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Multiple Linear Regression Analysis
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:
1) a listing of the original input data (option 6),
2) the (transformed) data matrix (option 1),
3) per (transformed) variable the:
mean, standard deviation, minimum and maximum,
4) the correlation matrix of the (transformed) variables (option 2),
5) the multiple correlation coefficient (with adjustment),
6) the proportion of variation explained (with adjustment),
7) the standard deviation of the error term,
8) the estimates for the regression parameters with
estimated standard deviation, F-ratio and right tail probability,
9) the correlation matrix of the estimates (option 2),
10) the analysis of variance table,
11) the residual analysis (option 3).
Ad 1) cf. "Help"/Data.
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.'.
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.
Ad 5), 6) and 7) cf. "Help"/Theory.
Ad 8) The F-ratio and right tail probability give the user the opportunity
to test the significance of a particular regression coefficient
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).
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.
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.