CHAPTER 13. SIMPLE LINEAR REGRESSION
1.
a)
b)
c)
d)
The Y-intercept (b0) represents the
predicted value of Y when X = 0.
change in estimated Y per unit change in X.
predicted value of Y.
variation around the sample regression line.
2.
a)
b)
c)
d)
The Y-intercept (b0) represents the
estimated average Y when X = 0.
change in estimated average Y per unit change in X.
predicted value of Y.
variation around the sample regression line.
3.
a)
b)
c)
d)
The slope (b1) represents
predicted value of Y when X = 0.
the estimated average change in Y per unit change in X.
the predicted value of Y.
variation around the line of regression.
4.
a)
b)
c)
d)
The least squares method minimizes which of the following?
SSR
SSE
SST
All of the above
SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative education job
experience on marketability in the work place. She takes a random sample of 4 students. For these 4, she finds out
how many times each had a cooperative education job and how many job offers they received upon graduation.
These data are presented in the table below.
Student
1
2
3
4
5.
Coop Jobs
1
2
1
0
Job Offer
4
6
3
1
Referring to Scenario 13-3, the least squares estimate of the slope is
.
ANSWER:
2.50
6.
Referring to Scenario 13-3, the least squares estimate of the Y-intercept is
ANSWER:
1.00
7.
Referring to Scenario 13-3, the prediction for the number of job offers for a person with 2 coop jobs is
.
ANSWER: 6
.
8.
Referring to Scenario 13-3, the total sum of squares (SST) is
.
ANSWER:
13.0
9.
Referring to Scenario 13-3, the regression sum of squares (SSR) is
.
ANSWER:
12.5
10.
Referring to Scenario 13-3, the error or residual sum of squares (SSE) is
.
ANSWER:
0.50
11.
Referring to Scenario 13-3, the coefficient of determination is
.
ANSWER:
0.962
12.
Referring to Scenario 13-3, the standard error of estimate is
.
ANSWER:
0.50
13.
Referring to Scenario 13-3, the coefficient of correlation is
.
ANSWER:
0.981
14. Referring to Scenario 13-3, suppose the director of cooperative education wants to construct a 95% confidenceinterval estimate for the mean number of job offers received by students who have had exactly one cooperative
education job. The t critical value she would use is
.
ANSWER:
4.3027
15. Referring to Scenario 13-3, suppose the director of cooperative education wants to construct a 95% confidence
interval estimate for the mean number of job offers received by students who have had exactly one cooperative
education job. The confidence interval is from
to
.
ANSWER:
2.424 to 4.576
16. Referring to Scenario 13-3, suppose the director of cooperative education wants to construct a 95% prediction
interval estimate for the number of job offers received by students who have had exactly one cooperative education
job. The prediction interval is from
to
.
ANSWER:
1.0947 to 5.9053
17. True or False: Referring to Scenario 13-3, suppose the director of cooperative education wants to construct two
95% confidence interval estimates. One is for the mean number of job offers received by students who have had exactly
one cooperative education job and one for students who have had two. The confidence interval for students who have
had one cooperative education job would be the wider of the two intervals.
ANSWER:
False
18. Referring to Scenario 13-3, suppose the director of cooperative education wants to construct a 95% prediction
interval for the number of job offers received by a student who has had exactly two cooperative education jobs. The t
critical value she would use is
.
ANSWER:
4.3027
19. Referring to Scenario 13-3, suppose the director of cooperative education wants to construct a 95%
prediction interval for the number of job offers received by a student who has had exactly two cooperative
education jobs. The prediction interval is from
to
.
ANSWER:
3.154 to 8.846
20. True or False: Referring to Scenario 13-3, suppose the director of cooperative education wants to
construct both a 95% confidence interval estimate and a 95% prediction interval for X = 2. The confidence
interval estimate would be the wider of the two intervals.
ANSWER:
False
21. Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis that the
population slope was equal to 0. The denominator of the test statistic is sb . The value of
1
.
sb in this sample1 is
ANSWER:
0.3536
22. Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis that
the population slope was equal to 0. The value of the test statistic is
.
ANSWER:
7.07
23. Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis that
the population slope was equal to 3.0. The value of the test statistic is
.
ANSWER:
-1.4142
Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis that the population slope was
equal to 0. For a test with a level of significance of 0.05, the null hypothesis should be rejected if the value of the test statistic is
.
ANSWER:
> 4.3027 or < -4.3027
24. Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis that the
population slope was equal to 3.0. For a test with a level of significance of 0.05, the null hypothesis should be rejected
if the value of the test statistic is
.
ANSWER:
> 4.3027 or < -4.3027
25. Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis that the
population slope was equal to 0. The p-value of the test is between
and
.
ANSWER:
0.01 and 0.02 using the Table, or 0.0194 using Excel or Minitab
SCENARIO 13-6
The following Excel tables are obtained when "Score received on an exam (measured in percentage points)" (Y) is
regressed on "percentage attendance" (X) for 22 students in a Statistics for Business and Economics course.
Regression Statistics
Multiple R
R Square
Standard Error
Observations
Intercept
Attendance
26.
a)
b)
c)
d)
27.
0.142620229
0.02034053
20.25979924
22
Coefficients
Standard Error
39.39027309
37.24347659
0.340583573
0.52852452
T Stat
1.057642216
0.644404489
P-value
0.302826622
0.526635689
Referring to Scenario 13-6, which of the following statements is true?
14.26% of the total variability in score received can be explained by percentage attendance.
14.2% of the total variability in percentage attendance can be explained by score received.
2% of the total variability in score received can be explained by percentage attendance.
2% of the total variability in percentage attendance can be explained by score received.
Referring to Scenario 13-6, which of the following statements is true?
a) If attendance increases by 0.341%, the estimated mean score received will increase by 1 percentage point.
b) If attendance increases by 1%, the estimated mean score received will increase by 39.39 percentage points.
c) If attendance increases by 1%, the estimated mean score received will increase by 0.341 percentage
points.
d) If the score received increases by 39.39%, the estimated mean attendance will go up by 1%.