9 .95 .98 .99 .995 .999
*-----*-------*--*---*-----*----*-----*----*---*---*---*---*----*-----*----*-----*---*--*-------*-----
I ' + I
I ' I
P I ' I
O I ' I
S I ' I
I I ' I
T I ' I
I I ' I
V I ' I
E I ' + I
I ' + I
I ' I
I ' + I
I ' I
I ' I
I ' I
I ' + I
I ' + I
I ' I
I ' I
I ' + I
R I ' + I
E I ' I
S I ' + I
I I ' + I
D I ' I
U I ' I
A 0 I-------------------------------------------------++-------------------------------------------------I
L I ' I
S I ' I
I ' I
I + ' I
I ' I
I + ' I
I ' I
I + + ' I
I + + ' I
I ' I
I ' I
I + ' I
I ' I
N I ' I
E I ' I
G I ' I
A I ' I
T I + ' I
I I + ' I
V I ' I
E I ' I
I ' I
I + ' I
*-----*-------*--*---*-----*----*-----*----*---*---*---*---*----*-----*----*-----*---*--*-------*-----
.0002 .001 .005 .01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8 .9 .95 .98 .99 .995 .999
CUMULATIVE FREQUENCY, NORMAL GRID
1 FIRST BROWNLEE DEP VAR 1: DEATHS RESIDUAL VS. FITTED Y
32.724 60.855 88.986
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I + I
I I
P I I
O I I
S I I
I I I
T I I
I I I
V I I
E I + I
I + I
I I
I + I
I I
I I
I I
I + I
I + I
I I
I I
I + I
R I + I
E I I
S I + I
I I + I
D I I
U I I
A 0 I---------------------------------+-----------------------------------------------------------------+I
L I I
S I I
I I
I + I
I I
I + I
I I
I+ + I
I + + I
I I
I I
I + I
I I
N I I
E I I
G I I
A I I
T I + I
I I + I
V I I
E I I
I I
I + I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
32.724 60.855 88.986
FITTED Y
1 CP VALUES FOR THE SELECTION OF VARIABLES
FIRST BROWNLEE DEP VAR 1: DEATHS SEARCH NUMBER 1
VARIABLES IN FACTORIAL SEARCH
0 1 2 3
TELEPH F. CAL AP.CAL
0
NUMBER OF OBSERVATIONS 22
NUMBER OF VARIABLES IN FULL EQUATION 4
NUMBER OF VARIABLES IN BASIC EQUATION 1
REMAINDER OF VARIABLES TO BE SEARCHED 3
0EQUATION P CP VARIABLES IN EQUATION
0 5 5.0 FULL EQUATION
0 2 9.1 BASIC SET OF VARIABLES 4
UN IND
RMS = 336.72318
0 1 4 3.5 BASIC SET PLUS 2 3
F. CAL AP.CAL
RMS = 242.38715
0 2 5 5.0 BASIC SET PLUS 1 2 3
TELEPH F. CAL AP.CAL
RMS = 248.63052
0 3 4 3.2 BASIC SET PLUS 1 3
TELEPH AP.CAL
RMS = 236.99366
0 4 3 2.0 BASIC SET PLUS 3
AP.CAL
RMS = 235.62449
0SWEEP NUMBER 7, DELTA Z(K,K) = 2.E-19
1ESTIMATE OF VARIANCE
0RMS OF FULL EQUATION 248.63052149
RMS OF SUBSET EQUATION 4 235.62448686
RMS PROVIDED BY USER 235.00000000
ESTIMATED VARIANCE USED TO RECALCULATE AND PLOT CP VALUES.
0 P CP
FULL EQUATION 5 6.0
SUBSET EQUATION 4 3 3.1
0
SEQ EQUATION P ORDERED CP
1 4 3 3.1
2 3 4 4.2
3 1 4 4.6
4 2 5 6.0
1 FIRST BROWNLEE DEP VAR 1: DEATHS CP PLOT SEARCH NUMBER 1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
17 I I
I I
I I
16 I I
I I
I I
15 I I
I I
I I
14 I I
I I
I I
13 I I
I I
I I
12 I I
I I
I I
11 I I
I I
I I
10 I I
I I
I I
9 I I
CP I I
I I
8 I I
I I
I I
7 I I
I I
I I
6 I + I
I I
I I
5 I I
I + I
I I
4 I + I
I I
I I
3 I + I
I I
I I
2 I I
I I
I I
1 I I
I I
I I
0 *----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
P
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
1979 VERSION OF THE LINWOOD 40 VARIABLE, 1000 OBSERVATION PROGRAM
REFER TO FITTING EQUATIONS TO DATA BY DANIEL AND WOOD, SECOND EDITION, WILEY PUBLISHER,
FOR GLOSSARY OF TERMS, USER'S MANUAL, DETAILS OF CALCULATIONS AND INTERPRETATION OF RESULTS.
0NEXT BROWNLEE
0 CONTROL CARD INFORMATION ORDER OF CARDS
COL. INPUT MAX. ITEM (NOTE: BLANK ON CARD = 0) FIRST PROBLEM
1-18 PROBLEM IDENTIFICATION. 1 CONTROL CARD.
19-20 4 NUMBER OF INDEPENDENT VARIABLES READ IN 2 FORMAT CARD(S), IF ANY.
(ALLOW SPACE FOR TRANSFORMATIONS). 3 DELETE OBSERVATIONS CARD(S), IF ANY.
21-22 3 NUMBER OF DEPENDENT VARIABLES READ IN. 4 INDICATOR-VARIABLE-OBSERVATIONS CARD(S), IF ANY.
7 65 TOTAL NUMBER OF VARIABLES (BEFORE TRANSFORMATIONS, IF ANY). 5 TRANSFORMATION CARD(S), IF ANY.
24 E CAUSES Y, FITTED Y AND RESIDUALS TO BE 6 INFORMATION CARD(S) FOR PRINTOUT, IF ANY.
LISTED WITH AN E RATHER THAN AN F FORMAT. 7 NAMES OF VARIABLES CARD(S) FOR PRINTOUT, IF ANY.
25 1 1 DO TRANSFORMATIONS. 8 CP FACTORIAL SEARCH CARD, IF ANY.
26 0 1 WEIGHT OBSERVATIONS. WEIGHT ENTERED IN LAST POSITION. 9 DATA CARDS (IF NOT READ FROM A FILE).
2 WEIGHT BY 1/VAR. OF OBSERVATION. VARIANCE ENTERED. 10 END CARD (END IN COLUMNS 1 - 3 OF IDENTIFICATION
27 0 1 LET B(0) = ZERO, OTHERWISE B(0) IS CALCULATED VALUE. FIELD). THE NUMBER OF END CARDS MUST EQUAL THE
28 0 1 CHECK OBSERVATION NUMBER SEQUENCE. NUMBER OF CARDS PER OBSERVATION. (END CARDS
29 0 1 CHECK SEQUENCE WITHIN OBSERVATION NUMBER. ARE NOT NEEDED IF DATA ARE READ FROM A FILE).
30 0 1 DO BACK TRANSFORMATION OF DEPENDENT VARIABLE. 11 ESTIMATE OF VARIANCE CARD, IF ANY.
31 0 1 PUNCH DATA FOR CONFIDENCE INTERVAL PROGRAM. 12 ADDITIONAL CP FACTORIAL SEARCH AND ESTIMATE OF
32 0 0 LIST ALL INPUT DATA. VARIANCE CARDS, IF ANY.
1 LIST ONLY 1ST OBSERVATION.
2 DO NOT LIST ANY INPUT DATA. SECOND PROBLEM
33 0 0 LIST TRANSFORMATIONS AND ALL TRANSFORMED DATA. IF DATA ARE REUSED FROM FIRST PROBLEM,
1 LIST TRANSFORMATIONS AND 1ST TRANSFORMED OBSERVATION. DELETE THE FORMAT, DATA AND END CARDS.
2 DO NOT LIST TRANSFORMATIONS OR TRANSFORMED DATA. IF NAMES ARE REUSED,
34 0 1 DO NOT LIST SUMS OF VARIABLES. DELETE THE NAME CARDS.
35 0 1 DO NOT LIST RAW SUMS AND CROSS PRODUCTS WHEN B(O)=O. IF DIFFERENT INPUT DATA AND NAMES,
36 0 1 DO NOT LIST RESIDUAL SUMS AND CROSS PRODUCTS. REPEAT 1 - 12 ABOVE.
37 0 1 DO NOT LIST MEANS AND ROOT MEAN SQUARES OF VARIABLES.
38 0 1 DO NOT LIST SIMPLE CORRELATION COEFFICIENTS.
39 0 1 DO NOT LIST INVERSE MATRIX.
40 0 1 DO NOT PRINT PLOTS OF RESIDUALS VS. FITTED Y.
2 PLOT (A) RESIDUALS AND (B) COMPONENT AND COMPONENT-
PLUS-RESIDUALS VS. EACH INDEPENDENT VARIABLE.
3 PLOT (A) RESIDUALS ONLY.
4 PLOT (B) COMPONENT AND COMPONENT-PLUS-RESIDUALS ONLY.
5 PLOT (B) BUT EXPAND SCALE TO FILL EACH PLOT.
41 1 0 READ DATA WITH STANDARD FORMAT (A6, I4, I2, 10F6.3).
1 READ DATA WITH FORMAT TO BE READ, 1 CARD (72COL) ASSUMED.
2 READ DATA WITH READ DATA (REDATA) SUBROUTINE.
42 0 0 DO NOT SAVE DATA FOR NEXT PROBLEM.
1 SAVE DATA FOR NEXT PROBLEM.
2 REUSE DATA FROM PREVIOUS PROBLEM.
43-44 0 18 NUMBER OF VARIABLES IN CP SEARCH IF GREATER THAN 12.
45 0 8 NUMBER OF FORMAT CARDS IF GREATER THAN 1.
46-47 10 12 NUMBER OF INFORMATION CARDS TO BE READ FOR DISPLAY ON
PRINTOUT IF DESIRED, 72 COL. EACH.
48 1 1 READ NAMES OF VARIABLES FOR DISPLAY ON PRINTOUT.
NAMES IN SAME POSITIONS AS VARIABLES ON TRANSFORMATION
CARDS - COLS. 1-6, 11-16, - - - , 61-66.
NAMES ARE NOT MOVED, ONLY LISTED OR DELETED.
2 REUSE NAMES OF VARIABLES FROM PREVIOUS PROBLEM.
49 0 SEARCH FOR CANDIDATE EQUATIONS VIA CP. USE ESTIMATE
OF VARIANCE (RMS) FROM:
1 FULL EQUATION,
2 SUBSET EQUATION WITH MINIMUM RMS VALUE, OR
3 ESTIMATE OF VARIANCE CARD, F16.8 FORMAT.
50 0 NUMBER OF CP FACTORIAL SEARCH CARDS TO BE READ PER
DEPENDENT VARIABLE. KEYPUNCH IN ASCENDING ORDER THE
IDENTIFING NUMBER OF THE VARIABLES (AFTER TRANSFOR-
MATIONS) TO BE USED IN THAT SEARCH, 18(2X,I2) FORMAT.
ALL OTHER VARIABLES WILL BE PLACED IN BASIC EQUATION.
51 0 1 LIST COMPONENT-EFFECT TABLE, REQUIRED X(I) PRECISION,
ESTIMATE OF STANDARD DEVIATION FROM NEAR NEIGHBORS,
AND FUNCTIONS OF FITTED Y.
2 LIST ONLY ESTIMATE OF STD. DEVIATION AND FUNCTIONS.
3 LIST ONLY FUNCTIONS OF FITTED Y.
52-53 0 NUMBER OF FILE IF DATA ARE READ FROM SEPARATE FILE,
NO END CARD IF ONLY ONE SET OF DATA IS ON EACH FILE.
54-55 0 NUMBER OF INDEPENDENT VARIABLES GREATER THAN THE 99
ALLOWED IN COLS 19-20.
56-58 0 TO REDUCE PRINTOUT WITH MANY OBSERVATIONS,
NUMBER OF CENTRAL OBSERVATIONS AND RESIDUALS NOT
TO BE PRINTED. THIS REQUIRES AN E IN COL 24.
59 2 CROSS VERIFICATION OF MODEL AND COEFFICIENTS WITH A
SECOND SAMPLE OF DATA:
1 WRITE B(0) AND B(I)S ON FILE IN ONE PROBLEM
(TRANSFORMATIONS ARE NOT SAVED).
2 READ B(0) AND B(I)S FROM FILE IN NEXT PROBLEM
WITH SECOND SET OF OBSERVATIONS.
60 0 5 NUMBER OF DELETE-OBSERVATIONS CARDS. KEYPUNCH
OBSERVATION NUMBER OF DATA TO BE DELETED IN ORDER READ
BY COMPUTER USING 7(I4,6X) FORMAT.
61 1 5 NUMBER OF INDICATOR-VARIABLE-OBSERVATIONS CARDS.
USING A 7(I4,2X,I3,1X) FORMAT, KEYPUNCH OBSERVATION
NUMBER (IN ORDER READ) AND VARIABLE NUMBER (BEFORE
TRANSFORMATIONS) INTO WHICH A 1 IS TO BE INSERTED.
0PROBLEM HAS ONE EQUATION
0DATA READ WITH SPECIAL FORMAT
0FORMAT CARD 1 ( A6, I4, I2, 2F6.3, F5.2, F1.0, F6.3, 2F1.0 )
0BZERO = CALCULATED VALUE
0OBSERVATIONS AND INDICATOR VARIABLES INTO WHICH A 1 IS TO BE INSERTED
23 4
0INFORMATION CARDS
EXAMPLE OF CROSS VERIFICATION WITH SAVED COEFFICIENTS FROM FIT WITH
FIRST SET OF DATA. THIS SECOND SET OF DATA CONTAINS USA, OBSERVATION
22, DELETED FROM FIRST SET OF DATA.
Y = B(0) + B(1)X1 + B(2)X2 + B(3)X3 + B(4)X4
Y = 100( LOG(NUMBER OF DEATHS FROM HEART DISEASE PER 100,000 FOR MALES
IN THE 55 TO 59 AGE GROUP) - 2 )
X1 = 1000(TELEPHONES PER PERSON)
X2 = FAT CALORIES AS PER CENT OF TOTAL CALORIES
X3 = ANIMAL PROTEIN CALORIES AS PER CENT TOTAL CALORIES
X4 = INDICATOR VARIABLE, 1 FOR OBSERVATION 23 (U.N.), 0 OTHERWISE.
0DATA TRANSFORMATIONS
POSITION CODE OPERATION CONSTANT LOCATION OMIT VARIABLE NAME
1 NONE 1 0 1 TELEPH
2 NONE 2 0 2 F. CAL
3 NONE 3 0 3 AP.CAL
4 NONE 4 0 4 UN IND
5 2 COMMON LOG 6 1
6 8 ADD CONSTANT -2. 7 1
7 6 MULTIPLY BY CONSTANT 100. 7 0 5 DEATHS
0
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
NEXT BROWNLEE
0DATA INPUT 4 INDEPENDENT VARIABLES 3 DEPENDENT VARIABLE(S)
OBSV. SEQ. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 0 124.000 33.000 8.000 0.000 646.000 0.000 0.000
2 0 49.000 31.000 6.000 0.000 355.000 0.000 0.000
3 0 181.000 38.000 8.000 0.000 631.000 0.000 0.000
4 0 4.000 17.000 2.000 0.000 174.000 0.000 0.000
5 0 22.000 20.000 4.000 0.000 603.000 0.000 0.000
6 0 152.000 39.000 6.000 0.000 331.000 0.000 0.000
7 0 75.000 30.000 7.000 0.000 759.000 0.000 0.000
8 0 54.000 29.000 7.000 0.000 282.000 0.000 0.000
9 0 43.000 35.000 6.000 0.000 316.000 0.000 0.000
10 0 41.000 31.000 5.000 0.000 490.000 0.000 0.000
11 0 17.000 23.000 4.000 0.000 457.000 0.000 0.000
12 0 22.000 21.000 3.000 0.000 282.000 0.000 0.000
13 0 16.000 8.000 3.000 0.000 174.000 0.000 0.000
14 0 10.000 23.000 3.000 0.000 269.000 0.000 0.000
15 0 63.000 37.000 6.000 0.000 240.000 0.000 0.000
16 0 170.000 40.000 8.000 0.000 525.000 0.000 0.000
17 0 125.000 38.000 6.000 0.000 257.000 0.000 0.000
18 0 15.000 25.000 4.000 0.000 240.000 0.000 0.000
19 0 221.000 39.000 7.000 0.000 331.000 0.000 0.000
20 0 171.000 33.000 7.000 0.000 331.000 0.000 0.000
21 0 97.000 38.000 6.000 0.000 457.000 0.000 0.000
22 0 254.000 39.000 8.000 0.000 776.000 0.000 0.000
A VALUE OF 1.0 HAS BEEN PLACED IN VARIABLE 4 OF OBSERVATION 23
23 0 87.000 30.000 5.000 1.000 776.000 0.000 0.000
0DATA TRANSFORMATIONS
POSITION CODE OPERATION CONSTANT LOCATION OMIT VARIABLE NAME
1 NONE 1 0 1 TELEPH
2 NONE 2 0 2 F. CAL
3 NONE 3 0 3 AP.CAL
4 NONE 4 0 4 UN IND
5 2 COMMON LOG 6 1
6 8 ADD CONSTANT -2. 7 1
7 6 MULTIPLY BY CONSTANT 100. 7 0 5 DEATHS
0DATA AFTER TRANSFORMATIONS THE FITTED EQUATION HAS 4 INDEPENDENT VARIABLES, 1 DEPENDENT VARIABLE(S)
TELEPH F. CAL AP.CAL UN IND DEATHS
OBSV. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 1.24000E+02 3.30000E+01 8.00000E+00 0.00000E+00 8.10233E+01
2 4.90000E+01 3.10000E+01 6.00000E+00 0.00000E+00 5.50228E+01
3 1.81000E+02 3.80000E+01 8.00000E+00 0.00000E+00 8.00029E+01
4 4.00000E+00 1.70000E+01 2.00000E+00 0.00000E+00 2.40549E+01
5 2.20000E+01 2.00000E+01 4.00000E+00 0.00000E+00 7.80317E+01
6 1.52000E+02 3.90000E+01 6.00000E+00 0.00000E+00 5.19828E+01
7 7.50000E+01 3.00000E+01 7.00000E+00 0.00000E+00 8.80242E+01
8 5.40000E+01 2.90000E+01 7.00000E+00 0.00000E+00 4.50249E+01
9 4.30000E+01 3.50000E+01 6.00000E+00 0.00000E+00 4.99687E+01
10 4.10000E+01 3.10000E+01 5.00000E+00 0.00000E+00 6.90196E+01
11 1.70000E+01 2.30000E+01 4.00000E+00 0.00000E+00 6.59916E+01
12 2.20000E+01 2.10000E+01 3.00000E+00 0.00000E+00 4.50249E+01
13 1.60000E+01 8.00000E+00 3.00000E+00 0.00000E+00 2.40549E+01
14 1.00000E+01 2.30000E+01 3.00000E+00 0.00000E+00 4.29752E+01
15 6.30000E+01 3.70000E+01 6.00000E+00 0.00000E+00 3.80211E+01
16 1.70000E+02 4.00000E+01 8.00000E+00 0.00000E+00 7.20159E+01
17 1.25000E+02 3.80000E+01 6.00000E+00 0.00000E+00 4.09933E+01
18 1.50000E+01 2.50000E+01 4.00000E+00 0.00000E+00 3.80211E+01
19 2.21000E+02 3.90000E+01 7.00000E+00 0.00000E+00 5.19828E+01
20 1.71000E+02 3.30000E+01 7.00000E+00 0.00000E+00 5.19828E+01
21 9.70000E+01 3.80000E+01 6.00000E+00 0.00000E+00 6.59916E+01
22 2.54000E+02 3.90000E+01 8.00000E+00 0.00000E+00 8.89862E+01
23 8.70000E+01 3.00000E+01 5.00000E+00 1.00000E+00 8.89862E+01
0SUMS OF VARIABLES
2.01300E+03 6.97000E+02 1.29000E+02 1.00000E+00 1.33718E+03
0RESIDUAL SUMS OF SQUARES + CROSS PRODUCTS
1 1.19456E+05
2 1.04453E+04 1.58487E+03
3 2.37070E+03 2.82739E+02 7.34783E+01
4 -5.21739E-01-3.04348E-01-6.08696E-01 9.56522E-01
5 1.42991E+04 1.55935E+03 4.49837E+02 3.08478E+01 8.81889E+03
0MEANS OF VARIABLES
8.75217E+01 3.03043E+01 5.60870E+00 4.34783E-02 5.81384E+01
0ROOT MEAN SQUARES OF VARIABLES
7.36872E+01 8.48761E+00 1.82755E+00 2.08514E-01 2.00214E+01
0SIMPLE CORRELATION COEFFICIENTS, R(I,I PRIME)
1 1.000
2 0.759 1.000
3 0.800 0.829 1.000
4 -0.002 -0.008 -0.073 1.000
5 0.441 0.417 0.559 0.336 1.000
0INVERSE, C(I,I PRIME)
1 3.044
2 -0.913 3.491
3 -1.689 -2.172 4.171
4 -0.125 -0.132 0.283 1.019
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
NEXT BROWNLEE DEP VAR 1: DEATHS MIN Y = 2.405E+01 MAX Y = 8.899E+01 RANGE Y = 6.493E+01
EXAMPLE OF CROSS VERIFICATION WITH SAVED COEFFICIENTS FROM FIT WITH
FIRST SET OF DATA. THIS SECOND SET OF DATA CONTAINS USA, OBSERVATION
22, DELETED FROM FIRST SET OF DATA.
Y = B(0) + B(1)X1 + B(2)X2 + B(3)X3 + B(4)X4
Y = 100( LOG(NUMBER OF DEATHS FROM HEART DISEASE PER 100,000 FOR MALES
IN THE 55 TO 59 AGE GROUP) - 2 )
X1 = 1000(TELEPHONES PER PERSON)
X2 = FAT CALORIES AS PER CENT OF TOTAL CALORIES
X3 = ANIMAL PROTEIN CALORIES AS PER CENT TOTAL CALORIES
X4 = INDICATOR VARIABLE, 1 FOR OBSERVATION 23 (U.N.), 0 OTHERWISE.
