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

544 CHAPTER 16 | Introduction to Regression
LEARNING CHECK
1. A researcher obtains a correlation of r = 0.60 for a set of n = 18 pairs of X and
Y values. If the Y scores have SS = 100, then what is the standard error of estimate
for the regression equation for predicting Y from X?
a. 2 points
b. 4 points
c. 8 points
d. 16 points
2. A researcher conducts an analysis of regression to evaluate the significance of the
regression equation and obtains F = 4.25 with df = 1, 24. How many pairs of X and
Y values were in the original data?
a. 23
b. 24
c. 25
d. 26
ANSWERS
1. A, 2. D
16.3 Introduction to Multiple Regression
with Two Predictor Variables
Thus far, we have looked at regression in situations in which one variable is being used to
predict a second variable. For example, IQ scores can be used to predict academic performance
for a group of college students. However, a variable such as academic performance
is usually related to a variety of other factors. For example, college GPA is probably related
to motivation, self-esteem, SAT score, rank in high school graduating class, parents’ highest
level of education, and many other variables. In this case, it is possible to combine
several predictor variables to obtain a more accurate prediction. For example, IQ predicts
some of academic performance, but you can probably get a better prediction if you use IQ
and SAT scores together. The process of using several predictor variables to help obtain
more accurate predictions is called multiple regression.
Although it is possible to combine a large number of predictor variables in a single
multiple-regression equation, we limit our discussion to the two-predictor case. There are
two practical reasons for this limitation.
1. Multiple regression, even limited to two predictors, can be relatively complex.
Although we present equations for the two-predictor case, the calculations are
usually performed by a computer, so there is not much point in developing a set
of complex equations when people are going to use a computer instead.
2. Usually, different predictor variables are related to each other, which means that
they are often measuring and predicting the same thing. Because the variables may
overlap with each other, adding another predictor variable to a regression equation
does not always add to the accuracy of prediction. This situation is shown in
Figure 16.7. In the figure, IQ overlaps with academic performance, which means