Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

548 CHAPTER 16 | Introduction to Regression
Model Summary
Model
R
R Square
Adjusted R
Square
Std. Error of
the Estimate
1
.746 a .557 .430 2.38788
a. Predictors: (Constant), VAR00003, VAR00002
ANOVA b
Model
Sum of
Squares
df Mean Square F Sig.
1 Regression
50.086
2
25.043 4.392 .058 a
Residual
39.914
7
5.702
Total
90.000
9
a. Predictors: (Constant), VAR00003, VAR00002
b. Dependent Variable: VAR00001
Coefficients a
Unstandardized Coefficients
Standardized
Coefficients
Model
B Std. Error Beta t Sig.
1
(Constant)
2.552
1.944
1.313
.231
VAR00002
.672
.407
.558
1.652
.142
VAR00003
.293
.401
.247
.732
.488
a. Dependent Variable: VAR00001
F I G U R E 16.8
The SPSS output for the multiple regression in Example 16.6.
The unpredicted, or residual, variance is determined by 1 – R 2 . For the data in Table 16.2,
this is
SS residual
= (1 – R 2 )SS Y
= 0.4438(90) = 39.94
■ The Standard Error of Estimate
On p. 538 we defined the standard error of estimate for a linear regression equation as the
standard distance between the regression line and the actual data points. In more general
terms, the standard error of estimate can be defined as the standard distance between the
predicted Y values (from the regression equation) and the actual Y values (in the data). The
more general definition applies equally well to both linear and multiple regression.
To find the standard error of estimate for either linear regression or multiple regression,
we begin with SS residual
. For linear regression with one predictor, SS residual
= (1 – r 2 )SS Y
and