0IND.VAR(I) NAME COEF.B(I) S.E. COEF. T-VALUE R(I)SQRD MIN X(I) MAX X(I) RANGE X(I) REL.INF.X(I)
0 2.39806E+01
1 TELEPH -6.87054E-03 8.14E-02 0.1 0.6715 4.000E+00 2.540E+02 2.500E+02 0.03
2 F. CAL -4.80840E-01 7.57E-01 0.6 0.7136 8.000E+00 4.000E+01 3.200E+01 0.24
3 AP.CAL 8.50465E+00 3.84E+00 2.2 0.7603 2.000E+00 8.000E+00 6.000E+00 0.79
4 UN IND 3.75052E+01 1.67E+01 2.3 0.0190 0.000E+00 1.000E+00 1.000E+00 0.58
0NO. OF OBSERVATIONS 23
NO. OF IND. VARIABLES 4
RESIDUAL DEGREES OF FREEDOM 18
F-VALUE 4.0
RESIDUAL ROOT MEAN SQUARE 16.13185806
RESIDUAL MEAN SQUARE 260.23684450
RESIDUAL SUM OF SQUARES 4684.26320100
TOTAL SUM OF SQUARES 8818.88546632
MULT. CORREL. COEF. SQUARED .4688
ADJ. MULT. CORR. COEF. SQUARED .3508
0IND.VAR(I) NAME COEF.B(I) MIN X(I) MAX X(I) RANGE X(I) REL.INF.X(I)
0*** COEFFICIENTS FROM PREVIOUS FIT ***
0 2.02254E+01
1 TELEPH -6.76016E-02 4.000E+00 2.540E+02 2.500E+02 0.26
2 F. CAL -2.98541E-01 8.000E+00 4.000E+01 3.200E+01 0.15
3 AP.CAL 8.92234E+00 2.000E+00 8.000E+00 6.000E+00 0.82
4 UN IND 3.89866E+01 0.000E+00 1.000E+00 1.000E+00 0.60
1 LINEAR LEAST-SQUARES CURVE FITTING PROGRAM
0NEXT BROWNLEE DEP VAR 1: DEATHS
0FIT OF SECOND SAMPLE USING COEFFICIENTS FROM FIRST SAMPLE OF DATA
0NO. OF OBSERVATIONS 23
NO. OF PARAMETERS 5
RESIDUAL DEGREES OF FREEDOM 18
RESIDUAL ROOT MEAN SQUARE 16.99990815
RESIDUAL MEAN SQUARE 288.99687695
RESIDUAL SUM OF SQUARES 4912.94690819
TOTAL SUM OF SQUARES 8818.88546632
MULT. CORREL. COEF. SQUARED .4429
0-----------------ORDERED BY COMPUTER INPUT--------- --------- ---------------------ORDERED BY RESIDUALS---------------------
IDENT. OBSV. WSS DISTANCE OBS. Y FITTED Y RESIDUAL OBSV. OBS. Y FITTED Y ORDERED RESID. STUD.RESID. SEQ
AUSTRL 1 2. 81.023 73.370 7.654 5 78.032 48.457 29.575 1.8 1
ASTRIA 2 0. 55.023 61.192 -6.169 22 88.986 62.790 26.196 1.4 2
CANADA 3 2. 80.003 68.024 11.979 7 88.024 68.655 19.369 1.1 3
CEYLON 4 4. 24.055 32.724 -8.670 11 65.992 47.899 18.093 1.1 4
CHILE 5 1. 78.032 48.457 29.575 10 69.020 52.811 16.209 1.0 5
DENMK 6 0. 51.983 51.841 0.142 3 80.003 68.024 11.979 0.7 6
FINLND 7 1. 88.024 68.655 19.369 21 65.992 55.858 10.134 0.6 7
FRANCE 8 1. 45.025 70.374 -25.349 1 81.023 73.370 7.654 0.4 8
GMANY 9 0. 49.969 60.404 -10.435 12 45.025 39.236 5.789 0.3 9
IRELND 10 0. 69.020 52.811 16.209 16 72.016 68.170 3.846 0.2 10
ISRAEL 11 1. 65.992 47.899 18.093 14 42.975 39.450 3.525 0.2 11
ITALY 12 2. 45.025 39.236 5.789 6 51.983 51.841 0.142 0.0 12
JAPAN 13 2. 24.055 43.522 -19.468 23 88.986 88.986 0.000 0.0 13
MEXICO 14 2. 42.975 39.450 3.525 19 51.983 56.099 -4.116 -0.2 14
NTHLDS 15 0. 38.021 58.455 -20.433 2 55.023 61.192 -6.169 -0.4 15
NWZEAL 16 2. 72.016 68.170 3.846 4 24.055 32.724 -8.670 -0.5 16
NORWAY 17 0. 40.993 53.965 -12.971 20 51.983 61.270 -9.287 -0.5 17
PORTGL 18 1. 38.021 47.437 -9.416 18 38.021 47.437 -9.416 -0.6 18
SWEDEN 19 1. 51.983 56.099 -4.116 9 49.969 60.404 -10.435 -0.6 19
SWITZD 20 1. 51.983 61.270 -9.287 17 40.993 53.965 -12.971 -0.8 20
UNKING 21 0. 65.992 55.858 10.134 13 24.055 43.522 -19.468 -1.0 21
U.S.A. 22 2. 88.986 62.790 26.196 15 38.021 58.455 -20.433 -1.2 22
U.N. 23 5. 88.986 88.986 0.000 8 45.025 70.374 -25.349 -1.4 23
1 NEXT BROWNLEE DEP VAR 1: DEATHS CUMULATIVE DISTRIBUTION OF RESIDUALS
.0002 .001 .005 .01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8 .9 .95 .98 .99 .995 .999
*-----*-------*--*---*-----*----*-----*----*---*---*---*---*----*-----*----*-----*---*--*-------*-----
I ' + I
I ' I
P I ' I
O I ' + I
S I ' I
I I ' I
T I ' I
I I ' I
V I ' I
E I ' + I
I ' + I
I ' I
I ' + I
I ' I
I ' I
I ' I
I ' + I
I ' + I
I ' I
I ' I
I ' + I
R I ' + I
E I ' I
S I ' + I
I I '+ I
D I ' I
U I ' I
A 0 I------------------------------------------------++--------------------------------------------------I
L I ' I
S I ' I
I ' I
I + ' I
I ' I
I + ' I
I ' I
I + + ' I
I + + ' I
I ' I
I ' I
I + ' I
I ' I
N I ' I
E I ' I
G I ' I
A I ' I
T I + ' I
I I + ' I
V I ' I
E I ' I
I ' I
I + ' I
*-----*-------*--*---*-----*----*-----*----*---*---*---*---*----*-----*----*-----*---*--*-------*-----
.0002 .001 .005 .01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8 .9 .95 .98 .99 .995 .999
CUMULATIVE FREQUENCY, NORMAL GRID
1 NEXT BROWNLEE DEP VAR 1: DEATHS RESIDUAL VS. FITTED Y
32.724 60.855 88.986
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I + I
I I
P I I
O I + I
S I I
I I I
T I I
I I I
V I I
E I + I
I + I
I I
I + I
I I
I I
I I
I + I
I + I
I I
I I
I + I
R I + I
E I I
S I + I
I I + I
D I I
U I I
A 0 I---------------------------------+-----------------------------------------------------------------+I
L I I
S I I
I I
I + I
I I
I + I
I I
I+ + I
I + + I
I I
I I
I + I
I I
N I I
E I I
G I I
A I I
T I + I
I I + I
V I I
E I I
I I
I + I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
32.724 60.855 88.986
FITTED Y
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
1979 VERSION OF THE LINWOOD 40 VARIABLE, 1000 OBSERVATION PROGRAM
REFER TO FITTING EQUATIONS TO DATA BY DANIEL AND WOOD, SECOND EDITION, WILEY PUBLISHER,
FOR GLOSSARY OF TERMS, USER'S MANUAL, DETAILS OF CALCULATIONS AND INTERPRETATION OF RESULTS.
0MANDEL WEIGHT OBSV
0 CONTROL CARD INFORMATION ORDER OF CARDS
COL. INPUT MAX. ITEM (NOTE: BLANK ON CARD = 0) FIRST PROBLEM
1-18 PROBLEM IDENTIFICATION. 1 CONTROL CARD.
19-20 1 NUMBER OF INDEPENDENT VARIABLES READ IN 2 FORMAT CARD(S), IF ANY.
(ALLOW SPACE FOR TRANSFORMATIONS). 3 DELETE OBSERVATIONS CARD(S), IF ANY.
21-22 1 NUMBER OF DEPENDENT VARIABLES READ IN. 4 INDICATOR-VARIABLE-OBSERVATIONS CARD(S), IF ANY.
2 65 TOTAL NUMBER OF VARIABLES (BEFORE TRANSFORMATIONS, IF ANY). 5 TRANSFORMATION CARD(S), IF ANY.
24 E CAUSES Y, FITTED Y AND RESIDUALS TO BE 6 INFORMATION CARD(S) FOR PRINTOUT, IF ANY.
LISTED WITH AN E RATHER THAN AN F FORMAT. 7 NAMES OF VARIABLES CARD(S) FOR PRINTOUT, IF ANY.
25 0 1 DO TRANSFORMATIONS. 8 CP FACTORIAL SEARCH CARD, IF ANY.
26 1 1 WEIGHT OBSERVATIONS. WEIGHT ENTERED IN LAST POSITION. 9 DATA CARDS (IF NOT READ FROM A FILE).
2 WEIGHT BY 1/VAR. OF OBSERVATION. VARIANCE ENTERED. 10 END CARD (END IN COLUMNS 1 - 3 OF IDENTIFICATION
27 0 1 LET B(0) = ZERO, OTHERWISE B(0) IS CALCULATED VALUE. FIELD). THE NUMBER OF END CARDS MUST EQUAL THE
28 0 1 CHECK OBSERVATION NUMBER SEQUENCE. NUMBER OF CARDS PER OBSERVATION. (END CARDS
29 0 1 CHECK SEQUENCE WITHIN OBSERVATION NUMBER. ARE NOT NEEDED IF DATA ARE READ FROM A FILE).
30 0 1 DO BACK TRANSFORMATION OF DEPENDENT VARIABLE. 11 ESTIMATE OF VARIANCE CARD, IF ANY.
31 0 1 PUNCH DATA FOR CONFIDENCE INTERVAL PROGRAM. 12 ADDITIONAL CP FACTORIAL SEARCH AND ESTIMATE OF
32 0 0 LIST ALL INPUT DATA. VARIANCE CARDS, IF ANY.
1 LIST ONLY 1ST OBSERVATION.
2 DO NOT LIST ANY INPUT DATA. SECOND PROBLEM
33 0 0 LIST TRANSFORMATIONS AND ALL TRANSFORMED DATA. IF DATA ARE REUSED FROM FIRST PROBLEM,
1 LIST TRANSFORMATIONS AND 1ST TRANSFORMED OBSERVATION. DELETE THE FORMAT, DATA AND END CARDS.
2 DO NOT LIST TRANSFORMATIONS OR TRANSFORMED DATA. IF NAMES ARE REUSED,
34 0 1 DO NOT LIST SUMS OF VARIABLES. DELETE THE NAME CARDS.
35 0 1 DO NOT LIST RAW SUMS AND CROSS PRODUCTS WHEN B(O)=O. IF DIFFERENT INPUT DATA AND NAMES,
36 0 1 DO NOT LIST RESIDUAL SUMS AND CROSS PRODUCTS. REPEAT 1 - 12 ABOVE.
37 0 1 DO NOT LIST MEANS AND ROOT MEAN SQUARES OF VARIABLES.
38 0 1 DO NOT LIST SIMPLE CORRELATION COEFFICIENTS.
39 0 1 DO NOT LIST INVERSE MATRIX.
40 1 1 DO NOT PRINT PLOTS OF RESIDUALS VS. FITTED Y.
2 PLOT (A) RESIDUALS AND (B) COMPONENT AND COMPONENT-
PLUS-RESIDUALS VS. EACH INDEPENDENT VARIABLE.
3 PLOT (A) RESIDUALS ONLY.
4 PLOT (B) COMPONENT AND COMPONENT-PLUS-RESIDUALS ONLY.
5 PLOT (B) BUT EXPAND SCALE TO FILL EACH PLOT.
41 0 0 READ DATA WITH STANDARD FORMAT (A6, I4, I2, 10F6.3).
1 READ DATA WITH FORMAT TO BE READ, 1 CARD (72COL) ASSUMED.
2 READ DATA WITH READ DATA (REDATA) SUBROUTINE.
42 0 0 DO NOT SAVE DATA FOR NEXT PROBLEM.
1 SAVE DATA FOR NEXT PROBLEM.
2 REUSE DATA FROM PREVIOUS PROBLEM.
43-44 0 18 NUMBER OF VARIABLES IN CP SEARCH IF GREATER THAN 12.
45 0 8 NUMBER OF FORMAT CARDS IF GREATER THAN 1.
46-47 5 12 NUMBER OF INFORMATION CARDS TO BE READ FOR DISPLAY ON
PRINTOUT IF DESIRED, 72 COL. EACH.
48 1 1 READ NAMES OF VARIABLES FOR DISPLAY ON PRINTOUT.
NAMES IN SAME POSITIONS AS VARIABLES ON TRANSFORMATION
CARDS - COLS. 1-6, 11-16, - - - , 61-66.
NAMES ARE NOT MOVED, ONLY LISTED OR DELETED.
2 REUSE NAMES OF VARIABLES FROM PREVIOUS PROBLEM.
49 0 SEARCH FOR CANDIDATE EQUATIONS VIA CP. USE ESTIMATE
OF VARIANCE (RMS) FROM:
1 FULL EQUATION,
2 SUBSET EQUATION WITH MINIMUM RMS VALUE, OR
3 ESTIMATE OF VARIANCE CARD, F16.8 FORMAT.
50 0 NUMBER OF CP FACTORIAL SEARCH CARDS TO BE READ PER
DEPENDENT VARIABLE. KEYPUNCH IN ASCENDING ORDER THE
IDENTIFING NUMBER OF THE VARIABLES (AFTER TRANSFOR-
MATIONS) TO BE USED IN THAT SEARCH, 18(2X,I2) FORMAT.
ALL OTHER VARIABLES WILL BE PLACED IN BASIC EQUATION.
51 0 1 LIST COMPONENT-EFFECT TABLE, REQUIRED X(I) PRECISION,
ESTIMATE OF STANDARD DEVIATION FROM NEAR NEIGHBORS,
AND FUNCTIONS OF FITTED Y.
2 LIST ONLY ESTIMATE OF STD. DEVIATION AND FUNCTIONS.
3 LIST ONLY FUNCTIONS OF FITTED Y.
52-53 0 NUMBER OF FILE IF DATA ARE READ FROM SEPARATE FILE,
NO END CARD IF ONLY ONE SET OF DATA IS ON EACH FILE.
54-55 0 NUMBER OF INDEPENDENT VARIABLES GREATER THAN THE 99
ALLOWED IN COLS 19-20.
56-58 0 TO REDUCE PRINTOUT WITH MANY OBSERVATIONS,
NUMBER OF CENTRAL OBSERVATIONS AND RESIDUALS NOT
TO BE PRINTED. THIS REQUIRES AN E IN COL 24.
59 0 CROSS VERIFICATION OF MODEL AND COEFFICIENTS WITH A
SECOND SAMPLE OF DATA:
1 WRITE B(0) AND B(I)S ON FILE IN ONE PROBLEM
(TRANSFORMATIONS ARE NOT SAVED).
2 READ B(0) AND B(I)S FROM FILE IN NEXT PROBLEM
WITH SECOND SET OF OBSERVATIONS.
60 0 5 NUMBER OF DELETE-OBSERVATIONS CARDS. KEYPUNCH
OBSERVATION NUMBER OF DATA TO BE DELETED IN ORDER READ
BY COMPUTER USING 7(I4,6X) FORMAT.
61 0 5 NUMBER OF INDICATOR-VARIABLE-OBSERVATIONS CARDS.
USING A 7(I4,2X,I3,1X) FORMAT, KEYPUNCH OBSERVATION
NUMBER (IN ORDER READ) AND VARIABLE NUMBER (BEFORE
TRANSFORMATIONS) INTO WHICH A 1 IS TO BE INSERTED.
0PROBLEM HAS ONE EQUATION
0DATA READ WITH STANDARD FORMAT (A6, I4, I2, 10F6.3)
0BZERO = CALCULATED VALUE
0INFORMATION CARDS
SAMPLE LEVEL OF X WEIGHT OF OBSERVATION
1 10 1
2 20 4
3 30 1
4 40 1
0NAMES OF VARIABLES
LEVEL
0
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
MANDEL WEIGHT OBSV
0DATA INPUT 1 INDEPENDENT VARIABLES 1 DEPENDENT VARIABLE(S) WEIGHT OF OBSERVATION
OBSV. SEQ. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 0 10.000 33.800 1.000
2 0 20.000 62.200 4.000
3 0 30.000 92.000 1.000
4 0 40.000 122.400 1.000
0SUMS OF VARIABLES
1.60000E+02 4.97000E+02
0RESIDUAL SUMS OF SQUARES + CROSS PRODUCTS
1 5.42857E+02
2 1.61000E+03 4.77656E+03
0MEANS OF VARIABLES
2.28571E+01 7.10000E+01
0ROOT MEAN SQUARES OF VARIABLES
9.51190E+00 2.82151E+01
0SIMPLE CORRELATION COEFFICIENTS, R(I,I PRIME)
1 1.000
2 1.000 1.000
0INVERSE, C(I,I PRIME)
1 1.000
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
MANDEL WEIGHT OBSV DEP VAR 1: MIN Y = 3.380E+01 MAX Y = 1.224E+02 RANGE Y = 8.860E+01
SAMPLE LEVEL OF X WEIGHT OF OBSERVATION
1 10 1
2 20 4
3 30 1
4 40 1
0IND.VAR(I) NAME COEF.B(I) S.E. COEF. T-VALUE R(I)SQRD MIN X(I) MAX X(I) RANGE X(I) REL.INF.X(I)
0 3.21053E+00
1 LEVEL 2.96579E+00 3.89E-02 76.3 0.0000 1.000E+01 4.000E+01 3.000E+01 1.00
0NO. OF OBSERVATIONS 4
NO. OF IND. VARIABLES 1
RESIDUAL DEGREES OF FREEDOM 2
F-VALUE 5826.8
RESIDUAL ROOT MEAN SQUARE 0.90524786
RESIDUAL MEAN SQUARE 0.81947368
RESIDUAL SUM OF SQUARES 1.63894737
TOTAL SUM OF SQUARES 4776.56000000
MULT. CORREL. COEF. SQUARED .9997
ADJ. MULT. CORR. COEF. SQUARED .9995
0-----------------ORDERED BY COMPUTER INPUT--------- --------- ---------------------ORDERED BY RESIDUALS---------------------
IDENT. OBSV. WSS DISTANCE OBS. Y FITTED Y RESIDUAL OBSV. OBS. Y FITTED Y ORDERED RESID. STUD.RESID. SEQ
1 1774. 33.800 32.868 0.932 1 33.800 32.868 0.932 1.4 1
2 88. 62.200 62.526 -0.326 4 122.400 121.842 0.558 1.1 2
3 548. 92.000 92.184 -0.184 3 92.000 92.184 -0.184 -0.2 3
4 3154. 122.400 121.842 0.558 2 62.200 62.526 -0.326 -1.2 4
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
1979 VERSION OF THE LINWOOD 40 VARIABLE, 1000 OBSERVATION PROGRAM
REFER TO FITTING EQUATIONS TO DATA BY DANIEL AND WOOD, SECOND EDITION, WILEY PUBLISHER,
FOR GLOSSARY OF TERMS, USER'S MANUAL, DETAILS OF CALCULATIONS AND INTERPRETATION OF RESULTS.
0PRECISION - EMPLOY
0 CONTROL CARD INFORMATION ORDER OF CARDS
COL. INPUT MAX. ITEM (NOTE: BLANK ON CARD = 0) FIRST PROBLEM
1-18 PROBLEM IDENTIFICATION. 1 CONTROL CARD.
19-20 6 NUMBER OF INDEPENDENT VARIABLES READ IN 2 FORMAT CARD(S), IF ANY.
(ALLOW SPACE FOR TRANSFORMATIONS). 3 DELETE OBSERVATIONS CARD(S), IF ANY.
21-22 8 NUMBER OF DEPENDENT VARIABLES READ IN. 4 INDICATOR-VARIABLE-OBSERVATIONS CARD(S), IF ANY.
14 65 TOTAL NUMBER OF VARIABLES (BEFORE TRANSFORMATIONS, IF ANY). 5 TRANSFORMATION CARD(S), IF ANY.
24 E CAUSES Y, FITTED Y AND RESIDUALS TO BE 6 INFORMATION CARD(S) FOR PRINTOUT, IF ANY.
LISTED WITH AN E RATHER THAN AN F FORMAT. 7 NAMES OF VARIABLES CARD(S) FOR PRINTOUT, IF ANY.
25 1 1 DO TRANSFORMATIONS. 8 CP FACTORIAL SEARCH CARD, IF ANY.
26 0 1 WEIGHT OBSERVATIONS. WEIGHT ENTERED IN LAST POSITION. 9 DATA CARDS (IF NOT READ FROM A FILE).
2 WEIGHT BY 1/VAR. OF OBSERVATION. VARIANCE ENTERED. 10 END CARD (END IN COLUMNS 1 - 3 OF IDENTIFICATION
27 0 1 LET B(0) = ZERO, OTHERWISE B(0) IS CALCULATED VALUE. FIELD). THE NUMBER OF END CARDS MUST EQUAL THE
28 0 1 CHECK OBSERVATION NUMBER SEQUENCE. NUMBER OF CARDS PER OBSERVATION. (END CARDS
29 0 1 CHECK SEQUENCE WITHIN OBSERVATION NUMBER. ARE NOT NEEDED IF DATA ARE READ FROM A FILE).
30 0 1 DO BACK TRANSFORMATION OF DEPENDENT VARIABLE. 11 ESTIMATE OF VARIANCE CARD, IF ANY.
31 0 1 PUNCH DATA FOR CONFIDENCE INTERVAL PROGRAM. 12 ADDITIONAL CP FACTORIAL SEARCH AND ESTIMATE OF
32 0 0 LIST ALL INPUT DATA. VARIANCE CARDS, IF ANY.
1 LIST ONLY 1ST OBSERVATION.
2 DO NOT LIST ANY INPUT DATA. SECOND PROBLEM
33 1 0 LIST TRANSFORMATIONS AND ALL TRANSFORMED DATA. IF DATA ARE REUSED FROM FIRST PROBLEM,
1 LIST TRANSFORMATIONS AND 1ST TRANSFORMED OBSERVATION. DELETE THE FORMAT, DATA AND END CARDS.
2 DO NOT LIST TRANSFORMATIONS OR TRANSFORMED DATA. IF NAMES ARE REUSED,
34 1 1 DO NOT LIST SUMS OF VARIABLES. DELETE THE NAME CARDS.
35 1 1 DO NOT LIST RAW SUMS AND CROSS PRODUCTS WHEN B(O)=O. IF DIFFERENT INPUT DATA AND NAMES,
36 1 1 DO NOT LIST RESIDUAL SUMS AND CROSS PRODUCTS. REPEAT 1 - 12 ABOVE.
37 0 1 DO NOT LIST MEANS AND ROOT MEAN SQUARES OF VARIABLES.
38 0 1 DO NOT LIST SIMPLE CORRELATION COEFFICIENTS.
39 1 1 DO NOT LIST INVERSE MATRIX.
40 0 1 DO NOT PRINT PLOTS OF RESIDUALS VS. FITTED Y.
