HP -15C Advanced Functions Handbook page 136

134 Section 4: Using Matrix Operations
The program calculates the regression sum of squares unadjusted
for the mean because a constant term may not be in the model. To
include a constant term, include in the model a variable that is
identically equal to one. The corresponding parameter is then the
constant term.
To calculate the mean-adjusted regression sum of squares for a
model containing a constant term, first use the program to fit the
model and to find the unadjusted regression sum of squares. Then
fit the simpler model y = b± + r by dropping all variables but the
one identically equal to one (b-\, for example) and find the
regression sum of squares for this model, (Reg SS)
C
. The mean-
adjusted regression sum of squares (Reg SS)
A
= Reg SS ~
(Reg SS)
C
. Then the ANOVA table becomes:
ANOVA Table
Source
Regression |
Constant
Constant
Residual
Total
Degrees of
Freedom
p-\
n p
n
Sum of
Squares
(RegSS)
A
(RegSS)
c
ResSS
TotSS
Mean
Square
(FtegSS)
A
(P-D
(ResSS)
c
(ResSS)
(n-p)
F Ratio
(RegMS)
A
(Res MS)
You can then use the F ratio to test whether the full model fits data
significantly better than the simpler model y = b± + r.
You may want to perform a series of regressions, dropping
independent variables between each. To do this, order the variables
in the reverse order that they will be dropped from the model. They
can be dropped by transposing the matrix A, redimensioning A to
have fewer rows, and then transposing A once again.
You will need the original dependent variable data for each
regression. If there is not enough room to store the original data in
matrix E, you can compute it from the output of the regression fit.
A subroutine has been included to do this.