Chapter 22 2 After Some Consideration Developed The Multiple Regression

subject Type Homework Help
subject Pages 11
subject Words 2734
subject Textbook Business Statistics 5th Edition
subject Authors Eliyathamby A. Selvanathan, Gerald Keller, Saroja Selvanathan
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page-pf1
10. An actuary wanted to develop a model to predict how long individuals will live. After consulting a
number of physicians, she collected the age at death (y), the average number of hours of exercise per
week (
1
x
), the cholesterol level (
2
x
), and the number of points by which the individual’s blood
pressure exceeded the recommended value (
3
x
). A random sample of 40 individuals was selected. The
computer output of the multiple regression model is shown below:
THE REGRESSION EQUATION IS
=y
321 016.0021.079.18.55 xxx −−+
Predictor
Coef
StDev
Constant
55.8
11.8
1
x
1.79
0.44
2
x
–0.021
0.011
3
x
–0.016
0.014
S = 9.47 R-Sq = 22.5%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
936
312
3.477
Error
36
3230
89.722
Total
39
4166
Is there enough evidence at the 5% significance level to infer that the cholesterol level and the age at
death are negatively linearly related?
11. An actuary wanted to develop a model to predict how long individuals will live. After consulting a
number of physicians, she collected the age at death (y), the average number of hours of exercise per
week (
1
x
), the cholesterol level (
2
x
), and the number of points by which the individual’s blood
pressure exceeded the recommended value (
3
x
). A random sample of 40 individuals was selected. The
computer output of the multiple regression model is shown below:
page-pf2
THE REGRESSION EQUATION IS
=y
321 016.0021.079.18.55 xxx −−+
Predictor
Coef
StDev
Constant
55.8
11.8
1
x
1.79
0.44
2
x
–0.021
0.011
3
x
–0.016
0.014
S = 9.47 R-Sq = 22.5%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
936
312
3.477
Error
36
3230
89.722
Total
39
4166
Is there enough evidence at the 5% significance level to infer that the number of points by which the
individual’s blood pressure exceeded the recommended value and the age at death are negatively
linearly related?
12. An actuary wanted to develop a model to predict how long individuals will live. After consulting a
number of physicians, she collected the age at death (y), the average number of hours of exercise per
week (
1
x
), the cholesterol level (
2
x
), and the number of points by which the individual’s blood
pressure exceeded the recommended value (
3
x
). A random sample of 40 individuals was selected. The
computer output of the multiple regression model is shown below:
THE REGRESSION EQUATION IS
=y
321 016.0021.079.18.55 xxx −−+
Predictor
Coef
StDev
Constant
55.8
11.8
1
x
1.79
0.44
2
x
–0.021
0.011
3
x
–0.016
0.014
S = 9.47 R-Sq = 22.5%.
page-pf3
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
936
312
3.477
Error
36
3230
89.722
Total
39
4166
What is the coefficient of determination? What does this statistic tell you?
13. An actuary wanted to develop a model to predict how long individuals will live. After consulting a
number of physicians, she collected the age at death (y), the average number of hours of exercise per
week (
1
x
), the cholesterol level (
2
x
), and the number of points by which the individual’s blood
pressure exceeded the recommended value (
3
x
). A random sample of 40 individuals was selected. The
computer output of the multiple regression model is shown below:
THE REGRESSION EQUATION IS
=y
321 016.0021.079.18.55 xxx −−+
Predictor
Coef
StDev
Constant
55.8
11.8
1
x
1.79
0.44
2
x
–0.021
0.011
3
x
–0.016
0.014
S = 9.47 R-Sq = 22.5%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
936
312
3.477
Error
36
3230
89.722
Total
39
4166
Interpret the coefficient
2
b
.
page-pf4
14. A statistician wanted to determine whether the demographic variables of age, education and income
influence the number of hours of television watched per week. A random sample of 25 adults was
selected to estimate the multiple regression model
++++= 3322110 xxxy
.
Where:
y = number of hours of television watched last week.
1
x
= age.
2
x
= number of years of education.
3
x
= income (in $1000s).
The computer output is shown below.
THE REGRESSION EQUATION IS
=y
321 12.029.041.03.22 xxx −−+
Predictor
Coef
StDev
T
Constant
22.3
10.7
2.084
1
x
0.41
0.19
2.158
2
x
–0.29
0.13
–2.231
3
x
–0.12
0.03
–4.00
S = 4.51 R-Sq = 34.8%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
227
75.667
3.730
Error
21
426
20.286
Total
24
653
Test the overall validity of the model at the 5% significance level.