2 PLOT (A) RESIDUALS AND (B) COMPONENT AND COMPONENT-
PLUS-RESIDUALS VS. EACH INDEPENDENT VARIABLE.
3 PLOT (A) RESIDUALS ONLY.
4 PLOT (B) COMPONENT AND COMPONENT-PLUS-RESIDUALS ONLY.
5 PLOT (B) BUT EXPAND SCALE TO FILL EACH PLOT.
41 1 0 READ DATA WITH STANDARD FORMAT (A6, I4, I2, 10F6.3).
1 READ DATA WITH FORMAT TO BE READ, 1 CARD (72COL) ASSUMED.
2 READ DATA WITH READ DATA (REDATA) SUBROUTINE.
42 1 0 DO NOT SAVE DATA FOR NEXT PROBLEM.
1 SAVE DATA FOR NEXT PROBLEM.
2 REUSE DATA FROM PREVIOUS PROBLEM.
43-44 0 18 NUMBER OF VARIABLES IN CP SEARCH IF GREATER THAN 12.
45 0 8 NUMBER OF FORMAT CARDS IF GREATER THAN 1.
46-47 8 12 NUMBER OF INFORMATION CARDS TO BE READ FOR DISPLAY ON
PRINTOUT IF DESIRED, 72 COL. EACH.
48 1 1 READ NAMES OF VARIABLES FOR DISPLAY ON PRINTOUT.
NAMES IN SAME POSITIONS AS VARIABLES ON TRANSFORMATION
CARDS - COLS. 1-6, 11-16, - - - , 61-66.
NAMES ARE NOT MOVED, ONLY LISTED OR DELETED.
2 REUSE NAMES OF VARIABLES FROM PREVIOUS PROBLEM.
49 2 SEARCH FOR CANDIDATE EQUATIONS VIA CP. USE ESTIMATE
OF VARIANCE (RMS) FROM:
1 FULL EQUATION,
2 SUBSET EQUATION WITH MINIMUM RMS VALUE, OR
3 ESTIMATE OF VARIANCE CARD, F16.8 FORMAT.
50 0 NUMBER OF CP FACTORIAL SEARCH CARDS TO BE READ PER
DEPENDENT VARIABLE. KEYPUNCH IN ASCENDING ORDER THE
IDENTIFING NUMBER OF THE VARIABLES (AFTER TRANSFOR-
MATIONS) TO BE USED IN THAT SEARCH, 18(2X,I2) FORMAT.
ALL OTHER VARIABLES WILL BE PLACED IN BASIC EQUATION.
51 2 1 LIST COMPONENT-EFFECT TABLE, REQUIRED X(I) PRECISION,
ESTIMATE OF STANDARD DEVIATION FROM NEAR NEIGHBORS,
AND FUNCTIONS OF FITTED Y.
2 LIST ONLY ESTIMATE OF STD. DEVIATION AND FUNCTIONS.
3 LIST ONLY FUNCTIONS OF FITTED Y.
52-53 0 NUMBER OF FILE IF DATA ARE READ FROM SEPARATE FILE,
NO END CARD IF ONLY ONE SET OF DATA IS ON EACH FILE.
54-55 0 NUMBER OF INDEPENDENT VARIABLES GREATER THAN THE 99
ALLOWED IN COLS 19-20.
56-58 0 TO REDUCE PRINTOUT WITH MANY OBSERVATIONS,
NUMBER OF CENTRAL OBSERVATIONS AND RESIDUALS NOT
TO BE PRINTED. THIS REQUIRES AN E IN COL 24.
59 0 CROSS VERIFICATION OF MODEL AND COEFFICIENTS WITH A
SECOND SAMPLE OF DATA:
1 WRITE B(0) AND B(I)S ON FILE IN ONE PROBLEM
(TRANSFORMATIONS ARE NOT SAVED).
2 READ B(0) AND B(I)S FROM FILE IN NEXT PROBLEM
WITH SECOND SET OF OBSERVATIONS.
60 0 5 NUMBER OF DELETE-OBSERVATIONS CARDS. KEYPUNCH
OBSERVATION NUMBER OF DATA TO BE DELETED IN ORDER READ
BY COMPUTER USING 7(I4,6X) FORMAT.
61 0 5 NUMBER OF INDICATOR-VARIABLE-OBSERVATIONS CARDS.
USING A 7(I4,2X,I3,1X) FORMAT, KEYPUNCH OBSERVATION
NUMBER (IN ORDER READ) AND VARIABLE NUMBER (BEFORE
TRANSFORMATIONS) INTO WHICH A 1 IS TO BE INSERTED.
0EQUATION 1 OF A MULTI-EQUATION PROBLEM
0DATA READ WITH SPECIAL FORMAT
0FORMAT CARD 1 ( A6,I4,I2, F6.1,9F6.0/ 12X, 4F6.0 )
0BZERO = CALCULATED VALUE
0INFORMATION CARDS
Y = B(0) + B(1)X1 + B(2)X2 + B(3)X3 + B(4)X4 + B(5)X5 + B(6)X6
Y = EMPLOYMENT
X1 = PRICE INDEX
X2 = GROSS NATIONAL PRODUCT
X3 = UNEMPLOYMENT
X4 = SIZE OF ARMED FORCES
X5 = NONINSTITIONAL POPULATION
X6 = TIME IN YEARS
0DATA TRANSFORMATIONS
POSITION CODE OPERATION CONSTANT LOCATION OMIT VARIABLE NAME
1 NONE 1 0 1 PRICE
2 NONE 2 0 2 GNP
3 NONE 3 0 3 UNEMPY
4 NONE 4 0 4 ARMY
5 NONE 5 0 5 NONIST
6 NONE 6 0 6 TIME
7 NONE 7 0 7 TOTAL
8 NONE 8 1 FARM
9 NONE 9 1 SELF
10 NONE 10 1 UNPAID
11 NONE 11 1 HOUSE
12 NONE 12 1 PRIVAT
13 NONE 13 1 FED GO
14 NONE 14 1 LOCALG
0
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
PRECISION - EMPLOY
0DATA INPUT 6 INDEPENDENT VARIABLES 8 DEPENDENT VARIABLE(S)
OBSV. SEQ. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1947 0 83.000 234289.000 2356.000 1590.000 107608.000 1947.000 60323.000 8256.000 6045.000 427.000
1 1714.000 38407.000 1892.000 3582.000
1948 0 88.500 259426.000 2325.000 1456.000 108632.000 1948.000 61122.000 7960.000 6139.000 401.000
1 1731.000 39241.000 1863.000 3787.000
1949 0 88.200 258054.000 3682.000 1616.000 109773.000 1949.000 60171.000 8017.000 6208.000 396.000
1 1772.000 37922.000 1908.000 3948.000
1950 0 89.500 284599.000 3351.000 1650.000 110929.000 1950.000 61187.000 7497.000 6069.000 404.000
1 1995.000 39196.000 1928.000 4098.000
1951 0 96.200 328975.000 2099.000 3099.000 112075.000 1951.000 63221.000 7048.000 5869.000 400.000
1 2055.000 41460.000 2302.000 4087.000
1952 0 98.100 346999.000 1932.000 3594.000 113270.000 1952.000 63639.000 6792.000 5670.000 431.000
1 1922.000 42216.000 2420.000 4188.000
1953 0 99.000 365385.000 1870.000 3547.000 115094.000 1953.000 64989.000 6555.000 5794.000 423.000
1 1985.000 43587.000 2305.000 4340.000
1954 0 100.000 363112.000 3578.000 3350.000 116219.000 1954.000 63761.000 6495.000 5880.000 445.000
1 1919.000 42271.000 2188.000 4563.000
1955 0 101.200 397469.000 2904.000 3048.000 117388.000 1955.000 66019.000 6718.000 5886.000 524.000
1 2216.000 43761.000 2187.000 4727.000
1956 0 104.600 419180.000 2822.000 2857.000 118734.000 1956.000 67857.000 6572.000 5936.000 581.000
1 2359.000 45131.000 2209.000 5069.000
1957 0 108.400 442769.000 2936.000 2798.000 120445.000 1957.000 68169.000 6222.000 6089.000 626.000
1 2328.000 45278.000 2217.000 5409.000
1958 0 110.800 444546.000 4681.000 2637.000 121950.000 1958.000 66513.000 5844.000 6185.000 605.000
1 2456.000 43530.000 2191.000 5702.000
1959 0 112.600 482704.000 3813.000 2552.000 123366.000 1959.000 68655.000 5836.000 6298.000 597.000
1 2520.000 45214.000 2233.000 5957.000
1960 0 114.200 502601.000 3931.000 2514.000 125368.000 1960.000 69564.000 5723.000 6367.000 615.000
1 2489.000 45850.000 2270.000 6250.000
1961 0 115.700 518173.000 4806.000 2572.000 127852.000 1961.000 69331.000 5463.000 6388.000 662.000
1 2594.000 45397.000 2279.000 6548.000
1962 0 116.900 554894.000 4007.000 2827.000 130081.000 1962.000 70551.000 5190.000 6271.000 623.000
1 2626.000 46652.000 2340.000 6849.000
0DATA TRANSFORMATIONS
POSITION CODE OPERATION CONSTANT LOCATION OMIT VARIABLE NAME
1 NONE 1 0 1 PRICE
2 NONE 2 0 2 GNP
3 NONE 3 0 3 UNEMPY
4 NONE 4 0 4 ARMY
5 NONE 5 0 5 NONIST
6 NONE 6 0 6 TIME
7 NONE 7 0 7 TOTAL
8 NONE 8 1 FARM
9 NONE 9 1 SELF
10 NONE 10 1 UNPAID
11 NONE 11 1 HOUSE
12 NONE 12 1 PRIVAT
13 NONE 13 1 FED GO
14 NONE 14 1 LOCALG
0FIRST OBSERVATION AFTER TRANSFORMATIONS THE FITTED EQUATION HAS 6 INDEPENDENT VARIABLES, 1 DEPENDENT VARIABLE(S)
PRICE GNP UNEMPY ARMY NONIST TIME TOTAL
OBSV. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1947 8.30000E+01 2.34289E+05 2.35600E+03 1.59000E+03 1.07608E+05 1.94700E+03 6.03230E+04
0MEANS OF VARIABLES
1.01681E+02 3.87698E+05 3.19331E+03 2.60669E+03 1.17424E+05 1.95450E+03 6.53170E+04
0ROOT MEAN SQUARES OF VARIABLES
1.07916E+01 9.93949E+04 9.34464E+02 6.95920E+02 6.95610E+03 4.76095E+00 3.51197E+03
0SIMPLE CORRELATION COEFFICIENTS, R(I,I PRIME)
1 1.000
2 0.992 1.000
3 0.621 0.604 1.000
4 0.465 0.446 -0.177 1.000
5 0.979 0.991 0.687 0.364 1.000
6 0.991 0.995 0.668 0.417 0.994 1.000
7 0.971 0.984 0.502 0.457 0.960 0.971 1.000
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
PRECISION - EMPLOY DEP VAR 1: TOTAL MIN Y = 6.017E+04 MAX Y = 7.055E+04 RANGE Y = 1.038E+04
Y = B(0) + B(1)X1 + B(2)X2 + B(3)X3 + B(4)X4 + B(5)X5 + B(6)X6
Y = EMPLOYMENT
X1 = PRICE INDEX
X2 = GROSS NATIONAL PRODUCT
X3 = UNEMPLOYMENT
X4 = SIZE OF ARMED FORCES
X5 = NONINSTITIONAL POPULATION
X6 = TIME IN YEARS
0IND.VAR(I) NAME COEF.B(I) S.E. COEF. T-VALUE R(I)SQRD MIN X(I) MAX X(I) RANGE X(I) REL.INF.X(I)
0 -3.48226E+06
1 PRICE 1.50619E+01 8.49E+01 0.2 0.9926 8.300E+01 1.169E+02 3.390E+01 0.05
2 GNP -3.58192E-02 3.35E-02 1.1 0.9994 2.343E+05 5.549E+05 3.206E+05 1.11
3 UNEMPY -2.02023E+00 4.88E-01 4.1 0.9703 1.870E+03 4.806E+03 2.936E+03 0.57
4 ARMY -1.03323E+00 2.14E-01 4.8 0.7214 1.456E+03 3.594E+03 2.138E+03 0.21
5 NONIST -5.11041E-02 2.26E-01 0.2 0.9975 1.076E+05 1.301E+05 2.247E+04 0.11
6 TIME 1.82915E+03 4.55E+02 4.0 0.9987 1.947E+03 1.962E+03 1.500E+01 2.64
0NO. OF OBSERVATIONS 16
NO. OF IND. VARIABLES 6
RESIDUAL DEGREES OF FREEDOM 9
F-VALUE 330.3
RESIDUAL ROOT MEAN SQUARE 304.85407356
RESIDUAL MEAN SQUARE 92936.00616731
RESIDUAL SUM OF SQUARES 836424.05550579
TOTAL SUM OF SQUARES 185008826.00000000
MULT. CORREL. COEF. SQUARED .9955
ADJ. MULT. CORR. COEF. SQUARED .9925
1 LINEAR LEAST-SQUARES CURVE FITTING PROGRAM
0PRECISION - EMPLOY DEP VAR 1: TOTAL RESIDUAL ROOT MEAN SQUARE OF FITTED EQUATION: 304.85
0STANDARD DEVIATION ESTIMATED FROM RESIDUALS OF NEIGHBORING OBSERVATIONS (OBSERVATIONS 1 TO 4 APART IN FITTED Y ORDER).
CUMULATIVE ---------ORDERED BY WSSD---------- ---------ORDERED BY FITTED Y---------
NO. STD DEV WSSD OBSV. OBSV. DEL RESIDUALS WSSD DEL RESIDUALS FITTED Y OBSV. SEQ.
1 100.78 40.96 1952 1953 85.26 229.22 221.05 60055.66 1947 1
2 91.69 42.21 1959 1960 69.88 117.23 140.30 60124.71 1949 2
3 234.92 43.30 1955 1956 441.09 199.56 316.10 61216.01 1948 3
4 315.87 44.41 1956 1957 472.66 156.29 719.83 61597.11 1950 4
5 384.85 44.57 1951 1952 559.03 437.40 322.89 62911.29 1951 5
6 391.90 45.08 1947 1948 361.35 267.51 236.13 63774.18 1954 6
7 412.98 50.60 1949 1950 456.40 40.96 85.26 63888.31 1952 7
8 424.54 73.19 1961 1960 427.60 208.19 178.35 65153.05 1953 8
9 380.98 73.34 1954 1955 27.49 496.03 53.36 66004.70 1955 9
10 407.74 83.54 1961 1962 548.69 305.59 494.45 66552.06 1958 10
11 383.19 89.34 1958 1959 116.49 44.41 472.66 67401.61 1956 11
12 365.08 117.23 1949 1948 140.30 200.78 138.28 68186.27 1957 12
13 402.44 156.29 1950 1951 719.83 205.27 497.48 68810.55 1959 13
14 386.44 164.67 1954 1953 150.87 73.19 427.60 68989.07 1961 14
15 398.01 167.19 1951 1953 473.76 183.78 121.09 69649.67 1960 15
16 374.74 170.14 1958 1957 21.79 45.08 361.35 70757.76 1962 16
1 LINEAR LEAST-SQUARES CURVE FITTING PROGRAM
0PRECISION - EMPLOY DEP VAR 1: TOTAL
0FUNCTIONS RELATED TO THE VARIANCE OF FITTED Y. OBSERVATIONS ORDERED BY COMPUTER INPUT.
0 STUDENTIZED DELETE-EFFECT
IDENT. OBSV. RESIDUAL RESIDUAL V(Y)/RMS V(R)/RMS V(Y)/V(R) VALUE PERCENT
JASA P 1947 267.340 1.2 0.4245 0.5755 0.7 0.1
JASA R 1948 -94.014 -0.5 0.5650 0.4350 1.3 0.0
JASA E 1949 46.287 0.2 0.3621 0.6379 0.6 0.0
JASA C 1950 -410.115 -1.7 0.3722 0.6278 0.6 0.2
JASA I 1951 309.715 1.6 0.6155 0.3845 1.6 0.6
JASA S 1952 -249.311 -1.0 0.3696 0.6304 0.6 0.1
JASA I 1953 -164.049 -0.8 0.4915 0.5085 1.0 0.1
JASA O 1954 -13.180 -0.1 0.5047 0.4953 1.0 0.0
JASA N 1955 14.305 0.1 0.4571 0.5429 0.8 0.0
JASA 1956 455.394 1.8 0.3306 0.6694 0.5 0.2
JASA T 1957 -17.269 -0.1 0.3599 0.6401 0.6 0.0
JASA E 1958 -39.055 -0.2 0.4831 0.5169 0.9 0.0
JASA S 1959 -155.550 -0.6 0.3743 0.6257 0.6 0.0
JASA T 1960 -85.671 -0.3 0.2284 0.7716 0.3 0.0
JASA 1961 341.932 1.4 0.3729 0.6271 0.6 0.2
JASA 1962 -206.758 -1.2 0.6886 0.3114 2.2 0.5
1 LINEAR LEAST-SQUARES CURVE FITTING PROGRAM
0PRECISION - EMPLOY DEP VAR 1: TOTAL
0-----------------ORDERED BY COMPUTER INPUT--------- --------- ---------------------ORDERED BY RESIDUALS---------------------
IDENT. OBSV. WSS DISTANCE OBS. Y FITTED Y RESIDUAL OBSV. OBS. Y FITTED Y ORDERED RESID. STUD.RESID. SEQ
JASA P 1947 2396. 60323.000 60055.660 267.340 1956 67857.000 67401.606 455.394 1.8 1
JASA R 1948 1799. 61122.000 61216.014 -94.014 1961 69331.000 68989.068 341.932 1.4 2
JASA E 1949 1345. 60171.000 60124.713 46.287 1951 63221.000 62911.285 309.715 1.6 3
JASA C 1950 889. 61187.000 61597.115 -410.115 1947 60323.000 60055.660 267.340 1.2 4
JASA I 1951 545. 63221.000 62911.285 309.715 1949 60171.000 60124.713 46.287 0.2 5
JASA S 1952 329. 63639.000 63888.311 -249.311 1955 66019.000 66004.695 14.305 0.1 6
JASA I 1953 175. 64989.000 65153.049 -164.049 1954 63761.000 63774.180 -13.180 -0.1 7
JASA O 1954 30. 63761.000 63774.180 -13.180 1957 68169.000 68186.269 -17.269 -0.1 8
JASA N 1955 16. 66019.000 66004.695 14.305 1958 66513.000 66552.055 -39.055 -0.2 9
JASA 1956 102. 67857.000 67401.606 455.394 1960 69564.000 69649.671 -85.671 -0.3 10
JASA T 1957 271. 68169.000 68186.269 -17.269 1948 61122.000 61216.014 -94.014 -0.5 11
JASA E 1958 584. 66513.000 66552.055 -39.055 1959 68655.000 68810.550 -155.550 -0.6 12
JASA S 1959 872. 68655.000 68810.550 -155.550 1953 64989.000 65153.049 -164.049 -0.8 13
JASA T 1960 1297. 69564.000 69649.671 -85.671 1962 70551.000 70757.758 -206.758 -1.2 14
JASA 1961 1874. 69331.000 68989.068 341.932 1952 63639.000 63888.311 -249.311 -1.0 15
JASA 1962 2446. 70551.000 70757.758 -206.758 1950 61187.000 61597.115 -410.115 -1.7 16
1 PRECISION - EMPLOY DEP VAR 1: TOTAL CUMULATIVE DISTRIBUTION OF RESIDUALS
.0002 .001 .005 .01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8 .9 .95 .98 .99 .995 .999
*-----*-------*--*---*-----*----*-----*----*---*---*---*---*----*-----*----*-----*---*--*-------*-----
I ' + I
I ' I
P I ' I
O I ' I
S I ' I
I I ' I
T I ' + I
I I ' I
V I ' + I
E I ' I
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I ' + I
I ' I
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I ' I
I ' I
I ' I
I ' I
I ' I
I ' I
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R I ' I
E I ' I
S I ' + I
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D I ' + I
U 0 I----------------------------------------------------------------------------------------------------I
A I '+ + I
L I + ' I
S I ' I
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*-----*-------*--*---*-----*----*-----*----*---*---*---*---*----*-----*----*-----*---*--*-------*-----
.0002 .001 .005 .01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8 .9 .95 .98 .99 .995 .999
CUMULATIVE FREQUENCY, NORMAL GRID
1 PRECISION - EMPLOY DEP VAR 1: TOTAL RESIDUAL VS. FITTED Y
60055.660 65406.709 70757.758
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I + I
I I
P I I
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U 0 I----------------------------------------------------------------------------------------------------I
A I + + I
L I + I
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*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
60055.660 65406.709 70757.758
FITTED Y
1 CP VALUES FOR THE SELECTION OF VARIABLES
PRECISION - EMPLOY DEP VAR 1: TOTAL SEARCH NUMBER 1
SELECTION OF VARIABLES FOR BASIC EQUATION
0CP =*****, VARIABLE ADDED 4 ARMY
0CP =864.3, VARIABLE ADDED 3 UNEMPY
0CP = 6.2, VARIABLE ADDED 6 TIME
0CP = 3.2, VARIABLE ADDED 2 GNP
0CP = 5.0, VARIABLE ADDED 5 NONIST
0
NUMBER OF OBSERVATIONS 16
NUMBER OF VARIABLES IN FULL EQUATION 6
NUMBER OF VARIABLES IN BASIC EQUATION 2
REMAINDER OF VARIABLES TO BE SEARCHED 4
0EQUATION P CP VARIABLES IN EQUATION
0 7 7.0 FULL EQUATION
0 3 864.3 BASIC SET OF VARIABLES 3 4
UNEMPY ARMY
RMS =***********
0 1 5 4.6 BASIC SET PLUS 5 6
NONIST TIME
RMS =89610.87709
0 2 6 6.1 BASIC SET PLUS 1 5 6
PRICE NONIST TIME
RMS =94273.03144
0 3 7 7.0 BASIC SET PLUS 1 2 5 6
PRICE GNP NONIST TIME
RMS =92936.00617
0 4 6 5.0 BASIC SET PLUS 2 5 6
GNP NONIST TIME
RMS =83934.80319
0 5 5 3.2 BASIC SET PLUS 2 6
GNP TIME
RMS =78061.85508
0 6 6 5.1 BASIC SET PLUS 1 2 6
PRICE GNP TIME
RMS =84117.30036
0 7 4 6.2 BASIC SET PLUS 6
TIME
RMS =***********
0SWEEP NUMBER 15, DELTA Z(K,K) = 1.E-19
1ESTIMATE OF VARIANCE
0RMS OF FULL EQUATION 92936.00616731
RMS OF SUBSET EQUATION 5 78061.85507545
0RMS OF SUBSET EQUATION USED TO RECALCULATE AND PLOT CP VALUES.
