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

558 CHAPTER 16 | Introduction to Regression
multiple regression to accomplish essentially the same
purpose. The data are as follows:
23. For the following data, find the multiple-regression
equation for predicting Y from X 1
and X 2
.
Number of
Crimes
Amount for
Prevention
Population
Size
3 6 1
4 7 1
6 3 1
7 4 1
8 11 2
9 12 2
11 8 2
12 9 2
13 16 3
14 17 3
16 13 3
17 14 3
a. Find the multiple regression equation for predicting
the number of crimes using the amount spent
on prevention and population as the two predictor
variables.
b. Find the value of R 2 for the regression equation.
22. For the data in problem 21, the correlation between
the number of crimes and population is r = 0.933,
which means that r 2 = 0.87 (87%) is the proportion
of variance in the number of crimes that is predicted
by population size. Does adding the amount spent on
crime prevention as a second variable in the multiple
regression equation add a significant amount to the
prediction? Test with α = .05.
X 1
X 2
Y
1 3 1
2 4 2
3 5 6
6 9 8
4 8 3
2 7 4
M = 3
SS X1
= 16
SP X1X2
= 18
SP X1Y
= 19
SP X2Y
= 21
M = 6
SS X2
= 28
M = 4
SS Y
= 34
24. A researcher evaluates the significance of a multipleregression
equation and obtains an F-ratio with
df = 2, 24. How many participants were in the
sample?