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

556 CHAPTER 16 | Introduction to Regression
PROBLEMS
1. Sketch a graph showing the line for the equation
Y = 2X – 1. On the same graph, show the line for
Y = –X + 8.
2. The regression equation is intended to be the “best
fitting” straight line for a set of data. What is the
criterion for “best fitting”?
3. A set of n = 18 pairs of scores (X and Y values) has
SS X
= 20, SS Y
= 80, and SP = 10. If the mean for the
X values is M X
= 8 and the mean for the Y values is
M Y
= 10.
a. Calculate the Pearson correlation for the scores.
b. Find the regression equation for predicting Y from
the X values.
4. A set of n = 15 pairs of scores (X and Y values) produces
a regression equation of Ŷ = 2X + 6. Find the
predicted Y value for each of the following X scores:
0, 2, 3, and –4.
5. Briefly explain what is measured by the standard error
of estimate.
6. In general, how is the magnitude of the standard error
of estimate related to the value of the correlation?
7. For the following set of data, find the linear regression
equation for predicting Y from X:
X
Y
2 1
7 10
5 8
3 0
3 4
4 13
8. For the following data:
a. Find the regression equation for predicting Y from X.
b. Calculate the Pearson correlation for these data.
Use r 2 and SS Y
to compute SS residual
and the
standard error of estimate for the equation.
X
Y
3 3
6 9
5 8
4 3
7 10
5 9
9. Does the regression equation from problem 8 account
for a significant portion of the variance in the
Y scores? Use α = .05 to evaluate the F-ratio.
10. For the following scores,
X
Y
3 8
5 8
2 6
2 3
4 6
1 4
4 7
a. Find the regression equation for predicting Y from X.
b. Calculate the predicted Y value for each X.
11. Problem 13 in Chapter 15 examined the relationship
between weight and income for a sample of n = 8
men. Weights were classified in five categories
and had a mean of M = 3 with SS = 18. Income,
measured in thousands, had a mean score of M = 88
with SS = 21,609, and SP = 330.
a. Find the regression equation for predicting income
from weight. (Identify the weight scores as
X values and the income scores as Y values.)
b. What percentage of the variance in the income
is accounted for by the regression equation?
(Compute the correlation, r, then find r 2 .)
c. Does the regression equation account for a
significant portion of the variance in income?
Use α = .05 to evaluate the F-ratio.
12. A professor obtains SAT scores and freshman grade
point averages (GPAs) for a group of n = 15 college
students. The SAT scores have a mean of M = 580
with SS = 22,400, and the GPAs have a mean of
3.10 with SS = 1.26, and SP = 84.
a. Find the regression equation for predicting
GPA from SAT scores.
b. What percentage of the variance in GPAs is
accounted for by the regression equation?
(Compute the correlation, r, then find r 2 .)
c. Does the regression equation account for a
significant portion of the variance in GPA? Use
α = .05 to evaluate the F-ratio.
13. Problem 14 in Chapter 15 described a study
examining the effectiveness of a 7-Minute Screen
test for Alzheimer’s disease. The study evaluated
the relationship between scores from the 7-Minute
Screen and scores for the same patients from a set
of cognitive exams that are typically used to test for