0 P CP
FULL EQUATION 7 8.7
SUBSET EQUATION 5 5 5.0
0
SEQ EQUATION P ORDERED CP
1 5 5 5.0
2 1 5 6.6
3 4 6 6.8
4 6 6 6.8
5 2 6 8.1
6 3 7 8.7
7 7 4 9.0
1 PRECISION - EMPLOY DEP VAR 1: TOTAL CP PLOT SEARCH NUMBER 1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
17 I I
I I
I I
16 I I
I I
I I
15 I I
I I
I I
14 I I
I I
I I
13 I I
I I
I I
12 I I
I I
I I
11 I I
I I
I I
10 I I
I I
I I
9 I + I
CP I + I
I I
8 I + I
I I
I I
7 I I
I + + I
I I
6 I I
I I
I I
5 I + I
I I
I I
4 I I
I I
I I
3 I I
I I
I I
2 I I
I I
I I
1 I I
I I
I I
0 *----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
P
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
1979 VERSION OF THE LINWOOD 40 VARIABLE, 1000 OBSERVATION PROGRAM
REFER TO FITTING EQUATIONS TO DATA BY DANIEL AND WOOD, SECOND EDITION, WILEY PUBLISHER,
FOR GLOSSARY OF TERMS, USER'S MANUAL, DETAILS OF CALCULATIONS AND INTERPRETATION OF RESULTS.
0B0=0 BRNLEE BLOOD
0 CONTROL CARD INFORMATION ORDER OF CARDS
COL. INPUT MAX. ITEM (NOTE: BLANK ON CARD = 0) FIRST PROBLEM
1-18 PROBLEM IDENTIFICATION. 1 CONTROL CARD.
19-20 1 NUMBER OF INDEPENDENT VARIABLES READ IN 2 FORMAT CARD(S), IF ANY.
(ALLOW SPACE FOR TRANSFORMATIONS). 3 DELETE OBSERVATIONS CARD(S), IF ANY.
21-22 1 NUMBER OF DEPENDENT VARIABLES READ IN. 4 INDICATOR-VARIABLE-OBSERVATIONS CARD(S), IF ANY.
2 65 TOTAL NUMBER OF VARIABLES (BEFORE TRANSFORMATIONS, IF ANY). 5 TRANSFORMATION CARD(S), IF ANY.
24 E CAUSES Y, FITTED Y AND RESIDUALS TO BE 6 INFORMATION CARD(S) FOR PRINTOUT, IF ANY.
LISTED WITH AN E RATHER THAN AN F FORMAT. 7 NAMES OF VARIABLES CARD(S) FOR PRINTOUT, IF ANY.
25 0 1 DO TRANSFORMATIONS. 8 CP FACTORIAL SEARCH CARD, IF ANY.
26 0 1 WEIGHT OBSERVATIONS. WEIGHT ENTERED IN LAST POSITION. 9 DATA CARDS (IF NOT READ FROM A FILE).
2 WEIGHT BY 1/VAR. OF OBSERVATION. VARIANCE ENTERED. 10 END CARD (END IN COLUMNS 1 - 3 OF IDENTIFICATION
27 1 1 LET B(0) = ZERO, OTHERWISE B(0) IS CALCULATED VALUE. FIELD). THE NUMBER OF END CARDS MUST EQUAL THE
28 0 1 CHECK OBSERVATION NUMBER SEQUENCE. NUMBER OF CARDS PER OBSERVATION. (END CARDS
29 0 1 CHECK SEQUENCE WITHIN OBSERVATION NUMBER. ARE NOT NEEDED IF DATA ARE READ FROM A FILE).
30 0 1 DO BACK TRANSFORMATION OF DEPENDENT VARIABLE. 11 ESTIMATE OF VARIANCE CARD, IF ANY.
31 0 1 PUNCH DATA FOR CONFIDENCE INTERVAL PROGRAM. 12 ADDITIONAL CP FACTORIAL SEARCH AND ESTIMATE OF
32 0 0 LIST ALL INPUT DATA. VARIANCE CARDS, IF ANY.
1 LIST ONLY 1ST OBSERVATION.
2 DO NOT LIST ANY INPUT DATA. SECOND PROBLEM
33 0 0 LIST TRANSFORMATIONS AND ALL TRANSFORMED DATA. IF DATA ARE REUSED FROM FIRST PROBLEM,
1 LIST TRANSFORMATIONS AND 1ST TRANSFORMED OBSERVATION. DELETE THE FORMAT, DATA AND END CARDS.
2 DO NOT LIST TRANSFORMATIONS OR TRANSFORMED DATA. IF NAMES ARE REUSED,
34 0 1 DO NOT LIST SUMS OF VARIABLES. DELETE THE NAME CARDS.
35 0 1 DO NOT LIST RAW SUMS AND CROSS PRODUCTS WHEN B(O)=O. IF DIFFERENT INPUT DATA AND NAMES,
36 0 1 DO NOT LIST RESIDUAL SUMS AND CROSS PRODUCTS. REPEAT 1 - 12 ABOVE.
37 0 1 DO NOT LIST MEANS AND ROOT MEAN SQUARES OF VARIABLES.
38 0 1 DO NOT LIST SIMPLE CORRELATION COEFFICIENTS.
39 0 1 DO NOT LIST INVERSE MATRIX.
40 0 1 DO NOT PRINT PLOTS OF RESIDUALS VS. FITTED Y.
2 PLOT (A) RESIDUALS AND (B) COMPONENT AND COMPONENT-
PLUS-RESIDUALS VS. EACH INDEPENDENT VARIABLE.
3 PLOT (A) RESIDUALS ONLY.
4 PLOT (B) COMPONENT AND COMPONENT-PLUS-RESIDUALS ONLY.
5 PLOT (B) BUT EXPAND SCALE TO FILL EACH PLOT.
41 1 0 READ DATA WITH STANDARD FORMAT (A6, I4, I2, 10F6.3).
1 READ DATA WITH FORMAT TO BE READ, 1 CARD (72COL) ASSUMED.
2 READ DATA WITH READ DATA (REDATA) SUBROUTINE.
42 1 0 DO NOT SAVE DATA FOR NEXT PROBLEM.
1 SAVE DATA FOR NEXT PROBLEM.
2 REUSE DATA FROM PREVIOUS PROBLEM.
43-44 0 18 NUMBER OF VARIABLES IN CP SEARCH IF GREATER THAN 12.
45 0 8 NUMBER OF FORMAT CARDS IF GREATER THAN 1.
46-47 5 12 NUMBER OF INFORMATION CARDS TO BE READ FOR DISPLAY ON
PRINTOUT IF DESIRED, 72 COL. EACH.
48 1 1 READ NAMES OF VARIABLES FOR DISPLAY ON PRINTOUT.
NAMES IN SAME POSITIONS AS VARIABLES ON TRANSFORMATION
CARDS - COLS. 1-6, 11-16, - - - , 61-66.
NAMES ARE NOT MOVED, ONLY LISTED OR DELETED.
2 REUSE NAMES OF VARIABLES FROM PREVIOUS PROBLEM.
49 0 SEARCH FOR CANDIDATE EQUATIONS VIA CP. USE ESTIMATE
OF VARIANCE (RMS) FROM:
1 FULL EQUATION,
2 SUBSET EQUATION WITH MINIMUM RMS VALUE, OR
3 ESTIMATE OF VARIANCE CARD, F16.8 FORMAT.
50 0 NUMBER OF CP FACTORIAL SEARCH CARDS TO BE READ PER
DEPENDENT VARIABLE. KEYPUNCH IN ASCENDING ORDER THE
IDENTIFING NUMBER OF THE VARIABLES (AFTER TRANSFOR-
MATIONS) TO BE USED IN THAT SEARCH, 18(2X,I2) FORMAT.
ALL OTHER VARIABLES WILL BE PLACED IN BASIC EQUATION.
51 0 1 LIST COMPONENT-EFFECT TABLE, REQUIRED X(I) PRECISION,
ESTIMATE OF STANDARD DEVIATION FROM NEAR NEIGHBORS,
AND FUNCTIONS OF FITTED Y.
2 LIST ONLY ESTIMATE OF STD. DEVIATION AND FUNCTIONS.
3 LIST ONLY FUNCTIONS OF FITTED Y.
52-53 0 NUMBER OF FILE IF DATA ARE READ FROM SEPARATE FILE,
NO END CARD IF ONLY ONE SET OF DATA IS ON EACH FILE.
54-55 0 NUMBER OF INDEPENDENT VARIABLES GREATER THAN THE 99
ALLOWED IN COLS 19-20.
56-58 0 TO REDUCE PRINTOUT WITH MANY OBSERVATIONS,
NUMBER OF CENTRAL OBSERVATIONS AND RESIDUALS NOT
TO BE PRINTED. THIS REQUIRES AN E IN COL 24.
59 0 CROSS VERIFICATION OF MODEL AND COEFFICIENTS WITH A
SECOND SAMPLE OF DATA:
1 WRITE B(0) AND B(I)S ON FILE IN ONE PROBLEM
(TRANSFORMATIONS ARE NOT SAVED).
2 READ B(0) AND B(I)S FROM FILE IN NEXT PROBLEM
WITH SECOND SET OF OBSERVATIONS.
60 0 5 NUMBER OF DELETE-OBSERVATIONS CARDS. KEYPUNCH
OBSERVATION NUMBER OF DATA TO BE DELETED IN ORDER READ
BY COMPUTER USING 7(I4,6X) FORMAT.
61 0 5 NUMBER OF INDICATOR-VARIABLE-OBSERVATIONS CARDS.
USING A 7(I4,2X,I3,1X) FORMAT, KEYPUNCH OBSERVATION
NUMBER (IN ORDER READ) AND VARIABLE NUMBER (BEFORE
TRANSFORMATIONS) INTO WHICH A 1 IS TO BE INSERTED.
0EQUATION 1 OF A MULTI-EQUATION PROBLEM
0DATA READ WITH SPECIAL FORMAT
0FORMAT CARD 1 (A3,2I2,F5.0,F7.0)
0BZERO = 0
0INFORMATION CARDS
PROBLEM FROM STATISTICAL THEORY AND METHODOLOGY BY BROWNLEE,
2ND EDITION, SECTION 11.4 .
Y = B(1)X1
Y = RATES OF BLOOD FLOW
X = MEASUREMENTS BY AN INSTRUMENT
0NAMES OF VARIABLES
A B
0
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
B0=0 BRNLEE BLOOD
0DATA INPUT 1 INDEPENDENT VARIABLES 1 DEPENDENT VARIABLE(S)
OBSV. SEQ. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 0 1190.000 1115.000
2 0 1455.000 1425.000
3 0 1550.000 1515.000
4 0 1730.000 1795.000
5 0 1745.000 1715.000
6 0 1770.000 1710.000
7 0 1900.000 1830.000
8 0 1920.000 1920.000
9 0 1960.000 1970.000
10 0 2295.000 2300.000
11 0 2335.000 2280.000
12 0 2490.000 2520.000
13 0 2720.000 2630.000
14 0 2710.000 2740.000
15 0 2530.000 2390.000
16 0 2900.000 2800.000
17 0 2760.000 2630.000
18 0 3010.000 2970.000
0SUMS OF VARIABLES
3.89700E+04 3.82550E+04
0RAW SUMS OF SQUARES + CROSS PRODUCTS
1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 8.93949E+07
2 8.77191E+07 8.61258E+07
0MEANS OF VARIABLES
2.16500E+03 2.12528E+03
0ROOT MEAN SQUARES OF VARIABLES
2.29315E+03 2.25083E+03
0SIMPLE CORRELATION COEFFICIENTS, R(I,I PRIME)
1 1.000
2 1.000 1.000
0INVERSE, C(I,I PRIME)
1 1.000
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
B0=0 BRNLEE BLOOD DEP VAR 1: B MIN Y = 1.115E+03 MAX Y = 2.970E+03 RANGE Y = 1.855E+03
PROBLEM FROM STATISTICAL THEORY AND METHODOLOGY BY BROWNLEE,
2ND EDITION, SECTION 11.4 .
Y = B(1)X1
Y = RATES OF BLOOD FLOW
X = MEASUREMENTS BY AN INSTRUMENT
0IND.VAR(I) NAME COEF.B(I) S.E. COEF. T-VALUE R(I)SQRD MIN X(I) MAX X(I) RANGE X(I) REL.INF.X(I)
0 B(0) = 0
1 A 9.81254E-01 5.80E-03 169.2 0.0000 1.190E+03 3.010E+03 1.820E+03 0.96
0NO. OF OBSERVATIONS 18
NO. OF IND. VARIABLES 1
RESIDUAL DEGREES OF FREEDOM 17
RESIDUAL ROOT MEAN SQUARE 54.83150293
RESIDUAL MEAN SQUARE 3006.49371332
RESIDUAL SUM OF SQUARES 51110.39312645
TOTAL SUM OF SQUARES 4823323.61111111
MULT. CORREL. COEF. SQUARED .9894
ADJ. MULT. CORR. COEF. SQUARED .9894
0-----------------ORDERED BY COMPUTER INPUT--------- --------- ---------------------ORDERED BY RESIDUALS---------------------
IDENT. OBSV. WSS DISTANCE OBS. Y FITTED Y RESIDUAL OBSV. OBS. Y FITTED Y ORDERED RESID. STUD.RESID. SEQ
1 304. 1115.000 1167.692 -52.692 4 1795.000 1697.569 97.431 1.8 1
2 161. 1425.000 1427.725 -2.725 14 2740.000 2659.198 80.802 1.5 2
3 121. 1515.000 1520.944 -5.944 12 2520.000 2443.322 76.678 1.4 3
4 61. 1795.000 1697.569 97.431 10 2300.000 2251.978 48.022 0.9 4
5 56. 1715.000 1712.288 2.712 9 1970.000 1923.258 46.742 0.9 5
6 50. 1710.000 1736.820 -26.820 8 1920.000 1884.008 35.992 0.7 6
7 22. 1830.000 1864.383 -34.383 18 2970.000 2953.574 16.426 0.3 7
8 19. 1920.000 1884.008 35.992 5 1715.000 1712.288 2.712 0.1 8
9 13. 1970.000 1923.258 46.742 2 1425.000 1427.725 -2.725 -0.1 9
10 5. 2300.000 2251.978 48.022 3 1515.000 1520.944 -5.944 -0.1 10
11 9. 2280.000 2291.228 -11.228 11 2280.000 2291.228 -11.228 -0.2 11
12 34. 2520.000 2443.322 76.678 6 1710.000 1736.820 -26.820 -0.5 12
13 99. 2630.000 2669.011 -39.011 7 1830.000 1864.383 -34.383 -0.6 13
14 95. 2740.000 2659.198 80.802 13 2630.000 2669.011 -39.011 -0.7 14
15 43. 2390.000 2482.573 -92.573 16 2800.000 2845.636 -45.636 -0.9 15
16 173. 2800.000 2845.636 -45.636 1 1115.000 1167.692 -52.692 -1.0 16
17 113. 2630.000 2708.261 -78.261 17 2630.000 2708.261 -78.261 -1.5 17
18 229. 2970.000 2953.574 16.426 15 2390.000 2482.573 -92.573 -1.7 18
1 B0=0 BRNLEE BLOOD DEP VAR 1: B CUMULATIVE DISTRIBUTION OF RESIDUALS
.0002 .001 .005 .01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8 .9 .95 .98 .99 .995 .999
*-----*-------*--*---*-----*----*-----*----*---*---*---*---*----*-----*----*-----*---*--*-------*-----
I ' + I
I ' I
P I ' I
O I ' I
S I ' + I
I I ' + I
T I ' I
I I ' I
V I ' I
E I ' I
I ' I
I ' I
I ' I
I ' + + I
I ' I
I ' I
I ' + I
I ' I
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D I ' + I
U 0 I--------------------------------------------------+-------------------------------------------------I
A I +' I
L I ' I
S I + ' I
I ' I
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I + ' I
I ' I
I + ' I
I + ' I
I ' I
I + ' I
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V I ' I
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*-----*-------*--*---*-----*----*-----*----*---*---*---*---*----*-----*----*-----*---*--*-------*-----
.0002 .001 .005 .01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8 .9 .95 .98 .99 .995 .999
CUMULATIVE FREQUENCY, NORMAL GRID
1 B0=0 BRNLEE BLOOD DEP VAR 1: B RESIDUAL VS. FITTED Y
1167.692 2060.633 2953.574
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I + I
I I
P I I
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T I I
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D I + I
U 0 I-------------+--------------------------------------------------------------------------------------I
A I + I
L I I
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*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
1167.692 2060.633 2953.574
FITTED Y
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
1979 VERSION OF THE LINWOOD 40 VARIABLE, 1000 OBSERVATION PROGRAM
REFER TO FITTING EQUATIONS TO DATA BY DANIEL AND WOOD, SECOND EDITION, WILEY PUBLISHER,
FOR GLOSSARY OF TERMS, USER'S MANUAL, DETAILS OF CALCULATIONS AND INTERPRETATION OF RESULTS.
0B0=0 BB,SWITCHES=1
0 CONTROL CARD INFORMATION ORDER OF CARDS
COL. INPUT MAX. ITEM (NOTE: BLANK ON CARD = 0) FIRST PROBLEM
1-18 PROBLEM IDENTIFICATION. 1 CONTROL CARD.
19-20 1 NUMBER OF INDEPENDENT VARIABLES READ IN 2 FORMAT CARD(S), IF ANY.
(ALLOW SPACE FOR TRANSFORMATIONS). 3 DELETE OBSERVATIONS CARD(S), IF ANY.
21-22 1 NUMBER OF DEPENDENT VARIABLES READ IN. 4 INDICATOR-VARIABLE-OBSERVATIONS CARD(S), IF ANY.
2 65 TOTAL NUMBER OF VARIABLES (BEFORE TRANSFORMATIONS, IF ANY). 5 TRANSFORMATION CARD(S), IF ANY.
24 E CAUSES Y, FITTED Y AND RESIDUALS TO BE 6 INFORMATION CARD(S) FOR PRINTOUT, IF ANY.
LISTED WITH AN E RATHER THAN AN F FORMAT. 7 NAMES OF VARIABLES CARD(S) FOR PRINTOUT, IF ANY.
25 0 1 DO TRANSFORMATIONS. 8 CP FACTORIAL SEARCH CARD, IF ANY.
26 0 1 WEIGHT OBSERVATIONS. WEIGHT ENTERED IN LAST POSITION. 9 DATA CARDS (IF NOT READ FROM A FILE).
2 WEIGHT BY 1/VAR. OF OBSERVATION. VARIANCE ENTERED. 10 END CARD (END IN COLUMNS 1 - 3 OF IDENTIFICATION
27 1 1 LET B(0) = ZERO, OTHERWISE B(0) IS CALCULATED VALUE. FIELD). THE NUMBER OF END CARDS MUST EQUAL THE
28 0 1 CHECK OBSERVATION NUMBER SEQUENCE. NUMBER OF CARDS PER OBSERVATION. (END CARDS
29 0 1 CHECK SEQUENCE WITHIN OBSERVATION NUMBER. ARE NOT NEEDED IF DATA ARE READ FROM A FILE).
30 0 1 DO BACK TRANSFORMATION OF DEPENDENT VARIABLE. 11 ESTIMATE OF VARIANCE CARD, IF ANY.
31 0 1 PUNCH DATA FOR CONFIDENCE INTERVAL PROGRAM. 12 ADDITIONAL CP FACTORIAL SEARCH AND ESTIMATE OF
32 1 0 LIST ALL INPUT DATA. VARIANCE CARDS, IF ANY.
1 LIST ONLY 1ST OBSERVATION.
2 DO NOT LIST ANY INPUT DATA. SECOND PROBLEM
33 1 0 LIST TRANSFORMATIONS AND ALL TRANSFORMED DATA. IF DATA ARE REUSED FROM FIRST PROBLEM,
1 LIST TRANSFORMATIONS AND 1ST TRANSFORMED OBSERVATION. DELETE THE FORMAT, DATA AND END CARDS.
2 DO NOT LIST TRANSFORMATIONS OR TRANSFORMED DATA. IF NAMES ARE REUSED,
34 1 1 DO NOT LIST SUMS OF VARIABLES. DELETE THE NAME CARDS.
35 1 1 DO NOT LIST RAW SUMS AND CROSS PRODUCTS WHEN B(O)=O. IF DIFFERENT INPUT DATA AND NAMES,
36 1 1 DO NOT LIST RESIDUAL SUMS AND CROSS PRODUCTS. REPEAT 1 - 12 ABOVE.
37 1 1 DO NOT LIST MEANS AND ROOT MEAN SQUARES OF VARIABLES.
38 1 1 DO NOT LIST SIMPLE CORRELATION COEFFICIENTS.
39 1 1 DO NOT LIST INVERSE MATRIX.
40 1 1 DO NOT PRINT PLOTS OF RESIDUALS VS. FITTED Y.
2 PLOT (A) RESIDUALS AND (B) COMPONENT AND COMPONENT-
PLUS-RESIDUALS VS. EACH INDEPENDENT VARIABLE.
3 PLOT (A) RESIDUALS ONLY.
4 PLOT (B) COMPONENT AND COMPONENT-PLUS-RESIDUALS ONLY.
5 PLOT (B) BUT EXPAND SCALE TO FILL EACH PLOT.
41 0 0 READ DATA WITH STANDARD FORMAT (A6, I4, I2, 10F6.3).
1 READ DATA WITH FORMAT TO BE READ, 1 CARD (72COL) ASSUMED.
2 READ DATA WITH READ DATA (REDATA) SUBROUTINE.
42 2 0 DO NOT SAVE DATA FOR NEXT PROBLEM.
1 SAVE DATA FOR NEXT PROBLEM.
2 REUSE DATA FROM PREVIOUS PROBLEM.
43-44 0 18 NUMBER OF VARIABLES IN CP SEARCH IF GREATER THAN 12.
45 0 8 NUMBER OF FORMAT CARDS IF GREATER THAN 1.
46-47 0 12 NUMBER OF INFORMATION CARDS TO BE READ FOR DISPLAY ON
PRINTOUT IF DESIRED, 72 COL. EACH.
48 2 1 READ NAMES OF VARIABLES FOR DISPLAY ON PRINTOUT.
NAMES IN SAME POSITIONS AS VARIABLES ON TRANSFORMATION
CARDS - COLS. 1-6, 11-16, - - - , 61-66.
NAMES ARE NOT MOVED, ONLY LISTED OR DELETED.
2 REUSE NAMES OF VARIABLES FROM PREVIOUS PROBLEM.
49 0 SEARCH FOR CANDIDATE EQUATIONS VIA CP. USE ESTIMATE
OF VARIANCE (RMS) FROM:
1 FULL EQUATION,
2 SUBSET EQUATION WITH MINIMUM RMS VALUE, OR
3 ESTIMATE OF VARIANCE CARD, F16.8 FORMAT.
50 0 NUMBER OF CP FACTORIAL SEARCH CARDS TO BE READ PER
DEPENDENT VARIABLE. KEYPUNCH IN ASCENDING ORDER THE
IDENTIFING NUMBER OF THE VARIABLES (AFTER TRANSFOR-
MATIONS) TO BE USED IN THAT SEARCH, 18(2X,I2) FORMAT.
