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.LM0;.RM75;.LC;.AP;.FLAG CAPITAL;.NO PAGING;.NO NUMBER;#
.BR;^MULTIPLE ^LINEAR ^REGRESSION ^ANALYSIS
.SK;^^STANDARD AND OPTIONAL PRINTED OUTPUT\\
 ^AFTER HAVING READ THE KEYWORD "^RUN", THE PROCESSING OF THE JOB 
IS INITIATED. ^FIRST THE MODEL, INPUT AND OPTION TEXTS ARE PRINTED IN 
THIS ORDER. ^NEXT AN ATTEMPT IS MADE AT TRANSLATING THE SPECIFICATIONS. 
^ERRORS AGAINST SYNTAX OR SEMANTICS CAUSE ERROR MESSAGES TO BE 
PRINTED BELOW EACH SPECIFICATION, WHILE FURTHER PROCESSING OF THAT JOB 
CEASES. ^NOTE THAT THE PROCESSING OF THE NEXT JOB, IF PRESENT, WILL BE OF LITTLE OR NO USE 
UNLESS THE SPECIFICATION WHICH DEVELOPED THE ERROR(S) IS CHANGED. 
^NEXT THE (TRANSFORMED) DATA MATRIX IS FORMED AND PASSED TO THE 
REGRESSION ROUTINES, WHICH SUPPLY THE FOLLOWING PRINTED OUTPUT IN THE ORDER 
INDICATED:
.LM+3;.SK;#1)#A LISTING OF THE ORIGINAL INPUT DATA (OPTION 6),
.BR;#2)#THE (TRANSFORMED) DATA MATRIX (OPTION 1),
.BR;#3)#PER (TRANSFORMED) VARIABLE THE:
.BR;.I4;MEAN, STANDARD DEVIATION, MINIMUM AND MAXIMUM,
.BR;#4)#THE CORRELATION MATRIX OF THE (TRANSFORMED) VARIABLES (OPTION 2),
.BR;#5)#THE MULTIPLE CORRELATION COEFFICIENT (WITH ADJUSTMENT),
.BR;#6)#THE PROPORTION OF VARIATION EXPLAINED (WITH ADJUSTMENT),
.BR;#7)#THE STANDARD DEVIATION OF THE ERROR TERM,
.BR;#8)#THE ESTIMATES FOR THE REGRESSION PARAMETERS WITH
.BR;.I4;ESTIMATED STANDARD DEVIATION, ^F-RATIO AND RIGHT TAIL PROBABILITY,
.BR;#9)#THE CORRELATION MATRIX OF THE ESTIMATES (OPTION 2),
.BR;10)#THE ANALYSIS OF VARIANCE TABLE,
.BR;11)#THE RESIDUAL ANALYSIS (OPTION 3).
.LM+4;.SK;.I-6;^AD#1)#CF.#"^HELP"/^DATA.
.BR;.I-6;^AD#2)#^THE TRANSFORMED DATA MATRIX GIVES THE INPUT DATA AFTER 
POSSIBLE TRANSFORMATIONS ACCORDING TO THE MODEL SPECIFICATIONS HAVE BEEN 
APPLIED. ^IF THE MODEL FORMULA CONTAINS NO TRANSFORMATIONS, THE ORIGINAL INPUT DATA 
ARE GIVEN. ^THE DEPENDENT VARIABLE IS GIVEN AS A SEPARATE COLUMN.
^IN THE CASE OF REPLICATIONS FOR THE DEPENDENT VARIABLE, THE MEAN VALUE OF THEM IS 
GIVEN, AND THE NUMBER OF REPLICATIONS IS GIVEN AS AN EXTRA (LAST) COLUMN. 
^IF A WEIGHT- VARIABLE (OR -EXPRESSION) IS SPECIFIED IN THE MODEL FORMULA, THE (TRANSFORMED) DATA COMPRISING THE WEIGHTS ARE GIVEN AS AN EXTRA (LAST) COLUMN.
