Chapter 12 Exercises
Prerequisites
All
material presented in chapter 12
Selected answers
1. What is the equation for a regression line? What does each term in the line
refer to? (relevant
section)
2. The formula for a regression equation is Y' = 2X + 9. (a)
What would be the predicted score for a person scoring 6 on X?
(b) If someone's predicted score was 14, what was this person's
score on X? (relevant
section)
3. What criterion is used for deciding which regression line
fits best? (relevant
section)
4. What does the standard error of the estimate measure? What
is the formula for the standard error of the estimate? (relevant
section)
5. (a) In a regression analysis, the sum of squares for the predicted
scores is 100 and the sum of squares error is 200, what is R^{2}?
(b) In a different regression analysis, 40% of the variance was
explained. The sum of squares total is 1000. What is the sum of
squares of the predicted values? (relevant
section)
6. For the X,Y data below, compute:
(a) r and determine if it is significantly different from zero.
(b) the slope of the regression line and test if it differs significantly
from zero.
(c) the 95% confidence interval for the slope.
(relevant
section)
X 
Y 
2 
5 
4 
6 
4 
7 
5 
11 
6 
12 
7. What assumptions are needed to calculate the various inferential statistics
of linear regression? (relevant
section)
8. The correlation between years of education and salary in a
sample of 20 people from a certain company is .4. Is this correlation
statistically significant at the .05 level? (relevant
section)
9. A sample of X and Y scores is taken, and a regression line
is used to predict Y from X. If SSY' = 300, SSE = 500, and N =
50, what is: (relevant section relevant
section)
(a) SSY?
(b) the standard error of the estimate?
(c) R^{2}?
10. Using linear regression, find the predicted posttest score
for someone with a score of 43 on the pretest. (relevant
section)
Pre 
Post 
59 
56 
52 
63 
44 
55 
51 
50 
42 
66 
42 
48 
41 
58 
45 
36 
27 
13 
63 
50 
54 
81 
44 
56 
50 
64 
47 
50 
55 
63 
49 
57 
45 
73 
57 
63 
46 
46 
60 
60 
65 
47 
64 
73 
50 
58 
74 
85 
59 
44 
11. The equation for a regression line predicting the number
of hours of TV watched by children (Y) from the number of hours
of TV watched by their parents (X) is Y' = 4 + 1.2X. (a) If the
standard error of b is .4, is the slope statistically significant
at the .05 level? (relevant
section) (b) If the mean of X is 8, what is the mean of Y? (relevant
section)
12. Based on the table below, compute the regression line that
predicts Y from X. (relevant
section)
MX 
MY 
sX 
sY 
r 
10 
12 
2.5 
3.0 
0.6 
13. Does A or B have a larger standard error of the estimate?
(relevant
section)
14. True/false: If the slope of a simple linear regression line
is statistically significant, then the correlation will also always
be significant. (relevant
section)
15. True/false: If the slope of the relationship between X an
Y is larger for Population 1 than for Population 2, the correlation
will necesarily be larger in Population 1 than in Populstion 2.
Why or why not? (relevant
section)
16. True/false: If the correlation is .8, then 40% of the variance
is explained. (relevant
section)
17. True/false: If the actual Y score was 31, but the predicted
score was 28, then the error of prediction is 3. (relevant
section)
Questions from Case Studies:
The following question is from the Angry
Moods (AM) case study.
18. (AM#23) Find the regression line for predicting AngerOut
from ControlOut.
(a) What is the slope?
(b) What is the intercept?
(c) Is the relationship at least approximately linear?
(d) Test to see if the slope is significantly different from 0.
(e) What is the standard error of the estimate?
(relevant section, relevant
section, relevant section)
The following question is from the SAT
and GPA (SG) case study.
19. (SG#3) Find the regression line for predicting the overall
university GPA from the high school GPA.
(a) What is the slope?
(b) What is the yintercept?
(c) If someone had a 2.2 GPA in high school, what is the best estimate of
his or her college GPA?
(d) If someone had a 4.0 GPA in high school, what is the best estimate of
his or her college GPA?
(relevant section)
The following questions are from the Driving (D)
case study.
20. (D#5) What is the correlation between age and how often
the person chooses to drive in inclement weather? Is this correlation
statistically significant at the .01 level? Are older people more
or less likely to report that they drive in inclement weather?
(relevant section, relevant section )
21. (D#8) What is the correlation between how often a person chooses to
drive in inclement weather and the percentage of accidents the person believes
occur in inclement weather? Is this correlation significantly different from
0? (relevant section, relevant section )
22. (D#10) Use linear regression to predict how often someone
rides public transportation in inclement weather from what percentage
of accidents that person thinks occur in inclement weather. (Pubtran
by Accident)
(a) Create a scatter plot of this data and add a regression
line.
(b) What is the slope?
(c) What is the intercept?
(d) Is the relationship at least approximately linear?
(e) Test if the slope is significantly different from 0.
(f) Comment on possible assumption violations for the test of the slope.
(g) What is the standard error of the estimate?
(relevant section, relevant section, relevant section)
Answers:
2) (a) 21
5) (a) .33
6) (b) b = 1.91
9) (a) 800
12) a = 19.2
18) (e) 3.45
19) (c) 2.6
20) r = .43
22) (b) .35