ALL OTHER VARIABLES WILL BE PLACED IN BASIC EQUATION.
51 0 1 LIST COMPONENT-EFFECT TABLE, REQUIRED X(I) PRECISION,
ESTIMATE OF STANDARD DEVIATION FROM NEAR NEIGHBORS,
AND FUNCTIONS OF FITTED Y.
2 LIST ONLY ESTIMATE OF STD. DEVIATION AND FUNCTIONS.
3 LIST ONLY FUNCTIONS OF FITTED Y.
52-53 0 NUMBER OF FILE IF DATA ARE READ FROM SEPARATE FILE,
NO END CARD IF ONLY ONE SET OF DATA IS ON EACH FILE.
54-55 0 NUMBER OF INDEPENDENT VARIABLES GREATER THAN THE 99
ALLOWED IN COLS 19-20.
56-58 0 TO REDUCE PRINTOUT WITH MANY OBSERVATIONS,
NUMBER OF CENTRAL OBSERVATIONS AND RESIDUALS NOT
TO BE PRINTED. THIS REQUIRES AN E IN COL 24.
59 0 CROSS VERIFICATION OF MODEL AND COEFFICIENTS WITH A
SECOND SAMPLE OF DATA:
1 WRITE B(0) AND B(I)S ON FILE IN ONE PROBLEM
(TRANSFORMATIONS ARE NOT SAVED).
2 READ B(0) AND B(I)S FROM FILE IN NEXT PROBLEM
WITH SECOND SET OF OBSERVATIONS.
60 0 5 NUMBER OF DELETE-OBSERVATIONS CARDS. KEYPUNCH
OBSERVATION NUMBER OF DATA TO BE DELETED IN ORDER READ
BY COMPUTER USING 7(I4,6X) FORMAT.
61 0 5 NUMBER OF INDICATOR-VARIABLE-OBSERVATIONS CARDS.
USING A 7(I4,2X,I3,1X) FORMAT, KEYPUNCH OBSERVATION
NUMBER (IN ORDER READ) AND VARIABLE NUMBER (BEFORE
TRANSFORMATIONS) INTO WHICH A 1 IS TO BE INSERTED.
0EQUATION 2 OF A MULTI-EQUATION PROBLEM
0BZERO = 0
0NAMES OF VARIABLES
A B
0
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
B0=0 BB,SWITCHES=1
0DATA INPUT 1 INDEPENDENT VARIABLES 1 DEPENDENT VARIABLE(S)
OBSV. SEQ. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 0 1190.000 1115.000
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
B0=0 BB,SWITCHES=1 DEP VAR 1: B MIN Y = 1.115E+03 MAX Y = 2.970E+03 RANGE Y = 1.855E+03
0IND.VAR(I) NAME COEF.B(I) S.E. COEF. T-VALUE R(I)SQRD MIN X(I) MAX X(I) RANGE X(I) REL.INF.X(I)
0 B(0) = 0
1 A 9.81254E-01 5.80E-03 169.2 0.0000 1.190E+03 3.010E+03 1.820E+03 0.96
0NO. OF OBSERVATIONS 18
NO. OF IND. VARIABLES 1
RESIDUAL DEGREES OF FREEDOM 17
RESIDUAL ROOT MEAN SQUARE 54.83150293
RESIDUAL MEAN SQUARE 3006.49371332
RESIDUAL SUM OF SQUARES 51110.39312645
TOTAL SUM OF SQUARES 4823323.61111111
MULT. CORREL. COEF. SQUARED .9894
ADJ. MULT. CORR. COEF. SQUARED .9894
0-----------------ORDERED BY COMPUTER INPUT--------- --------- ---------------------ORDERED BY RESIDUALS---------------------
IDENT. OBSV. WSS DISTANCE OBS. Y FITTED Y RESIDUAL OBSV. OBS. Y FITTED Y ORDERED RESID. STUD.RESID. SEQ
1 304. 1115.000 1167.692 -52.692 4 1795.000 1697.569 97.431 1.8 1
2 161. 1425.000 1427.725 -2.725 14 2740.000 2659.198 80.802 1.5 2
3 121. 1515.000 1520.944 -5.944 12 2520.000 2443.322 76.678 1.4 3
4 61. 1795.000 1697.569 97.431 10 2300.000 2251.978 48.022 0.9 4
5 56. 1715.000 1712.288 2.712 9 1970.000 1923.258 46.742 0.9 5
6 50. 1710.000 1736.820 -26.820 8 1920.000 1884.008 35.992 0.7 6
7 22. 1830.000 1864.383 -34.383 18 2970.000 2953.574 16.426 0.3 7
8 19. 1920.000 1884.008 35.992 5 1715.000 1712.288 2.712 0.1 8
9 13. 1970.000 1923.258 46.742 2 1425.000 1427.725 -2.725 -0.1 9
10 5. 2300.000 2251.978 48.022 3 1515.000 1520.944 -5.944 -0.1 10
11 9. 2280.000 2291.228 -11.228 11 2280.000 2291.228 -11.228 -0.2 11
12 34. 2520.000 2443.322 76.678 6 1710.000 1736.820 -26.820 -0.5 12
13 99. 2630.000 2669.011 -39.011 7 1830.000 1864.383 -34.383 -0.6 13
14 95. 2740.000 2659.198 80.802 13 2630.000 2669.011 -39.011 -0.7 14
15 43. 2390.000 2482.573 -92.573 16 2800.000 2845.636 -45.636 -0.9 15
16 173. 2800.000 2845.636 -45.636 1 1115.000 1167.692 -52.692 -1.0 16
17 113. 2630.000 2708.261 -78.261 17 2630.000 2708.261 -78.261 -1.5 17
18 229. 2970.000 2953.574 16.426 15 2390.000 2482.573 -92.573 -1.7 18
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
1979 VERSION OF THE LINWOOD 40 VARIABLE, 1000 OBSERVATION PROGRAM
REFER TO FITTING EQUATIONS TO DATA BY DANIEL AND WOOD, SECOND EDITION, WILEY PUBLISHER,
FOR GLOSSARY OF TERMS, USER'S MANUAL, DETAILS OF CALCULATIONS AND INTERPRETATION OF RESULTS.
0Y IS CONSTANT
0 CONTROL CARD INFORMATION ORDER OF CARDS
COL. INPUT MAX. ITEM (NOTE: BLANK ON CARD = 0) FIRST PROBLEM
1-18 PROBLEM IDENTIFICATION. 1 CONTROL CARD.
19-20 1 NUMBER OF INDEPENDENT VARIABLES READ IN 2 FORMAT CARD(S), IF ANY.
(ALLOW SPACE FOR TRANSFORMATIONS). 3 DELETE OBSERVATIONS CARD(S), IF ANY.
21-22 1 NUMBER OF DEPENDENT VARIABLES READ IN. 4 INDICATOR-VARIABLE-OBSERVATIONS CARD(S), IF ANY.
2 65 TOTAL NUMBER OF VARIABLES (BEFORE TRANSFORMATIONS, IF ANY). 5 TRANSFORMATION CARD(S), IF ANY.
24 E CAUSES Y, FITTED Y AND RESIDUALS TO BE 6 INFORMATION CARD(S) FOR PRINTOUT, IF ANY.
LISTED WITH AN E RATHER THAN AN F FORMAT. 7 NAMES OF VARIABLES CARD(S) FOR PRINTOUT, IF ANY.
25 0 1 DO TRANSFORMATIONS. 8 CP FACTORIAL SEARCH CARD, IF ANY.
26 0 1 WEIGHT OBSERVATIONS. WEIGHT ENTERED IN LAST POSITION. 9 DATA CARDS (IF NOT READ FROM A FILE).
2 WEIGHT BY 1/VAR. OF OBSERVATION. VARIANCE ENTERED. 10 END CARD (END IN COLUMNS 1 - 3 OF IDENTIFICATION
27 0 1 LET B(0) = ZERO, OTHERWISE B(0) IS CALCULATED VALUE. FIELD). THE NUMBER OF END CARDS MUST EQUAL THE
28 0 1 CHECK OBSERVATION NUMBER SEQUENCE. NUMBER OF CARDS PER OBSERVATION. (END CARDS
29 0 1 CHECK SEQUENCE WITHIN OBSERVATION NUMBER. ARE NOT NEEDED IF DATA ARE READ FROM A FILE).
30 0 1 DO BACK TRANSFORMATION OF DEPENDENT VARIABLE. 11 ESTIMATE OF VARIANCE CARD, IF ANY.
31 0 1 PUNCH DATA FOR CONFIDENCE INTERVAL PROGRAM. 12 ADDITIONAL CP FACTORIAL SEARCH AND ESTIMATE OF
32 0 0 LIST ALL INPUT DATA. VARIANCE CARDS, IF ANY.
1 LIST ONLY 1ST OBSERVATION.
2 DO NOT LIST ANY INPUT DATA. SECOND PROBLEM
33 0 0 LIST TRANSFORMATIONS AND ALL TRANSFORMED DATA. IF DATA ARE REUSED FROM FIRST PROBLEM,
1 LIST TRANSFORMATIONS AND 1ST TRANSFORMED OBSERVATION. DELETE THE FORMAT, DATA AND END CARDS.
2 DO NOT LIST TRANSFORMATIONS OR TRANSFORMED DATA. IF NAMES ARE REUSED,
34 0 1 DO NOT LIST SUMS OF VARIABLES. DELETE THE NAME CARDS.
35 0 1 DO NOT LIST RAW SUMS AND CROSS PRODUCTS WHEN B(O)=O. IF DIFFERENT INPUT DATA AND NAMES,
36 0 1 DO NOT LIST RESIDUAL SUMS AND CROSS PRODUCTS. REPEAT 1 - 12 ABOVE.
37 0 1 DO NOT LIST MEANS AND ROOT MEAN SQUARES OF VARIABLES.
38 0 1 DO NOT LIST SIMPLE CORRELATION COEFFICIENTS.
39 0 1 DO NOT LIST INVERSE MATRIX.
40 0 1 DO NOT PRINT PLOTS OF RESIDUALS VS. FITTED Y.
2 PLOT (A) RESIDUALS AND (B) COMPONENT AND COMPONENT-
PLUS-RESIDUALS VS. EACH INDEPENDENT VARIABLE.
3 PLOT (A) RESIDUALS ONLY.
4 PLOT (B) COMPONENT AND COMPONENT-PLUS-RESIDUALS ONLY.
5 PLOT (B) BUT EXPAND SCALE TO FILL EACH PLOT.
41 0 0 READ DATA WITH STANDARD FORMAT (A6, I4, I2, 10F6.3).
1 READ DATA WITH FORMAT TO BE READ, 1 CARD (72COL) ASSUMED.
2 READ DATA WITH READ DATA (REDATA) SUBROUTINE.
42 0 0 DO NOT SAVE DATA FOR NEXT PROBLEM.
1 SAVE DATA FOR NEXT PROBLEM.
2 REUSE DATA FROM PREVIOUS PROBLEM.
43-44 0 18 NUMBER OF VARIABLES IN CP SEARCH IF GREATER THAN 12.
45 0 8 NUMBER OF FORMAT CARDS IF GREATER THAN 1.
46-47 0 12 NUMBER OF INFORMATION CARDS TO BE READ FOR DISPLAY ON
PRINTOUT IF DESIRED, 72 COL. EACH.
48 0 1 READ NAMES OF VARIABLES FOR DISPLAY ON PRINTOUT.
NAMES IN SAME POSITIONS AS VARIABLES ON TRANSFORMATION
CARDS - COLS. 1-6, 11-16, - - - , 61-66.
NAMES ARE NOT MOVED, ONLY LISTED OR DELETED.
2 REUSE NAMES OF VARIABLES FROM PREVIOUS PROBLEM.
49 0 SEARCH FOR CANDIDATE EQUATIONS VIA CP. USE ESTIMATE
OF VARIANCE (RMS) FROM:
1 FULL EQUATION,
2 SUBSET EQUATION WITH MINIMUM RMS VALUE, OR
3 ESTIMATE OF VARIANCE CARD, F16.8 FORMAT.
50 0 NUMBER OF CP FACTORIAL SEARCH CARDS TO BE READ PER
DEPENDENT VARIABLE. KEYPUNCH IN ASCENDING ORDER THE
IDENTIFING NUMBER OF THE VARIABLES (AFTER TRANSFOR-
MATIONS) TO BE USED IN THAT SEARCH, 18(2X,I2) FORMAT.
ALL OTHER VARIABLES WILL BE PLACED IN BASIC EQUATION.
51 0 1 LIST COMPONENT-EFFECT TABLE, REQUIRED X(I) PRECISION,
ESTIMATE OF STANDARD DEVIATION FROM NEAR NEIGHBORS,
AND FUNCTIONS OF FITTED Y.
2 LIST ONLY ESTIMATE OF STD. DEVIATION AND FUNCTIONS.
3 LIST ONLY FUNCTIONS OF FITTED Y.
52-53 0 NUMBER OF FILE IF DATA ARE READ FROM SEPARATE FILE,
NO END CARD IF ONLY ONE SET OF DATA IS ON EACH FILE.
54-55 0 NUMBER OF INDEPENDENT VARIABLES GREATER THAN THE 99
ALLOWED IN COLS 19-20.
56-58 0 TO REDUCE PRINTOUT WITH MANY OBSERVATIONS,
NUMBER OF CENTRAL OBSERVATIONS AND RESIDUALS NOT
TO BE PRINTED. THIS REQUIRES AN E IN COL 24.
59 0 CROSS VERIFICATION OF MODEL AND COEFFICIENTS WITH A
SECOND SAMPLE OF DATA:
1 WRITE B(0) AND B(I)S ON FILE IN ONE PROBLEM
(TRANSFORMATIONS ARE NOT SAVED).
2 READ B(0) AND B(I)S FROM FILE IN NEXT PROBLEM
WITH SECOND SET OF OBSERVATIONS.
60 0 5 NUMBER OF DELETE-OBSERVATIONS CARDS. KEYPUNCH
OBSERVATION NUMBER OF DATA TO BE DELETED IN ORDER READ
BY COMPUTER USING 7(I4,6X) FORMAT.
61 0 5 NUMBER OF INDICATOR-VARIABLE-OBSERVATIONS CARDS.
USING A 7(I4,2X,I3,1X) FORMAT, KEYPUNCH OBSERVATION
NUMBER (IN ORDER READ) AND VARIABLE NUMBER (BEFORE
TRANSFORMATIONS) INTO WHICH A 1 IS TO BE INSERTED.
0PROBLEM HAS ONE EQUATION
0DATA READ WITH STANDARD FORMAT (A6, I4, I2, 10F6.3)
0BZERO = CALCULATED VALUE
0NAMES OF VARIABLES
0
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
Y IS CONSTANT
0DATA INPUT 1 INDEPENDENT VARIABLES 1 DEPENDENT VARIABLE(S)
OBSV. SEQ. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
0 0 1.000 3.000
0 0 2.000 3.000
0 0 3.000 3.000
0 0 3.000 3.000
0 0 4.000 3.000
0 0 5.000 3.000
0 0 6.000 3.000
0 0 7.000 3.000
0 0 8.000 3.000
0 0 9.000 3.000
0SUMS OF VARIABLES
4.80000E+01 3.00000E+01
0RESIDUAL SUMS OF SQUARES + CROSS PRODUCTS
1 6.36000E+01
2 0.00000E+00 0.00000E+00
0RESIDUAL DIFFERENCE FOR VARIABLE 2 IS ZERO. VARIABLE IS CONSTANT.
PROBLEM SKIPPED
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
1979 VERSION OF THE LINWOOD 40 VARIABLE, 1000 OBSERVATION PROGRAM
REFER TO FITTING EQUATIONS TO DATA BY DANIEL AND WOOD, SECOND EDITION, WILEY PUBLISHER,
FOR GLOSSARY OF TERMS, USER'S MANUAL, DETAILS OF CALCULATIONS AND INTERPRETATION OF RESULTS.
0VAR3 = VAR4
0 CONTROL CARD INFORMATION ORDER OF CARDS
COL. INPUT MAX. ITEM (NOTE: BLANK ON CARD = 0) FIRST PROBLEM
1-18 PROBLEM IDENTIFICATION. 1 CONTROL CARD.
19-20 4 NUMBER OF INDEPENDENT VARIABLES READ IN 2 FORMAT CARD(S), IF ANY.
(ALLOW SPACE FOR TRANSFORMATIONS). 3 DELETE OBSERVATIONS CARD(S), IF ANY.
21-22 1 NUMBER OF DEPENDENT VARIABLES READ IN. 4 INDICATOR-VARIABLE-OBSERVATIONS CARD(S), IF ANY.
5 65 TOTAL NUMBER OF VARIABLES (BEFORE TRANSFORMATIONS, IF ANY). 5 TRANSFORMATION CARD(S), IF ANY.
24 E CAUSES Y, FITTED Y AND RESIDUALS TO BE 6 INFORMATION CARD(S) FOR PRINTOUT, IF ANY.
LISTED WITH AN E RATHER THAN AN F FORMAT. 7 NAMES OF VARIABLES CARD(S) FOR PRINTOUT, IF ANY.
25 0 1 DO TRANSFORMATIONS. 8 CP FACTORIAL SEARCH CARD, IF ANY.
26 0 1 WEIGHT OBSERVATIONS. WEIGHT ENTERED IN LAST POSITION. 9 DATA CARDS (IF NOT READ FROM A FILE).
2 WEIGHT BY 1/VAR. OF OBSERVATION. VARIANCE ENTERED. 10 END CARD (END IN COLUMNS 1 - 3 OF IDENTIFICATION
27 0 1 LET B(0) = ZERO, OTHERWISE B(0) IS CALCULATED VALUE. FIELD). THE NUMBER OF END CARDS MUST EQUAL THE
28 0 1 CHECK OBSERVATION NUMBER SEQUENCE. NUMBER OF CARDS PER OBSERVATION. (END CARDS
29 0 1 CHECK SEQUENCE WITHIN OBSERVATION NUMBER. ARE NOT NEEDED IF DATA ARE READ FROM A FILE).
30 0 1 DO BACK TRANSFORMATION OF DEPENDENT VARIABLE. 11 ESTIMATE OF VARIANCE CARD, IF ANY.
31 0 1 PUNCH DATA FOR CONFIDENCE INTERVAL PROGRAM. 12 ADDITIONAL CP FACTORIAL SEARCH AND ESTIMATE OF
32 0 0 LIST ALL INPUT DATA. VARIANCE CARDS, IF ANY.
1 LIST ONLY 1ST OBSERVATION.
2 DO NOT LIST ANY INPUT DATA. SECOND PROBLEM
33 0 0 LIST TRANSFORMATIONS AND ALL TRANSFORMED DATA. IF DATA ARE REUSED FROM FIRST PROBLEM,
1 LIST TRANSFORMATIONS AND 1ST TRANSFORMED OBSERVATION. DELETE THE FORMAT, DATA AND END CARDS.
2 DO NOT LIST TRANSFORMATIONS OR TRANSFORMED DATA. IF NAMES ARE REUSED,
34 0 1 DO NOT LIST SUMS OF VARIABLES. DELETE THE NAME CARDS.
35 0 1 DO NOT LIST RAW SUMS AND CROSS PRODUCTS WHEN B(O)=O. IF DIFFERENT INPUT DATA AND NAMES,
36 0 1 DO NOT LIST RESIDUAL SUMS AND CROSS PRODUCTS. REPEAT 1 - 12 ABOVE.
37 0 1 DO NOT LIST MEANS AND ROOT MEAN SQUARES OF VARIABLES.
38 0 1 DO NOT LIST SIMPLE CORRELATION COEFFICIENTS.
39 0 1 DO NOT LIST INVERSE MATRIX.
40 0 1 DO NOT PRINT PLOTS OF RESIDUALS VS. FITTED Y.
2 PLOT (A) RESIDUALS AND (B) COMPONENT AND COMPONENT-
PLUS-RESIDUALS VS. EACH INDEPENDENT VARIABLE.
3 PLOT (A) RESIDUALS ONLY.
4 PLOT (B) COMPONENT AND COMPONENT-PLUS-RESIDUALS ONLY.
5 PLOT (B) BUT EXPAND SCALE TO FILL EACH PLOT.
41 1 0 READ DATA WITH STANDARD FORMAT (A6, I4, I2, 10F6.3).
1 READ DATA WITH FORMAT TO BE READ, 1 CARD (72COL) ASSUMED.
2 READ DATA WITH READ DATA (REDATA) SUBROUTINE.
42 0 0 DO NOT SAVE DATA FOR NEXT PROBLEM.
1 SAVE DATA FOR NEXT PROBLEM.
2 REUSE DATA FROM PREVIOUS PROBLEM.
43-44 0 18 NUMBER OF VARIABLES IN CP SEARCH IF GREATER THAN 12.
45 0 8 NUMBER OF FORMAT CARDS IF GREATER THAN 1.
46-47 0 12 NUMBER OF INFORMATION CARDS TO BE READ FOR DISPLAY ON
PRINTOUT IF DESIRED, 72 COL. EACH.
48 0 1 READ NAMES OF VARIABLES FOR DISPLAY ON PRINTOUT.
NAMES IN SAME POSITIONS AS VARIABLES ON TRANSFORMATION
CARDS - COLS. 1-6, 11-16, - - - , 61-66.
NAMES ARE NOT MOVED, ONLY LISTED OR DELETED.
2 REUSE NAMES OF VARIABLES FROM PREVIOUS PROBLEM.
49 0 SEARCH FOR CANDIDATE EQUATIONS VIA CP. USE ESTIMATE
OF VARIANCE (RMS) FROM:
1 FULL EQUATION,
2 SUBSET EQUATION WITH MINIMUM RMS VALUE, OR
3 ESTIMATE OF VARIANCE CARD, F16.8 FORMAT.
50 0 NUMBER OF CP FACTORIAL SEARCH CARDS TO BE READ PER
DEPENDENT VARIABLE. KEYPUNCH IN ASCENDING ORDER THE
IDENTIFING NUMBER OF THE VARIABLES (AFTER TRANSFOR-
MATIONS) TO BE USED IN THAT SEARCH, 18(2X,I2) FORMAT.
ALL OTHER VARIABLES WILL BE PLACED IN BASIC EQUATION.
51 0 1 LIST COMPONENT-EFFECT TABLE, REQUIRED X(I) PRECISION,
ESTIMATE OF STANDARD DEVIATION FROM NEAR NEIGHBORS,
AND FUNCTIONS OF FITTED Y.
2 LIST ONLY ESTIMATE OF STD. DEVIATION AND FUNCTIONS.
3 LIST ONLY FUNCTIONS OF FITTED Y.
52-53 0 NUMBER OF FILE IF DATA ARE READ FROM SEPARATE FILE,
NO END CARD IF ONLY ONE SET OF DATA IS ON EACH FILE.
54-55 0 NUMBER OF INDEPENDENT VARIABLES GREATER THAN THE 99
ALLOWED IN COLS 19-20.