^EACH (TRANSFORMED) INDEPENDENT VARIABLE IS INDICATED BY 
ITS CORRESPONDING PARAMETER. ^THIS ORIGINATED FROM THE FACT THAT
IT#IS#NOT OBVIOUS HOW TO DENOTE A VARIABLE WHICH IS TRANSFORMED LIKE:
^ARCSIN#(^SQRT#(Y+25)), WITH '^ARCSIN', WITH '^SQRT' OR PERHAPS WITH 'Y' ITSELF.
^THE DEPENDENT VARIABLE IS INDICATED BY 'DEP.VAR.'.
.BR;.I-6;^AD#4) AND 9) ^THE MATRIX OF THE ESTIMATED CORRELATION 
COEFFICIENTS OF THE VARIABLES AND OF THE ESTIMATES ARE BOTH SUPPLIED 
DEPENDING ON WHETHER OPTION 2 IS SPECIFIED OR NOT.
.BR;.I-6;^AD#5), 6) AND 7) CF.#"^HELP"/^THEORY.
.BR;.I-6;^AD#8)#^THE ^F-RATIO AND RIGHT TAIL PROBABILITY GIVE THE 
USER THE OPPORTUNITY TO TEST THE SIGNIFICANCE OF A PARTICULAR REGRESSION 
COEFFICIENT (CF.#"^HELP"/^TESTS).
.BR;.I-7;^AD#10)#^THE LAYOUT OF THE TABLE CLOSELY RESEMBLES THAT OF THE TABLE IN "^HELP"/^TESTS.
^THE ^F-RATIOS AND RIGHT TAIL PROBABILITIES GIVE THE 
USER THE OPPORTUNITY TO TEST THE SIGNIFICANCE OF ALL THE REGRESSION 
COEFFICIENTS OR OF A SUBSET OR COMBINATION THEREOF OR TO TEST THE ADEQUACY OF THE 
(LINEAR) MODEL (CF.#"^HELP"/^TESTS).
.BR;.I-7;^AD#11)#^A TABLE OF OBSERVATIONS, FITTED VALUES, STANDARD 
DEVIATIONS OF THE FITTED VALUES, RESIDUALS, STANDARDIZED RESIDUALS AND 
STUDENTIZED RESIDUALS IS PROVIDED (CF.#"^HELP"/^THEORY).
^AS A CHECK ON COMPUTA- TIONS, 
THE SUM OF THE RESIDUALS IS ALSO GIVEN. ^IF AN UNKNOWN CONSTANT TERM 
IS PRESENT IN THE MODEL FORMULA, THIS SUM SHOULD BE ZERO. ^FURTHERMORE THE 
UPPERBOUND FOR THE RIGHT TAIL PROBABILITY OF THE LARGEST ABSOLUTE STUDENTIZED 
RESIDUAL IS GIVEN.
.LM-7; ^WITHOUT OPTIONS SPECIFIED, THE PRINTED OUTPUT FROM THE PROGRAM CONSISTS 
OF 3), 5), 6), 7), 8) AND 10). ^IF OPTION 5 IS SPECIFIED, THE OUTPUT FOR THE 
MODEL ITSELF IS GIVEN AS SPECIFIED BY THE OTHER OPTIONS, BUT FOR THE 
SUBMODELS IT DEPENDS ON THE USE OF A SUBMODEL SPECIFIER LIST. 
^WITHOUT THAT LIST THE OUTPUT FROM THE OPTIONS 1, 2 AND 3 IS 
SUPPRESSED (EVEN IF THOSE OPTIONS ARE SPECIFIED). 
^WITH THAT LIST ONLY THE SUPERFLUOUS PARTS OF THE OUTPUT (THAT 
IS THE TRANSFORMED DATA MATRIX AND THE CORRELATION MATRIX OF THE 
VARIABLES) ARE SUPPRESSED.
.BR;#