56-58 0 TO REDUCE PRINTOUT WITH MANY OBSERVATIONS,
NUMBER OF CENTRAL OBSERVATIONS AND RESIDUALS NOT
TO BE PRINTED. THIS REQUIRES AN E IN COL 24.
59 0 CROSS VERIFICATION OF MODEL AND COEFFICIENTS WITH A
SECOND SAMPLE OF DATA:
1 WRITE B(0) AND B(I)S ON FILE IN ONE PROBLEM
(TRANSFORMATIONS ARE NOT SAVED).
2 READ B(0) AND B(I)S FROM FILE IN NEXT PROBLEM
WITH SECOND SET OF OBSERVATIONS.
60 0 5 NUMBER OF DELETE-OBSERVATIONS CARDS. KEYPUNCH
OBSERVATION NUMBER OF DATA TO BE DELETED IN ORDER READ
BY COMPUTER USING 7(I4,6X) FORMAT.
61 0 5 NUMBER OF INDICATOR-VARIABLE-OBSERVATIONS CARDS.
USING A 7(I4,2X,I3,1X) FORMAT, KEYPUNCH OBSERVATION
NUMBER (IN ORDER READ) AND VARIABLE NUMBER (BEFORE
TRANSFORMATIONS) INTO WHICH A 1 IS TO BE INSERTED.
0PROBLEM HAS ONE EQUATION
0DATA READ WITH SPECIAL FORMAT
0FORMAT CARD 1 (A6,I4,I2,3F6.3, T25, 2F6.3 )
0BZERO = CALCULATED VALUE
0NAMES OF VARIABLES
0
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
VAR3 = VAR4
0DATA INPUT 4 INDEPENDENT VARIABLES 1 DEPENDENT VARIABLE(S)
OBSV. SEQ. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 0 124.000 33.000 8.000 8.000 646.000
2 0 49.000 31.000 6.000 6.000 355.000
3 0 181.000 38.000 8.000 8.000 631.000
4 0 4.000 17.000 2.000 2.000 174.000
5 0 22.000 20.000 4.000 4.000 603.000
6 0 152.000 39.000 6.000 6.000 331.000
7 0 75.000 30.000 7.000 7.000 759.000
8 0 54.000 29.000 7.000 7.000 282.000
9 0 43.000 35.000 6.000 6.000 316.000
10 0 41.000 31.000 5.000 5.000 490.000
11 0 17.000 23.000 4.000 4.000 457.000
12 0 22.000 21.000 3.000 3.000 282.000
13 0 16.000 8.000 3.000 3.000 174.000
14 0 10.000 23.000 3.000 3.000 269.000
15 0 63.000 37.000 6.000 6.000 240.000
16 0 170.000 40.000 8.000 8.000 525.000
17 0 125.000 38.000 6.000 6.000 257.000
18 0 15.000 25.000 4.000 4.000 240.000
19 0 221.000 39.000 7.000 7.000 331.000
20 0 171.000 33.000 7.000 7.000 331.000
21 0 97.000 38.000 6.000 6.000 457.000
22 0 254.000 39.000 8.000 8.000 776.000
0SUMS OF VARIABLES
1.92600E+03 6.67000E+02 1.24000E+02 1.24000E+02 8.92600E+03
0RESIDUAL SUMS OF SQUARES + CROSS PRODUCTS
1 1.19455E+05
2 1.04452E+04 1.58477E+03
3 2.37036E+03 2.82545E+02 7.30909E+01
4 2.37036E+03 2.82545E+02 7.30909E+01 7.30909E+01
5 1.31111E+05 1.19259E+04 4.14382E+03 4.14382E+03 6.97018E+05
0MEANS OF VARIABLES
8.75455E+01 3.03182E+01 5.63636E+00 5.63636E+00 4.05727E+02
0ROOT MEAN SQUARES OF VARIABLES
7.54212E+01 8.68708E+00 1.86562E+00 1.86562E+00 1.82185E+02
0SIMPLE CORRELATION COEFFICIENTS, R(I,I PRIME)
1 1.000
2 0.759 1.000
3 0.802 0.830 1.000
4 0.802 0.830 1.000 1.000
5 0.454 0.359 0.581 0.581 1.000
0*******MATRIX OF SIMPLE CORRELATION COEFFICIENTS IS SINGULAR. MATRIX WILL NOT INVERT.*******
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
1979 VERSION OF THE LINWOOD 40 VARIABLE, 1000 OBSERVATION PROGRAM
REFER TO FITTING EQUATIONS TO DATA BY DANIEL AND WOOD, SECOND EDITION, WILEY PUBLISHER,
FOR GLOSSARY OF TERMS, USER'S MANUAL, DETAILS OF CALCULATIONS AND INTERPRETATION OF RESULTS.
02 VARIABLES PASS 1
0 CONTROL CARD INFORMATION ORDER OF CARDS
COL. INPUT MAX. ITEM (NOTE: BLANK ON CARD = 0) FIRST PROBLEM
1-18 PROBLEM IDENTIFICATION. 1 CONTROL CARD.
19-20 3 NUMBER OF INDEPENDENT VARIABLES READ IN 2 FORMAT CARD(S), IF ANY.
(ALLOW SPACE FOR TRANSFORMATIONS). 3 DELETE OBSERVATIONS CARD(S), IF ANY.
21-22 1 NUMBER OF DEPENDENT VARIABLES READ IN. 4 INDICATOR-VARIABLE-OBSERVATIONS CARD(S), IF ANY.
4 65 TOTAL NUMBER OF VARIABLES (BEFORE TRANSFORMATIONS, IF ANY). 5 TRANSFORMATION CARD(S), IF ANY.
24 E CAUSES Y, FITTED Y AND RESIDUALS TO BE 6 INFORMATION CARD(S) FOR PRINTOUT, IF ANY.
LISTED WITH AN E RATHER THAN AN F FORMAT. 7 NAMES OF VARIABLES CARD(S) FOR PRINTOUT, IF ANY.
25 1 1 DO TRANSFORMATIONS. 8 CP FACTORIAL SEARCH CARD, IF ANY.
26 0 1 WEIGHT OBSERVATIONS. WEIGHT ENTERED IN LAST POSITION. 9 DATA CARDS (IF NOT READ FROM A FILE).
2 WEIGHT BY 1/VAR. OF OBSERVATION. VARIANCE ENTERED. 10 END CARD (END IN COLUMNS 1 - 3 OF IDENTIFICATION
27 0 1 LET B(0) = ZERO, OTHERWISE B(0) IS CALCULATED VALUE. FIELD). THE NUMBER OF END CARDS MUST EQUAL THE
28 0 1 CHECK OBSERVATION NUMBER SEQUENCE. NUMBER OF CARDS PER OBSERVATION. (END CARDS
29 0 1 CHECK SEQUENCE WITHIN OBSERVATION NUMBER. ARE NOT NEEDED IF DATA ARE READ FROM A FILE).
30 0 1 DO BACK TRANSFORMATION OF DEPENDENT VARIABLE. 11 ESTIMATE OF VARIANCE CARD, IF ANY.
31 0 1 PUNCH DATA FOR CONFIDENCE INTERVAL PROGRAM. 12 ADDITIONAL CP FACTORIAL SEARCH AND ESTIMATE OF
32 0 0 LIST ALL INPUT DATA. VARIANCE CARDS, IF ANY.
1 LIST ONLY 1ST OBSERVATION.
2 DO NOT LIST ANY INPUT DATA. SECOND PROBLEM
33 1 0 LIST TRANSFORMATIONS AND ALL TRANSFORMED DATA. IF DATA ARE REUSED FROM FIRST PROBLEM,
1 LIST TRANSFORMATIONS AND 1ST TRANSFORMED OBSERVATION. DELETE THE FORMAT, DATA AND END CARDS.
2 DO NOT LIST TRANSFORMATIONS OR TRANSFORMED DATA. IF NAMES ARE REUSED,
34 0 1 DO NOT LIST SUMS OF VARIABLES. DELETE THE NAME CARDS.
35 0 1 DO NOT LIST RAW SUMS AND CROSS PRODUCTS WHEN B(O)=O. IF DIFFERENT INPUT DATA AND NAMES,
36 0 1 DO NOT LIST RESIDUAL SUMS AND CROSS PRODUCTS. REPEAT 1 - 12 ABOVE.
37 0 1 DO NOT LIST MEANS AND ROOT MEAN SQUARES OF VARIABLES.
38 0 1 DO NOT LIST SIMPLE CORRELATION COEFFICIENTS.
39 0 1 DO NOT LIST INVERSE MATRIX.
40 2 1 DO NOT PRINT PLOTS OF RESIDUALS VS. FITTED Y.
2 PLOT (A) RESIDUALS AND (B) COMPONENT AND COMPONENT-
PLUS-RESIDUALS VS. EACH INDEPENDENT VARIABLE.
3 PLOT (A) RESIDUALS ONLY.
4 PLOT (B) COMPONENT AND COMPONENT-PLUS-RESIDUALS ONLY.
5 PLOT (B) BUT EXPAND SCALE TO FILL EACH PLOT.
41 1 0 READ DATA WITH STANDARD FORMAT (A6, I4, I2, 10F6.3).
1 READ DATA WITH FORMAT TO BE READ, 1 CARD (72COL) ASSUMED.
2 READ DATA WITH READ DATA (REDATA) SUBROUTINE.
42 1 0 DO NOT SAVE DATA FOR NEXT PROBLEM.
1 SAVE DATA FOR NEXT PROBLEM.
2 REUSE DATA FROM PREVIOUS PROBLEM.
43-44 0 18 NUMBER OF VARIABLES IN CP SEARCH IF GREATER THAN 12.
45 0 8 NUMBER OF FORMAT CARDS IF GREATER THAN 1.
46-47 12 12 NUMBER OF INFORMATION CARDS TO BE READ FOR DISPLAY ON
PRINTOUT IF DESIRED, 72 COL. EACH.
48 1 1 READ NAMES OF VARIABLES FOR DISPLAY ON PRINTOUT.
NAMES IN SAME POSITIONS AS VARIABLES ON TRANSFORMATION
CARDS - COLS. 1-6, 11-16, - - - , 61-66.
NAMES ARE NOT MOVED, ONLY LISTED OR DELETED.
2 REUSE NAMES OF VARIABLES FROM PREVIOUS PROBLEM.
49 0 SEARCH FOR CANDIDATE EQUATIONS VIA CP. USE ESTIMATE
OF VARIANCE (RMS) FROM:
1 FULL EQUATION,
2 SUBSET EQUATION WITH MINIMUM RMS VALUE, OR
3 ESTIMATE OF VARIANCE CARD, F16.8 FORMAT.
50 0 NUMBER OF CP FACTORIAL SEARCH CARDS TO BE READ PER
DEPENDENT VARIABLE. KEYPUNCH IN ASCENDING ORDER THE
IDENTIFING NUMBER OF THE VARIABLES (AFTER TRANSFOR-
MATIONS) TO BE USED IN THAT SEARCH, 18(2X,I2) FORMAT.
ALL OTHER VARIABLES WILL BE PLACED IN BASIC EQUATION.
51 1 1 LIST COMPONENT-EFFECT TABLE, REQUIRED X(I) PRECISION,
ESTIMATE OF STANDARD DEVIATION FROM NEAR NEIGHBORS,
AND FUNCTIONS OF FITTED Y.
2 LIST ONLY ESTIMATE OF STD. DEVIATION AND FUNCTIONS.
3 LIST ONLY FUNCTIONS OF FITTED Y.
52-53 0 NUMBER OF FILE IF DATA ARE READ FROM SEPARATE FILE,
NO END CARD IF ONLY ONE SET OF DATA IS ON EACH FILE.
54-55 0 NUMBER OF INDEPENDENT VARIABLES GREATER THAN THE 99
ALLOWED IN COLS 19-20.
56-58 0 TO REDUCE PRINTOUT WITH MANY OBSERVATIONS,
NUMBER OF CENTRAL OBSERVATIONS AND RESIDUALS NOT
TO BE PRINTED. THIS REQUIRES AN E IN COL 24.
59 0 CROSS VERIFICATION OF MODEL AND COEFFICIENTS WITH A
SECOND SAMPLE OF DATA:
1 WRITE B(0) AND B(I)S ON FILE IN ONE PROBLEM
(TRANSFORMATIONS ARE NOT SAVED).
2 READ B(0) AND B(I)S FROM FILE IN NEXT PROBLEM
WITH SECOND SET OF OBSERVATIONS.
60 0 5 NUMBER OF DELETE-OBSERVATIONS CARDS. KEYPUNCH
OBSERVATION NUMBER OF DATA TO BE DELETED IN ORDER READ
BY COMPUTER USING 7(I4,6X) FORMAT.
61 0 5 NUMBER OF INDICATOR-VARIABLE-OBSERVATIONS CARDS.
USING A 7(I4,2X,I3,1X) FORMAT, KEYPUNCH OBSERVATION
NUMBER (IN ORDER READ) AND VARIABLE NUMBER (BEFORE
TRANSFORMATIONS) INTO WHICH A 1 IS TO BE INSERTED.
0EQUATION 1 OF A MULTI-EQUATION PROBLEM
0DATA READ WITH SPECIAL FORMAT
0FORMAT CARD 1 (6X, A4, I2, I1, F5.2, F6.2, F1.0, F10.4 )
0BZERO = CALCULATED VALUE
0INFORMATION CARDS
EQUATION: Y = 20 + 20X1 - 3X2 - 1X1SQRD + ERROR(0,1)
FITTED WITH Y = B0 + B1X1 + B2X2
ERROR FROM "A MILLION RANDOM DIGITS", RAND CORP., FREE PRESS, 1955.
1-20 OBSV. FROM TABLE PAGE 4, COL 4; 21-40 OBSV. FROM PAGE 12, COL 2.
OBSERVATIONS 21-40 ARE REPLICATES OF OBSERVATIONS 1-20.
STD. DEVIATION ESTIMATED FROM NEAR NEIGHBORS (1.0), IS MUCH LESS
THAN RRMS OF FIT, SUGGESTING A BETTER FORM OF EQUATION IS NEEDED.
NEED FOR SQUARED TERM CAN BE SEEN FROM RESIDUAL VS. INDEPENDENT
VARIABLE X1 PLOT. SLIGHT EFFECT ON CURVATURE CAN BE SEEN FROM
COMPONENT AND COMPONENT-PLUS-RESIDUAL VS. INDEPENDENT VARIABLE X1
PLOT. FROM "THE USE OF INDIVIDUAL EFFECTS AND RESIDUALS IN FITTING
EQUATIONS TO DATA" BY F.S.WOOD, TECHNOMETRICS VOL.15, NO 4, NOV. 1973.
0DATA TRANSFORMATIONS
POSITION CODE OPERATION CONSTANT LOCATION OMIT VARIABLE NAME
1 NONE 1 0 1 X1
2 NONE 2 0 2 X2
3 NONE 3 1
4 NONE 4 0 3 Y
0
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
2 VARIABLES PASS 1
0DATA INPUT 3 INDEPENDENT VARIABLES 1 DEPENDENT VARIABLE(S)
OBSV. SEQ. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 0 0.000 0.000 0.000 20.164
2 0 0.200 2.000 0.000 18.847
3 0 0.500 7.000 0.000 6.678
4 0 1.000 10.000 0.000 8.709
5 0 1.500 4.000 0.000 36.934
6 0 2.000 16.000 0.000 8.397
7 0 2.500 22.000 0.000 -1.778
8 0 3.000 6.000 0.000 53.136
9 0 3.500 9.000 0.000 51.883
10 0 4.000 18.000 0.000 31.564
11 0 4.500 28.000 0.000 5.739
12 0 5.000 34.000 0.000 -6.466
13 0 5.300 14.000 0.000 56.494
14 0 5.500 24.000 0.000 28.523
15 0 6.000 19.000 0.000 47.498
16 0 6.500 38.000 0.000 -4.575
17 0 7.000 33.000 0.000 10.730
18 0 7.500 35.000 0.000 8.214
19 0 7.800 30.000 0.000 23.790
20 0 8.000 40.000 0.000 -3.518
21 0 0.000 0.000 0.000 20.283
22 0 0.200 2.000 0.000 16.970
23 0 0.500 7.000 0.000 8.379
24 0 1.000 10.000 0.000 9.876
25 0 1.500 4.000 0.000 37.719
26 0 2.000 16.000 0.000 8.445
27 0 2.500 22.000 0.000 -1.841
28 0 3.000 6.000 0.000 54.339
29 0 3.500 9.000 0.000 51.646
30 0 4.000 18.000 0.000 30.738
31 0 4.500 28.000 0.000 5.373
32 0 5.000 34.000 0.000 -7.537
33 0 5.300 14.000 0.000 53.974
34 0 5.500 24.000 0.000 28.636
35 0 6.000 19.000 0.000 46.065
36 0 6.500 38.000 0.000 -6.327
37 0 7.000 33.000 0.000 13.001
38 0 7.500 35.000 0.000 7.855
39 0 7.800 30.000 0.000 26.869
40 0 8.000 40.000 0.000 -3.659
0DATA TRANSFORMATIONS
POSITION CODE OPERATION CONSTANT LOCATION OMIT VARIABLE NAME
1 NONE 1 0 1 X1
2 NONE 2 0 2 X2
3 NONE 3 1
4 NONE 4 0 3 Y
0FIRST OBSERVATION AFTER TRANSFORMATIONS THE FITTED EQUATION HAS 2 INDEPENDENT VARIABLES, 1 DEPENDENT VARIABLE(S)
X1 X2 Y
OBSV. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 0.00000E+00 0.00000E+00 2.01640E+01
0SUMS OF VARIABLES
1.62600E+02 7.78000E+02 8.01767E+02
0RESIDUAL SUMS OF SQUARES + CROSS PRODUCTS
1 2.64971E+02
2 1.11563E+03 6.22990E+03
3 -1.60588E+02-5.34992E+03 1.57550E+04
0MEANS OF VARIABLES
4.06500E+00 1.94500E+01 2.00442E+01
0ROOT MEAN SQUARES OF VARIABLES
2.60655E+00 1.26389E+01 2.00991E+01
0SIMPLE CORRELATION COEFFICIENTS, R(I,I PRIME)
1 1.000
2 0.868 1.000
3 -0.079 -0.540 1.000
0INVERSE, C(I,I PRIME)
1 4.065
2 -3.530 4.065
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
2 VARIABLES PASS 1 DEP VAR 1: Y MIN Y = -7.537E+00 MAX Y = 5.649E+01 RANGE Y = 6.403E+01
EQUATION: Y = 20 + 20X1 - 3X2 - 1X1SQRD + ERROR(0,1)
FITTED WITH Y = B0 + B1X1 + B2X2
ERROR FROM "A MILLION RANDOM DIGITS", RAND CORP., FREE PRESS, 1955.
1-20 OBSV. FROM TABLE PAGE 4, COL 4; 21-40 OBSV. FROM PAGE 12, COL 2.
OBSERVATIONS 21-40 ARE REPLICATES OF OBSERVATIONS 1-20.
STD. DEVIATION ESTIMATED FROM NEAR NEIGHBORS (1.0), IS MUCH LESS
THAN RRMS OF FIT, SUGGESTING A BETTER FORM OF EQUATION IS NEEDED.
NEED FOR SQUARED TERM CAN BE SEEN FROM RESIDUAL VS. INDEPENDENT
VARIABLE X1 PLOT. SLIGHT EFFECT ON CURVATURE CAN BE SEEN FROM
COMPONENT AND COMPONENT-PLUS-RESIDUAL VS. INDEPENDENT VARIABLE X1
PLOT. FROM "THE USE OF INDIVIDUAL EFFECTS AND RESIDUALS IN FITTING
EQUATIONS TO DATA" BY F.S.WOOD, TECHNOMETRICS VOL.15, NO 4, NOV. 1973.
0IND.VAR(I) NAME COEF.B(I) S.E. COEF. T-VALUE R(I)SQRD MIN X(I) MAX X(I) RANGE X(I) REL.INF.X(I)
0 2.96276E+01
1 X1 1.22333E+01 7.63E-01 16.0 0.7540 0.000E+00 8.000E+00 8.000E+00 1.53
2 X2 -3.04944E+00 1.57E-01 19.4 0.7540 0.000E+00 4.000E+01 4.000E+01 1.90
0NO. OF OBSERVATIONS 40
NO. OF IND. VARIABLES 2
RESIDUAL DEGREES OF FREEDOM 37
F-VALUE 188.9
RESIDUAL ROOT MEAN SQUARE 6.16279160
RESIDUAL MEAN SQUARE 37.98000027
RESIDUAL SUM OF SQUARES 1405.26001001
TOTAL SUM OF SQUARES 15755.02817978
MULT. CORREL. COEF. SQUARED .9108
ADJ. MULT. CORR. COEF. SQUARED .9060
0 REQUIRED X(I) PRECISION
(DIGIT RIGHT OF DECIMAL POSITIVE,
LEFT OF DECIMAL NEGATIVE)
0 IND.VAR(I) DIGIT
1 -1
2 -2
1 LINEAR LEAST-SQUARES CURVE FITTING PROGRAM
02 VARIABLES PASS 1 DEP VAR 1: Y
0COMPONENT EFFECT OF EACH VARIABLE ON EACH OBSERVATION (IN UNITS OF Y)
(VARIABLES ORDERED BY THEIR RELATIVE INFLUENCE --- OBSERVATIONS ORDERED BY INFLUENCE OF MOST INFLUENTIAL VARIABLE)
SEQ. OBSV. VARIABLES
2 1
X2 X1
1 1 59.31 -49.73
2 21 59.31 -49.73
3 2 53.21 -47.28
4 22 53.21 -47.28
5 5 47.11 -31.38
6 25 47.11 -31.38
7 8 41.02 -13.03
8 28 41.02 -13.03
9 3 37.97 -43.61
10 23 37.97 -43.61
11 9 31.87 -6.91
12 29 31.87 -6.91
13 4 28.82 -37.49
14 24 28.82 -37.49
15 13 16.62 15.11
16 33 16.62 15.11
17 6 10.52 -25.26
18 26 10.52 -25.26
19 10 4.42 -0.80
20 30 4.42 -0.80
21 15 1.37 23.67
22 35 1.37 23.67
23 7 -7.78 -19.15
24 27 -7.78 -19.15
25 14 -13.87 17.55
26 34 -13.87 17.55
27 11 -26.07 5.32
28 31 -26.07 5.32
29 19 -32.17 45.69
30 39 -32.17 45.69
31 17 -41.32 35.90
32 37 -41.32 35.90
33 12 -44.37 11.44
34 32 -44.37 11.44
35 18 -47.42 42.02
36 38 -47.42 42.02
37 16 -56.57 29.79
38 36 -56.57 29.79
39 20 -62.67 48.14
40 40 -62.67 48.14
1 LINEAR LEAST-SQUARES CURVE FITTING PROGRAM
02 VARIABLES PASS 1 DEP VAR 1: Y RESIDUAL ROOT MEAN SQUARE OF FITTED EQUATION: 6.16
0STANDARD DEVIATION ESTIMATED FROM RESIDUALS OF NEIGHBORING OBSERVATIONS (OBSERVATIONS 1 TO 4 APART IN FITTED Y ORDER).
CUMULATIVE ---------ORDERED BY WSSD---------- ---------ORDERED BY FITTED Y---------
NO. STD DEV WSSD OBSV. OBSV. DEL RESIDUALS WSSD DEL RESIDUALS FITTED Y OBSV. SEQ.
1 2.32 0.00 33 13 2.52 0.00 1.07 -12.89 32 1
2 1.72 0.00 28 8 1.20 59.88 1.39 -12.89 12 2
3 1.58 0.00 35 15 1.43 0.00 0.06 -6.88 27 3
4 1.24 0.00 29 9 0.24 125.72 4.69 -6.88 7 4
5 1.14 0.00 25 5 0.79 0.00 1.75 -6.73 36 5
6 1.42 0.00 39 19 3.08 40.25 3.92 -6.73 16 6
7 1.23 0.00 21 1 0.12 0.00 0.37 -0.71 31 7
8 1.30 0.00 22 2 1.88 59.88 3.30 -0.71 11 8
9 1.16 0.00 34 14 0.11 0.00 0.05 5.30 26 9
10 1.12 0.00 30 10 0.83 282.88 12.27 5.30 6 10
11 1.05 0.00 38 18 0.36 0.00 0.14 5.52 40 11
12 1.14 0.00 37 17 2.27 413.43 7.54 5.52 20 12
13 1.17 0.00 23 3 1.70 0.00 1.17 11.37 24 13
14 1.16 0.00 24 4 1.17 3.19 3.36 11.37 4 14
15 1.10 0.00 40 20 0.14 0.00 1.70 14.40 23 15
16 1.03 0.00 26 6 0.05 331.99 6.09 14.40 3 16
17 0.99 0.00 31 11 0.37 0.00 2.27 14.63 37 17
18 1.02 0.00 36 16 1.75 1.96 2.89 14.63 17 18
19 0.97 0.00 27 7 0.06 0.00 0.36 14.65 38 19
20 0.97 0.00 32 12 1.07 119.03 13.50 14.65 18 20
21 0.95 1.14 22 1 0.46 0.00 0.83 23.67 30 21
22 1.00 1.14 2 1 2.34 17.68 2.98 23.67 10 22
23 0.97 1.14 22 21 0.34 0.00 0.11 23.72 34 23
24 1.02 1.14 2 21 2.22 229.19 13.80 23.72 14 24
25 1.15 1.96 37 18 4.80 0.00 1.88 25.98 22 25
26 1.20 1.96 17 18 2.53 1.14 2.22 25.98 2 26
27 1.33 1.96 37 38 5.16 0.00 0.12 29.63 21 27
28 1.38 1.96 17 38 2.89 460.09 2.77 29.63 1 28
29 1.53 3.19 24 3 6.23 0.00 3.08 33.56 39 29
30 1.63 3.19 4 3 5.06 321.90 11.71 33.56 19 30
31 1.72 3.19 24 23 4.53 0.00 0.79 35.78 25 31
32 1.76 3.19 4 23 3.36 21.88 5.49 35.78 5 32
33 1.76 3.19 9 8 1.78 0.00 0.24 45.00 29 33
34 1.71 3.19 29 28 0.34 49.11 5.91 45.00 9 34
35 1.68 3.19 9 28 0.58 0.00 1.43 45.09 35 35
36 1.69 8.05 15 13 2.31 76.84 3.90 45.09 15 36
37 1.68 8.05 35 33 1.23 0.00 1.20 48.03 28 37
38 1.64 8.05 15 33 0.21 36.51 2.90 48.03 8 38
39 1.73 12.75 6 4 5.75 0.00 2.52 51.77 33 39
40 1.79 12.75 26 24 4.63 59.88 0.31 51.77 13 40
1 LINEAR LEAST-SQUARES CURVE FITTING PROGRAM
02 VARIABLES PASS 1 DEP VAR 1: Y
0FUNCTIONS RELATED TO THE VARIANCE OF FITTED Y. OBSERVATIONS ORDERED BY COMPUTER INPUT.
0 STUDENTIZED DELETE-EFFECT
IDENT. OBSV. RESIDUAL RESIDUAL V(Y)/RMS V(R)/RMS V(Y)/V(R) VALUE PERCENT
1 1 -9.464 -1.6 0.0909 0.9091 0.1 0.1
2 2 -7.128 -1.2 0.0823 0.9177 0.1 0.0
3 3 -7.720 -1.3 0.0772 0.9228 0.1 0.0
4 4 -2.657 -0.4 0.0682 0.9318 0.1 0.0
5 5 1.154 0.2 0.0639 0.9361 0.1 0.0
6 6 3.094 0.5 0.0590 0.9410 0.1 0.0
7 7 5.099 0.9 0.0887 0.9113 0.1 0.0
8 8 5.105 0.9 0.0817 0.9183 0.1 0.0
9 9 6.884 1.2 0.0687 0.9313 0.1 0.0
10 10 7.893 1.3 0.0259 0.9741 0.0 0.0
11 11 6.446 1.1 0.0552 0.9448 0.1 0.0
12 12 6.421 1.1 0.1018 0.8982 0.1 0.0
13 13 4.722 0.8 0.1048 0.8952 0.1 0.0
14 14 4.799 0.8 0.0342 0.9658 0.0 0.0
15 15 2.410 0.4 0.0874 0.9126 0.1 0.0
16 16 2.160 0.4 0.0923 0.9077 0.1 0.0
17 17 -3.899 -0.7 0.0584 0.9416 0.1 0.0
18 18 -6.433 -1.1 0.0703 0.9297 0.1 0.0
19 19 -9.774 -1.7 0.0951 0.9049 0.1 0.1
20 20 -9.034 -1.5 0.0938 0.9062 0.1 0.1
1 21 -9.345 -1.6 0.0909 0.9091 0.1 0.1
2 22 -9.005 -1.5 0.0823 0.9177 0.1 0.1
3 23 -6.019 -1.0 0.0772 0.9228 0.1 0.0
4 24 -1.490 -0.3 0.0682 0.9318 0.1 0.0
5 25 1.939 0.3 0.0639 0.9361 0.1 0.0
6 26 3.142 0.5 0.0590 0.9410 0.1 0.0
7 27 5.036 0.9 0.0887 0.9113 0.1 0.0
8 28 6.308 1.1 0.0817 0.9183 0.1 0.0
9 29 6.647 1.1 0.0687 0.9313 0.1 0.0
10 30 7.067 1.2 0.0259 0.9741 0.0 0.0
11 31 6.080 1.0 0.0552 0.9448 0.1 0.0
12 32 5.350 0.9 0.1018 0.8982 0.1 0.0
13 33 2.202 0.4 0.1048 0.8952 0.1 0.0
14 34 4.912 0.8 0.0342 0.9658 0.0 0.0
15 35 0.977 0.2 0.0874 0.9126 0.1 0.0
16 36 0.408 0.1 0.0923 0.9077 0.1 0.0
17 37 -1.628 -0.3 0.0584 0.9416 0.1 0.0
18 38 -6.792 -1.1 0.0703 0.9297 0.1 0.0
19 39 -6.695 -1.1 0.0951 0.9049 0.1 0.0
20 40 -9.175 -1.6 0.0938 0.9062 0.1 0.1
1 LINEAR LEAST-SQUARES CURVE FITTING PROGRAM
02 VARIABLES PASS 1 DEP VAR 1: Y
0-----------------ORDERED BY COMPUTER INPUT--------- --------- ---------------------ORDERED BY RESIDUALS---------------------
IDENT. OBSV. WSS DISTANCE OBS. Y FITTED Y RESIDUAL OBSV. OBS. Y FITTED Y ORDERED RESID. STUD.RESID. SEQ
1 1 158. 20.164 29.628 -9.464 10 31.564 23.671 7.893 1.3 1
2 2 133. 18.847 25.975 -7.128 30 30.738 23.671 7.067 1.2 2
3 3 88. 6.678 14.398 -7.720 9 51.883 44.999 6.884 1.2 3
4 4 59. 8.709 11.366 -2.657 29 51.646 44.999 6.647 1.1 4
5 5 84. 36.934 35.780 1.154 11 5.739 -0.707 6.446 1.1 5
6 6 20. 8.397 5.303 3.094 12 -6.466 -12.887 6.421 1.1 6
7 7 11. -1.778 -6.877 5.099 28 54.339 48.031 6.308 1.1 7
8 8 49. 53.136 48.031 5.105 31 5.373 -0.707 6.080 1.0 8
9 9 28. 51.883 44.999 6.884 32 -7.537 -12.887 5.350 0.9 9
10 10 1. 31.564 23.671 7.893 8 53.136 48.031 5.105 0.9 10
11 11 19. 5.739 -0.707 6.446 7 -1.778 -6.877 5.099 0.9 11
12 12 55. -6.466 -12.887 6.421 27 -1.841 -6.877 5.036 0.9 12
13 13 13. 56.494 51.772 4.722 34 28.636 23.724 4.912 0.8 13
14 14 13. 28.523 23.724 4.799 14 28.523 23.724 4.799 0.8 14
15 15 15. 47.498 45.088 2.410 13 56.494 51.772 4.722 0.8 15
16 16 108. -4.575 -6.735 2.160 26 8.445 5.303 3.142 0.5 16
17 17 79. 10.730 14.629 -3.899 6 8.397 5.303 3.094 0.5 17
18 18 106. 8.214 14.647 -6.433 15 47.498 45.088 2.410 0.4 18
19 19 82. 23.790 33.564 -9.774 33 53.974 51.772 2.202 0.4 19
20 20 164. -3.518 5.516 -9.034 16 -4.575 -6.735 2.160 0.4 20
1 21 158. 20.283 29.628 -9.345 25 37.719 35.780 1.939 0.3 21
2 22 133. 16.970 25.975 -9.005 5 36.934 35.780 1.154 0.2 22
3 23 88. 8.379 14.398 -6.019 35 46.065 45.088 0.977 0.2 23
4 24 59. 9.876 11.366 -1.490 36 -6.327 -6.735 0.408 0.1 24
5 25 84. 37.719 35.780 1.939 24 9.876 11.366 -1.490 -0.3 25
6 26 20. 8.445 5.303 3.142 37 13.001 14.629 -1.628 -0.3 26
7 27 11. -1.841 -6.877 5.036 4 8.709 11.366 -2.657 -0.4 27
8 28 49. 54.339 48.031 6.308 17 10.730 14.629 -3.899 -0.7 28
9 29 28. 51.646 44.999 6.647 23 8.379 14.398 -6.019 -1.0 29
10 30 1. 30.738 23.671 7.067 18 8.214 14.647 -6.433 -1.1 30
11 31 19. 5.373 -0.707 6.080 39 26.869 33.564 -6.695 -1.1 31
12 32 55. -7.537 -12.887 5.350 38 7.855 14.647 -6.792 -1.1 32
13 33 13. 53.974 51.772 2.202 2 18.847 25.975 -7.128 -1.2 33
14 34 13. 28.636 23.724 4.912 3 6.678 14.398 -7.720 -1.3 34
15 35 15. 46.065 45.088 0.977 22 16.970 25.975 -9.005 -1.5 35
16 36 108. -6.327 -6.735 0.408 20 -3.518 5.516 -9.034 -1.5 36
17 37 79. 13.001 14.629 -1.628 40 -3.659 5.516 -9.175 -1.6 37
18 38 106. 7.855 14.647 -6.792 21 20.283 29.628 -9.345 -1.6 38
19 39 82. 26.869 33.564 -6.695 1 20.164 29.628 -9.464 -1.6 39
20 40 164. -3.659 5.516 -9.175 19 23.790 33.564 -9.774 -1.7 40
1 2 VARIABLES PASS 1 DEP VAR 1: Y CUMULATIVE DISTRIBUTION OF RESIDUALS
.0002 .001 .005 .01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8 .9 .95 .98 .99 .995 .999
*-----*-------*--*---*-----*----*-----*----*---*---*---*---*----*-----*----*-----*---*--*-------*-----
I ' + I
I ' I
P I ' + + I
O I ' + I
S I ' ++ + I
I I ' + I
T I ' I
I I ' + I
V I ' ++ +++ I
E I ' + I
I ' I
I ' I
I ' I
I ' ++ I
I ' I
I ' + I
I ++ I
I +' I
I ' I
I ++ ' I
I ' I
R I + ' I
E 0 I----------------------------------------------------------------------------------------------------I
S I ' I
I I ' I
D I ' I
U I + ' I
A I + ' I
L I ' I
S I ' I
I + ' I
I ' I
I ' I
I + ' I
I ' I
I ' I
I ' I
I ' I
I ' I
I + ' I
I ' I
N I ++ ' I
E I + ' I
G I + ' I
A I + ' I
T I ' I
I I ' I
V I ' I
E I + + ' I
I + + + ' I
I + ' I
*-----*-------*--*---*-----*----*-----*----*---*---*---*---*----*-----*----*-----*---*--*-------*-----
.0002 .001 .005 .01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8 .9 .95 .98 .99 .995 .999
CUMULATIVE FREQUENCY, NORMAL GRID
1 2 VARIABLES PASS 1 DEP VAR 1: Y RESIDUAL VS. FITTED Y
-12.887 19.442 51.772
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I + I
I I
P I + + I
O I + I
S I+ + + I
I I + I
T I I
I I+ I
V I + + + I
E I +I
I I
I I
I I
I + I
I I
I + I
I + +I
I + I
I I
I + + I
I I
R I + I
E 0 I----------------------------------------------------------------------------------------------------I
S I I
I I I
D I I
U I + I
A I + I
L I I
S I I
I + I
I I
I I
I + I
I I
I I
I I
I I
I I
I + I
I I
N I + + I
E I + I
G I + I
A I + I
T I I
I I I
V I I
E I + + I
I + + I
I + I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
-12.887 19.442 51.772
FITTED Y
1 2 VARIABLES PASS 1 DEP VAR 1: Y RESIDUALS VS. INDEPENDENT VARIABLE 1: X1
0.000 2.000 4.000 6.000 8.000
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I + I
I I
P I + + I
O I + I
S I + + + I
I I + I
T I I
I I + I
V I + + + I
E I + I
I I
I I
I I
I + I
I I
I + I
I + + I
I + I
I I
I + + I
I I
R I + I
E 0 I----------------------------------------------------------------------------------------------------I
S I I
I I I
D I I
U I I
A I + + I
L I I
S I I
I + I
I I
I I
I I
I + I
I I
I I
I I
I I
I I
I + I
N I + I
E I + + I
G I + I
A I I
T I + I
I I I
V I I
E I + +I
I+ +I
I+ + I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
0.000 2.000 4.000 6.000 8.000
0 INDEPENDENT VARIABLE 1: X1
1 2 VARIABLES PASS 1 DEP VAR 1: Y COMPONENT WITH RESIDUALS VS. INDEPENDENT VARIABLE 1: X1
C = COMPONENT, + = WITH RESIDUAL, * = BOTH
0.000 2.000 4.000 6.000 8.000
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I I
I I
I I
I I
I CI
I C I
I I
I C I
I + +I
I C + + I
I + + I
I * I
I I
I + I
C I + C I
O I + I
M I + + C I
P I C I
O I + C I
N I I
E I + I
C N I C I
O T I I
M I + C I
P A P I I
O N L I I
N D U I + C I
E S I I
N I + C I
T R I I
E I C I
S I + I
I I + I
D I C I
U I + I
A I C I
L I I
S I C I
I + I
I + I
I C I
I C I
IC + I
I + I
I + I
I + I
I+ I
I I
I I
I I
I I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
0.000 2.000 4.000 6.000 8.000
0 INDEPENDENT VARIABLE 1: X1
0 RESIDUALS OUTSIDE OF PLOT
1 2 VARIABLES PASS 1 DEP VAR 1: Y RESIDUALS VS. INDEPENDENT VARIABLE 2: X2
0.000 10.000 20.000 30.000 40.000
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I + I
I I
P I + + I
O I + I
S I + + + I
I I + I
T I I
I I + I
V I + + + I
E I + I
I I
I I
I I
I + I
I I
I + I
I + + I
I + I
I I
I + + I
I I
R I + I
E 0 I----------------------------------------------------------------------------------------------------I
S I I
I I I
D I I
U I I
A I + + I
L I I
S I I
I + I
I I
I I
I I
I + I
I I
I I
I I
I I
I I
I + I
N I + I
E I + + I
G I + I
A I I
T I + I
I I I
V I I
E I + +I
I+ +I
I+ + I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
0.000 10.000 20.000 30.000 40.000
0 INDEPENDENT VARIABLE 2: X2
1 2 VARIABLES PASS 1 DEP VAR 1: Y COMPONENT WITH RESIDUALS VS. INDEPENDENT VARIABLE 2: X2
C = COMPONENT, + = WITH RESIDUAL, * = BOTH
0.000 10.000 20.000 30.000 40.000
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
IC I
I I
I C I
I+ + I
I C + I
I + + I
I I
I C + I
I C + I
I I
I + C I
I + C I
I + I
I I
C I + I
O I + I
M I C I
P I + I
O I C + I
N I I
E I I
C N I C + I
O T I * I
M I I
P A P I + I
O N L I I
N D U I C + I
E S I I
N I C I
T R I I
E I + I
S I I
I I I
D I C I
U I I
A I C I
L I I
S I + I
I + + I
I + * I
I + C I
I C I
I I
I + I
I + + I
I C I
I I
I CI
I I
I I
I +I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
0.000 10.000 20.000 30.000 40.000
0 INDEPENDENT VARIABLE 2: X2
0 RESIDUALS OUTSIDE OF PLOT
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
1979 VERSION OF THE LINWOOD 40 VARIABLE, 1000 OBSERVATION PROGRAM
REFER TO FITTING EQUATIONS TO DATA BY DANIEL AND WOOD, SECOND EDITION, WILEY PUBLISHER,
FOR GLOSSARY OF TERMS, USER'S MANUAL, DETAILS OF CALCULATIONS AND INTERPRETATION OF RESULTS.
02 VARIABLES PASS 2
0 CONTROL CARD INFORMATION ORDER OF CARDS
COL. INPUT MAX. ITEM (NOTE: BLANK ON CARD = 0) FIRST PROBLEM
1-18 PROBLEM IDENTIFICATION. 1 CONTROL CARD.
19-20 3 NUMBER OF INDEPENDENT VARIABLES READ IN 2 FORMAT CARD(S), IF ANY.
(ALLOW SPACE FOR TRANSFORMATIONS). 3 DELETE OBSERVATIONS CARD(S), IF ANY.
21-22 1 NUMBER OF DEPENDENT VARIABLES READ IN. 4 INDICATOR-VARIABLE-OBSERVATIONS CARD(S), IF ANY.
4 65 TOTAL NUMBER OF VARIABLES (BEFORE TRANSFORMATIONS, IF ANY). 5 TRANSFORMATION CARD(S), IF ANY.
24 E CAUSES Y, FITTED Y AND RESIDUALS TO BE 6 INFORMATION CARD(S) FOR PRINTOUT, IF ANY.
LISTED WITH AN E RATHER THAN AN F FORMAT. 7 NAMES OF VARIABLES CARD(S) FOR PRINTOUT, IF ANY.
25 1 1 DO TRANSFORMATIONS. 8 CP FACTORIAL SEARCH CARD, IF ANY.
26 0 1 WEIGHT OBSERVATIONS. WEIGHT ENTERED IN LAST POSITION. 9 DATA CARDS (IF NOT READ FROM A FILE).
2 WEIGHT BY 1/VAR. OF OBSERVATION. VARIANCE ENTERED. 10 END CARD (END IN COLUMNS 1 - 3 OF IDENTIFICATION
27 0 1 LET B(0) = ZERO, OTHERWISE B(0) IS CALCULATED VALUE. FIELD). THE NUMBER OF END CARDS MUST EQUAL THE
28 0 1 CHECK OBSERVATION NUMBER SEQUENCE. NUMBER OF CARDS PER OBSERVATION. (END CARDS
29 0 1 CHECK SEQUENCE WITHIN OBSERVATION NUMBER. ARE NOT NEEDED IF DATA ARE READ FROM A FILE).
30 0 1 DO BACK TRANSFORMATION OF DEPENDENT VARIABLE. 11 ESTIMATE OF VARIANCE CARD, IF ANY.
31 0 1 PUNCH DATA FOR CONFIDENCE INTERVAL PROGRAM. 12 ADDITIONAL CP FACTORIAL SEARCH AND ESTIMATE OF
32 0 0 LIST ALL INPUT DATA. VARIANCE CARDS, IF ANY.
1 LIST ONLY 1ST OBSERVATION.
2 DO NOT LIST ANY INPUT DATA. SECOND PROBLEM
33 1 0 LIST TRANSFORMATIONS AND ALL TRANSFORMED DATA. IF DATA ARE REUSED FROM FIRST PROBLEM,
1 LIST TRANSFORMATIONS AND 1ST TRANSFORMED OBSERVATION. DELETE THE FORMAT, DATA AND END CARDS.
2 DO NOT LIST TRANSFORMATIONS OR TRANSFORMED DATA. IF NAMES ARE REUSED,
34 0 1 DO NOT LIST SUMS OF VARIABLES. DELETE THE NAME CARDS.
35 0 1 DO NOT LIST RAW SUMS AND CROSS PRODUCTS WHEN B(O)=O. IF DIFFERENT INPUT DATA AND NAMES,
36 0 1 DO NOT LIST RESIDUAL SUMS AND CROSS PRODUCTS. REPEAT 1 - 12 ABOVE.
37 0 1 DO NOT LIST MEANS AND ROOT MEAN SQUARES OF VARIABLES.
38 0 1 DO NOT LIST SIMPLE CORRELATION COEFFICIENTS.
39 0 1 DO NOT LIST INVERSE MATRIX.
40 2 1 DO NOT PRINT PLOTS OF RESIDUALS VS. FITTED Y.
2 PLOT (A) RESIDUALS AND (B) COMPONENT AND COMPONENT-
PLUS-RESIDUALS VS. EACH INDEPENDENT VARIABLE.
3 PLOT (A) RESIDUALS ONLY.
4 PLOT (B) COMPONENT AND COMPONENT-PLUS-RESIDUALS ONLY.
5 PLOT (B) BUT EXPAND SCALE TO FILL EACH PLOT.
41 1 0 READ DATA WITH STANDARD FORMAT (A6, I4, I2, 10F6.3).
1 READ DATA WITH FORMAT TO BE READ, 1 CARD (72COL) ASSUMED.
2 READ DATA WITH READ DATA (REDATA) SUBROUTINE.
42 2 0 DO NOT SAVE DATA FOR NEXT PROBLEM.
1 SAVE DATA FOR NEXT PROBLEM.
2 REUSE DATA FROM PREVIOUS PROBLEM.
43-44 0 18 NUMBER OF VARIABLES IN CP SEARCH IF GREATER THAN 12.
45 0 8 NUMBER OF FORMAT CARDS IF GREATER THAN 1.
46-47 8 12 NUMBER OF INFORMATION CARDS TO BE READ FOR DISPLAY ON
PRINTOUT IF DESIRED, 72 COL. EACH.
48 1 1 READ NAMES OF VARIABLES FOR DISPLAY ON PRINTOUT.
NAMES IN SAME POSITIONS AS VARIABLES ON TRANSFORMATION
CARDS - COLS. 1-6, 11-16, - - - , 61-66.
NAMES ARE NOT MOVED, ONLY LISTED OR DELETED.
2 REUSE NAMES OF VARIABLES FROM PREVIOUS PROBLEM.
49 0 SEARCH FOR CANDIDATE EQUATIONS VIA CP. USE ESTIMATE
OF VARIANCE (RMS) FROM:
1 FULL EQUATION,
2 SUBSET EQUATION WITH MINIMUM RMS VALUE, OR
3 ESTIMATE OF VARIANCE CARD, F16.8 FORMAT.
50 0 NUMBER OF CP FACTORIAL SEARCH CARDS TO BE READ PER
DEPENDENT VARIABLE. KEYPUNCH IN ASCENDING ORDER THE
IDENTIFING NUMBER OF THE VARIABLES (AFTER TRANSFOR-
MATIONS) TO BE USED IN THAT SEARCH, 18(2X,I2) FORMAT.
ALL OTHER VARIABLES WILL BE PLACED IN BASIC EQUATION.
51 0 1 LIST COMPONENT-EFFECT TABLE, REQUIRED X(I) PRECISION,
ESTIMATE OF STANDARD DEVIATION FROM NEAR NEIGHBORS,
AND FUNCTIONS OF FITTED Y.
2 LIST ONLY ESTIMATE OF STD. DEVIATION AND FUNCTIONS.
3 LIST ONLY FUNCTIONS OF FITTED Y.
52-53 0 NUMBER OF FILE IF DATA ARE READ FROM SEPARATE FILE,
NO END CARD IF ONLY ONE SET OF DATA IS ON EACH FILE.
54-55 0 NUMBER OF INDEPENDENT VARIABLES GREATER THAN THE 99
ALLOWED IN COLS 19-20.
56-58 0 TO REDUCE PRINTOUT WITH MANY OBSERVATIONS,
NUMBER OF CENTRAL OBSERVATIONS AND RESIDUALS NOT
TO BE PRINTED. THIS REQUIRES AN E IN COL 24.
59 0 CROSS VERIFICATION OF MODEL AND COEFFICIENTS WITH A
SECOND SAMPLE OF DATA:
1 WRITE B(0) AND B(I)S ON FILE IN ONE PROBLEM
(TRANSFORMATIONS ARE NOT SAVED).
2 READ B(0) AND B(I)S FROM FILE IN NEXT PROBLEM
WITH SECOND SET OF OBSERVATIONS.
60 0 5 NUMBER OF DELETE-OBSERVATIONS CARDS. KEYPUNCH
OBSERVATION NUMBER OF DATA TO BE DELETED IN ORDER READ
BY COMPUTER USING 7(I4,6X) FORMAT.
61 0 5 NUMBER OF INDICATOR-VARIABLE-OBSERVATIONS CARDS.
USING A 7(I4,2X,I3,1X) FORMAT, KEYPUNCH OBSERVATION
NUMBER (IN ORDER READ) AND VARIABLE NUMBER (BEFORE
TRANSFORMATIONS) INTO WHICH A 1 IS TO BE INSERTED.
0EQUATION 2 OF A MULTI-EQUATION PROBLEM
0BZERO = CALCULATED VALUE
0INFORMATION CARDS
EQUATION: Y = 20 + 20X1 - 3X2 - 1X1SQRD + ERROR(0,1)
FITTED WITH Y = B0 + B1(X1-4.0) + B2X2 + B3(X1-4.0)SQRD
ERROR FROM "A MILLION RANDOM DIGITS", RAND CORP., FREE PRESS, 1955.
1-20 OBSV. FROM TABLE PAGE 4, COL 4; 21-40 OBSV. FROM PAGE 12, COL 2.
OBSERVATIONS 21-40 ARE REPLICATES OF OBSERVATIONS 1-20.
STD. DEVIATION ESTIMATED FROM NEAR NEIGHBORS (1.0), IS CLOSE TO
RRMS OF FIT.
UNCODED FITTED EQUATION: Y = 20.006 + 20.310X1 - 3.007X2 - 1.038X1SQRD
0DATA TRANSFORMATIONS
POSITION CODE OPERATION CONSTANT LOCATION OMIT VARIABLE NAME
1 8 ADD CONSTANT -4.0 1 0 1 X1-4.0
2 NONE 2 0 2 X2
3 9 MULTIPLY POSITIONS, 1X 1 3 0 3 X1SQRD
4 NONE 4 0 4 Y
0
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
2 VARIABLES PASS 2
0DATA INPUT 3 INDEPENDENT VARIABLES 1 DEPENDENT VARIABLE(S)
OBSV. SEQ. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 0 0.000 0.000 0.000 20.164
2 0 0.200 2.000 0.000 18.847
3 0 0.500 7.000 0.000 6.678
4 0 1.000 10.000 0.000 8.709
5 0 1.500 4.000 0.000 36.934
6 0 2.000 16.000 0.000 8.397
7 0 2.500 22.000 0.000 -1.778
8 0 3.000 6.000 0.000 53.136
9 0 3.500 9.000 0.000 51.883
10 0 4.000 18.000 0.000 31.564
11 0 4.500 28.000 0.000 5.739
12 0 5.000 34.000 0.000 -6.466
13 0 5.300 14.000 0.000 56.494
14 0 5.500 24.000 0.000 28.523
15 0 6.000 19.000 0.000 47.498
16 0 6.500 38.000 0.000 -4.575
17 0 7.000 33.000 0.000 10.730
18 0 7.500 35.000 0.000 8.214
19 0 7.800 30.000 0.000 23.790
20 0 8.000 40.000 0.000 -3.518
21 0 0.000 0.000 0.000 20.283
22 0 0.200 2.000 0.000 16.970
23 0 0.500 7.000 0.000 8.379
24 0 1.000 10.000 0.000 9.876
25 0 1.500 4.000 0.000 37.719
26 0 2.000 16.000 0.000 8.445
27 0 2.500 22.000 0.000 -1.841
28 0 3.000 6.000 0.000 54.339
29 0 3.500 9.000 0.000 51.646
30 0 4.000 18.000 0.000 30.738
31 0 4.500 28.000 0.000 5.373
32 0 5.000 34.000 0.000 -7.537
33 0 5.300 14.000 0.000 53.974
34 0 5.500 24.000 0.000 28.636
35 0 6.000 19.000 0.000 46.065
36 0 6.500 38.000 0.000 -6.327
37 0 7.000 33.000 0.000 13.001
38 0 7.500 35.000 0.000 7.855
39 0 7.800 30.000 0.000 26.869
40 0 8.000 40.000 0.000 -3.659
0DATA TRANSFORMATIONS
POSITION CODE OPERATION CONSTANT LOCATION OMIT VARIABLE NAME
1 8 ADD CONSTANT -4.0 1 0 1 X1-4.0
2 NONE 2 0 2 X2
3 9 MULTIPLY POSITIONS, 1X 1 3 0 3 X1SQRD
4 NONE 4 0 4 Y
0FIRST OBSERVATION AFTER TRANSFORMATIONS THE FITTED EQUATION HAS 3 INDEPENDENT VARIABLES, 1 DEPENDENT VARIABLE(S)
X1-4.0 X2 X1SQRD Y
OBSV. 1-11-21 2-12-22 3-13-23 4-14-24 5-15-25 6-16-26 7-17-27 8-18-28 9-19-29 10-20-30
1 -4.00000E+00 0.00000E+00 1.60000E+01 2.01640E+01
0SUMS OF VARIABLES
2.60000E+00 7.78000E+02 2.65140E+02 8.01767E+02
0RESIDUAL SUMS OF SQUARES + CROSS PRODUCTS
1 2.64971E+02
2 1.11563E+03 6.22990E+03
3 -1.28401E+01 8.00700E+00 1.27529E+03
4 -1.60588E+02-5.34992E+03-1.50199E+03 1.57550E+04
0MEANS OF VARIABLES
6.50000E-02 1.94500E+01 6.62850E+00 2.00442E+01
0ROOT MEAN SQUARES OF VARIABLES
2.60655E+00 1.26389E+01 5.71836E+00 2.00991E+01
0SIMPLE CORRELATION COEFFICIENTS, R(I,I PRIME)
1 1.000
2 0.868 1.000
3 -0.022 0.003 1.000
4 -0.079 -0.540 -0.335 1.000
0INVERSE, C(I,I PRIME)
1 4.075
2 -3.538 4.073
3 0.100 -0.090 1.002
1 LINEAR LEAST-SQUARES CURVE-FITTING PROGRAM
2 VARIABLES PASS 2 DEP VAR 1: Y MIN Y = -7.537E+00 MAX Y = 5.649E+01 RANGE Y = 6.403E+01
EQUATION: Y = 20 + 20X1 - 3X2 - 1X1SQRD + ERROR(0,1)
FITTED WITH Y = B0 + B1(X1-4.0) + B2X2 + B3(X1-4.0)SQRD
ERROR FROM "A MILLION RANDOM DIGITS", RAND CORP., FREE PRESS, 1955.
1-20 OBSV. FROM TABLE PAGE 4, COL 4; 21-40 OBSV. FROM PAGE 12, COL 2.
OBSERVATIONS 21-40 ARE REPLICATES OF OBSERVATIONS 1-20.
STD. DEVIATION ESTIMATED FROM NEAR NEIGHBORS (1.0), IS CLOSE TO
RRMS OF FIT.
UNCODED FITTED EQUATION: Y = 20.006 + 20.310X1 - 3.007X2 - 1.038X1SQRD
0IND.VAR(I) NAME COEF.B(I) S.E. COEF. T-VALUE R(I)SQRD MIN X(I) MAX X(I) RANGE X(I) REL.INF.X(I)
0 8.46383E+01
1 X1-4.0 1.20060E+01 1.22E-01 98.8 0.7546 -4.000E+00 4.000E+00 8.000E+00 1.50
2 X2 -3.00741E+00 2.51E-02 120.0 0.7545 0.000E+00 4.000E+01 4.000E+01 1.88
3 X1SQRD -1.03800E+00 2.75E-02 37.8 0.0025 0.000E+00 1.600E+01 1.600E+01 0.26
0NO. OF OBSERVATIONS 40
NO. OF IND. VARIABLES 3
RESIDUAL DEGREES OF FREEDOM 36
F-VALUE 5455.3
RESIDUAL ROOT MEAN SQUARE 0.98008387
RESIDUAL MEAN SQUARE 0.96056440
RESIDUAL SUM OF SQUARES 34.58031826
TOTAL SUM OF SQUARES 15755.02817978
MULT. CORREL. COEF. SQUARED .9978
ADJ. MULT. CORR. COEF. SQUARED .9976
0-----------------ORDERED BY COMPUTER INPUT--------- --------- ---------------------ORDERED BY RESIDUALS---------------------
IDENT. OBSV. WSS DISTANCE OBS. Y FITTED Y RESIDUAL OBSV. OBS. Y FITTED Y ORDERED RESID. STUD.RESID. SEQ
1 1 6140. 20.164 20.006 0.158 39 26.869 25.050 1.819 2.0 1
2 2 5177. 18.847 18.012 0.835 25 37.719 36.106 1.613 1.7 2
3 3 3402. 6.678 8.850 -2.172 16 -4.575 -6.116 1.541 1.7 3
4 4 2257. 8.709 9.204 -0.495 10 31.564 30.505 1.059 1.1 4
5 5 3235. 36.934 36.106 0.828 37 13.001 12.070 0.931 1.0 5
6 6 760. 8.397 8.356 0.041 2 18.847 18.012 0.835 0.9 6
7 7 450. -1.778 -1.869 0.091 5 36.934 36.106 0.828 0.9 7
8 8 1909. 53.136 53.550 -0.414 28 54.339 53.550 0.789 0.9 8
9 9 1122. 51.883 51.309 0.574 20 -3.518 -4.242 0.724 0.8 9
10 10 70. 31.564 30.505 1.059 24 9.876 9.204 0.672 0.7 10
11 11 762. 5.739 6.174 -0.435 40 -3.659 -4.242 0.583 0.7 11
12 12 2160. -6.466 -6.646 0.180 9 51.883 51.309 0.574 0.6 12
13 13 536. 56.494 56.388 0.106 34 28.636 28.134 0.502 0.5 13
14 14 525. 28.523 28.134 0.389 14 28.523 28.134 0.389 0.4 14
15 15 572. 47.498 47.357 0.141 29 51.646 51.309 0.337 0.4 15
16 16 4130. -4.575 -6.116 1.541 21 20.283 20.006 0.277 0.3 16
17 17 3028. 10.730 12.070 -1.340 30 30.738 30.505 0.233 0.2 17
18 18 4083. 8.214 8.684 -0.470 12 -6.466 -6.646 0.180 0.2 18
19 19 3210. 23.790 25.050 -1.260 1 20.164 20.006 0.158 0.2 19
20 20 6398. -3.518 -4.242 0.724 15 47.498 47.357 0.141 0.2 20
1 21 6140. 20.283 20.006 0.277 13 56.494 56.388 0.106 0.1 21
2 22 5177. 16.970 18.012 -1.042 7 -1.778 -1.869 0.091 0.1 22
3 23 3402. 8.379 8.850 -0.471 26 8.445 8.356 0.089 0.1 23
4 24 2257. 9.876 9.204 0.672 6 8.397 8.356 0.041 0.0 24
5 25 3235. 37.719 36.106 1.613 27 -1.841 -1.869 0.028 0.0 25
6 26 760. 8.445 8.356 0.089 36 -6.327 -6.116 -0.211 -0.2 26
7 27 450. -1.841 -1.869 0.028 8 53.136 53.550 -0.414 -0.4 27
8 28 1909. 54.339 53.550 0.789 11 5.739 6.174 -0.435 -0.5 28
9 29 1122. 51.646 51.309 0.337 18 8.214 8.684 -0.470 -0.5 29
10 30 70. 30.738 30.505 0.233 23 8.379 8.850 -0.471 -0.5 30
11 31 762. 5.373 6.174 -0.801 4 8.709 9.204 -0.495 -0.5 31
12 32 2160. -7.537 -6.646 -0.891 31 5.373 6.174 -0.801 -0.9 32
13 33 536. 53.974 56.388 -2.414 38 7.855 8.684 -0.829 -0.9 33
14 34 525. 28.636 28.134 0.502 32 -7.537 -6.646 -0.891 -1.0 34
15 35 572. 46.065 47.357 -1.292 22 16.970 18.012 -1.042 -1.1 35
16 36 4130. -6.327 -6.116 -0.211 19 23.790 25.050 -1.260 -1.4 36
17 37 3028. 13.001 12.070 0.931 35 46.065 47.357 -1.292 -1.4 37
18 38 4083. 7.855 8.684 -0.829 17 10.730 12.070 -1.340 -1.4 38
19 39 3210. 26.869 25.050 1.819 3 6.678 8.850 -2.172 -2.3 39
20 40 6398. -3.659 -4.242 0.583 33 53.974 56.388 -2.414 -2.6 40
1 2 VARIABLES PASS 2 DEP VAR 1: Y CUMULATIVE DISTRIBUTION OF RESIDUALS
.0002 .001 .005 .01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8 .9 .95 .98 .99 .995 .999
*-----*-------*--*---*-----*----*-----*----*---*---*---*---*----*-----*----*-----*---*--*-------*-----
I ' + I
I ' I
P I ' + I
O I ' + I
S I ' I
I I ' I
T I ' I
I I ' I
V I ' I
E I ' + I
I ' + I
I ' ++ I
I ' + I
I ' ++ I
I ' ++ I
I ' + I
I ' I
I ' + I
I ' + I
I '+++ I
I ++++ I
R 0 I---------------------------------------------++-----------------------------------------------------I
E I ' I
S I ' I
I I + ' I
D I ' I
U I + ' I
A I +++ + ' I
L I ' I
S I ' I
I ' I
I ++ ' I
I + ' I
I ' I
I + ' I
I ' I
I + ' I
I + + ' I
I ' I
I ' I
I ' I
N I ' I
E I ' I
G I ' I
A I ' I
T I ' I
I I ' I
V I + ' I
E I ' I
I ' I
I + ' I
*-----*-------*--*---*-----*----*-----*----*---*---*---*---*----*-----*----*-----*---*--*-------*-----
.0002 .001 .005 .01 .02 .05 .1 .2 .3 .4 .5 .6 .7 .8 .9 .95 .98 .99 .995 .999
CUMULATIVE FREQUENCY, NORMAL GRID
1 2 VARIABLES PASS 2 DEP VAR 1: Y RESIDUAL VS. FITTED Y
-6.646 24.871 56.388
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I + I
I I
P I + I
O I+ I
S I I
I I I
T I I
I I I
V I I
E I + I
I + I
I + + I
I + I
I + + I
I + + I
I + I
I I
I + + I
I + I
I+ + + I
I + + + +I
R 0 I------+---------------+-----------------------------------------------------------------------------I
E I I
S I I
I I+ I
D I I
U I + I
A I + ++ I
L I I
S I I
I I
I + + I
I+ I
I I
I + I
I I
I + I
I + + I
I I
I I
I I
N I I
E I I
G I I
A I I
T I I
I I I
V I + I
E I I
I I
I +I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
-6.646 24.871 56.388
FITTED Y
1 2 VARIABLES PASS 2 DEP VAR 1: Y RESIDUALS VS. INDEPENDENT VARIABLE 1: X1-4.0
-4.000 -2.000 0.000 2.000 4.000
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I + I
I I
P I + I
O I + I
S I I
I I I
T I I
I I I
V I I
E I + I
I + I
I + + I
I + I
I + +I
I + +I
I + I
I I
I + + I
I+ I
I + + I
I+ + + + + I
R 0 I------------------------+-----+---------------------------------------------------------------------I
E I I
S I I
I I + I
D I I
U I + I
A I + + + + I
L I I
S I I
I I
I + + I
I + I
I I
I + I
I I
I I
I + + I
I + I
I I
I I
N I I
E I I
G I I
A I I
T I I
I I I
V I I
E I + I
I I
I + I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
-4.000 -2.000 0.000 2.000 4.000
0 INDEPENDENT VARIABLE 1: X1-4.0
1 2 VARIABLES PASS 2 DEP VAR 1: Y COMPONENT WITH RESIDUALS VS. INDEPENDENT VARIABLE 1: X1-4.0
C = COMPONENT, + = WITH RESIDUAL, * = BOTH
-4.000 -2.000 0.000 2.000 4.000
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I I
I I
I I
I I
I +I
I + CI
I C I
I C I
I + I
I + I
I C I
I I
I * I
I I
C I I
O I * I
M I I
P I * I
O I C I
N I + I
E I * I
C N I I
O T I I
M I * I
P A P I I
O N L I * I
N D U I I
E S I + I
N I C I
T R I I
E I * I
S I I
I I I
D I * I
U I I
A I * I
L I I
S I + I
I C I
I I
I * I
I I
I I
I * I
I C + I
I*+ I
I I
I I
I I
I I
I I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
-4.000 -2.000 0.000 2.000 4.000
0 INDEPENDENT VARIABLE 1: X1-4.0
0 RESIDUALS OUTSIDE OF PLOT
1 2 VARIABLES PASS 2 DEP VAR 1: Y RESIDUALS VS. INDEPENDENT VARIABLE 2: X2
0.000 10.000 20.000 30.000 40.000
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I + I
I I
P I + I
O I + I
S I I
I I I
T I I
I I I
V I I
E I + I
I + I
I + + I
I + I
I + +I
I + +I
I + I
I I
I + + I
I+ I
I + + I
I+ + + + + I
R 0 I---------------------------------------+--------------+---------------------------------------------I
E I I
S I I
I I + I
D I I
U I + I
A I + + + + I
L I I
S I I
I I
I + + I
I + I
I I
I + I
I I
I I
I + + I
I + I
I I
I I
N I I
E I I
G I I
A I I
T I I
I I I
V I I
E I + I
I I
I + I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
0.000 10.000 20.000 30.000 40.000
0 INDEPENDENT VARIABLE 2: X2
1 2 VARIABLES PASS 2 DEP VAR 1: Y COMPONENT WITH RESIDUALS VS. INDEPENDENT VARIABLE 2: X2
C = COMPONENT, + = WITH RESIDUAL, * = BOTH
0.000 10.000 20.000 30.000 40.000
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I* I
I I
I C I
I + I
I + I
I C I
I I
I * I
I I
I * I
I I
I * I
I * I
I + I
C I I
O I I
M I I
P I C I
O I + I
N I I
E I * I
C N I I
O T I + I
M I C I
P A P I * I
O N L I I
N D U I I
E S I I
N I * I
T R I I
E I * I
S I I
I I I
D I I
U I I
A I C I
L I + I
S I + I
I C I
I I
I I
I + I
I C I
I * I
I * I
I I
I I
I + I
I * I
I I
I *I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
0.000 10.000 20.000 30.000 40.000
0 INDEPENDENT VARIABLE 2: X2
0 RESIDUALS OUTSIDE OF PLOT
1 2 VARIABLES PASS 2 DEP VAR 1: Y RESIDUALS VS. INDEPENDENT VARIABLE 3: X1SQRD
0.000 4.000 8.000 12.000 16.000
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I + I
I I
P I + I
O I + I
S I I
I I I
T I I
I I I
V I I
E I+ I
I + I
I + + I
I + I
I + +I
I+ +I
I + I
I I
I+ + I
I +I
I+ + I
I + + + +I
R 0 I-------------+----------+---------------------------------------------------------------------------I
E I I
S I I
I I + I
D I I
U I + I
A I+ + + I
L I I
S I I
I I
I+ + I
I + I
I I
I + I
I I
I I
I + + I
I + I
I I
I I
N I I
E I I
G I I
A I I
T I I
I I I
V I I
E I + I
I I
I + I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
0.000 4.000 8.000 12.000 16.000
0 INDEPENDENT VARIABLE 3: X1SQRD
1 2 VARIABLES PASS 2 DEP VAR 1: Y COMPONENT WITH RESIDUALS VS. INDEPENDENT VARIABLE 3: X1SQRD
C = COMPONENT, + = WITH RESIDUAL, * = BOTH
0.000 4.000 8.000 12.000 16.000
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
I I
I I
I I
I I
I I
I I
I I
I I
I I
I I
I I
I I
I I
I I
C I I
O I I
M I I
P I I
O I I
N I I
E I I
C N I+ I
O T I* * C + I
M I + C C I
P A P I + * I
O N L I * I
N D U I + I
E S I * + I
N I + C +I
T R I CI
E I I
S I I
I I I
D I I
U I I
A I I
L I I
S I I
I I
I I
I I
I I
I I
I I
I I
I I
I I
I I
I I
I I
I I
*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*----*-
0.000 4.000 8.000 12.000 16.000
0 INDEPENDENT VARIABLE 3: X1SQRD
0 RESIDUALS OUTSIDE OF PLOT