15. A statistician wanted to determine whether the demographic variables of age, education and income
influence the number of hours of television watched per week. A random sample of 25 adults was
selected to estimate the multiple regression model
++++= 3322110 xxxy
.
Where:
y = number of hours of television watched last week.
1
x
= age.
2
x
= number of years of education.
3
x
= income (in $1000s).
The computer output is shown below.
page-pf5
THE REGRESSION EQUATION IS
=y
321 12.029.041.03.22 xxx −−+
Predictor
Coef
StDev
T
Constant
22.3
10.7
2.084
1
x
0.41
0.19
2.158
2
x
–0.29
0.13
–2.231
3
x
–0.12
0.03
–4.00
S = 4.51 R-Sq = 34.8%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
227
75.667
3.730
Error
21
426
20.286
Total
24
653
Is there sufficient evidence at the 1% significance level to indicate that hours of television watched and
age are linearly related?
16. A statistician wanted to determine whether the demographic variables of age, education and income
influence the number of hours of television watched per week. A random sample of 25 adults was
selected to estimate the multiple regression model
++++= 3322110 xxxy
.
Where:
y = number of hours of television watched last week.
1
x
= age.
2
x
= number of years of education.
3
x
= income (in $1000s).
The computer output is shown below.
THE REGRESSION EQUATION IS
=y
321 12.029.041.03.22 xxx −−+
Predictor
Coef
StDev
T
Constant
22.3
10.7
2.084
1
x
0.41
0.19
2.158
2
x
–0.29
0.13
–2.231
3
x
–0.12
0.03
–4.00
page-pf6
S = 4.51 R-Sq = 34.8%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
227
75.667
3.730
Error
21
426
20.286
Total
24
653
Is there sufficient evidence at the 1% significance level to indicate that hours of television watched and
education are negatively linearly related?
17. A statistician wanted to determine whether the demographic variables of age, education and income
influence the number of hours of television watched per week. A random sample of 25 adults was
selected to estimate the multiple regression model
++++= 3322110 xxxy
.
Where:
y = number of hours of television watched last week.
1
x
= age.
2
x
= number of years of education.
3
x
= income (in $1000s).
The computer output is shown below.
THE REGRESSION EQUATION IS
=y
321 12.029.041.03.22 xxx −−+
Predictor
Coef
StDev
T
Constant
22.3
10.7
2.084
1
x
0.41
0.19
2.158
2
x
–0.29
0.13
–2.231
3
x
–0.12
0.03
–4.00
S = 4.51 R-Sq = 34.8%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
227
75.667
3.730
Error
21
426
20.286
Total
24
653
page-pf7
What is the coefficient of determination? What does this statistic tell you?
18. A statistician wanted to determine whether the demographic variables of age, education and income
influence the number of hours of television watched per week. A random sample of 25 adults was
selected to estimate the multiple regression model
++++= 3322110 xxxy
.
Where:
y = number of hours of television watched last week.
1
x
= age.
2
x
= number of years of education.
3
x
= income (in $1000s).
The computer output is shown below.
THE REGRESSION EQUATION IS
=y
321 12.029.041.03.22 xxx −−+
Predictor
Coef
StDev
T
Constant
22.3
10.7
2.084
1
x
0.41
0.19
2.158
2
x
–0.29
0.13
–2.231
3
x
–0.12
0.03
–4.00
S = 4.51 R-Sq = 34.8%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
227
75.667
3.730
Error
21
426
20.286
Total
24
653
Interpret the coefficient
2
b
.
19. An economist wanted to develop a multiple regression model to enable him to predict the annual
family expenditure on clothes. After some consideration, he developed the multiple regression model:
++++= 3322110 xxxy
.
Where:
page-pf8
y = annual family clothes expenditure (in $1000s)
1
x
= annual household income (in $1000s)
2
x
= number of family members
3
x
= number of children under 10 years of age
The computer output is shown below.
THE REGRESSION EQUATION IS
=y
321 26.093.0091.074.1 xxx +++
Predictor
Coef
StDev
T
Constant
1.74
0.630
2.762
1
x
0.091
0.025
3.640
2
x
0.93
0.290
3.207
3
x
0.26
0.180
1.444
S = 2.06 R-Sq = 59.6%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
288
96
22.647
Error
46
195
4.239
Total
49
483
Test the overall model’s validity at the 5% significance level.
20. An economist wanted to develop a multiple regression model to enable him to predict the annual
family expenditure on clothes. After some consideration, he developed the multiple regression model:
++++= 3322110 xxxy
.
Where:
y = annual family clothes expenditure (in $1000s)
1
x
= annual household income (in $1000s)
2
x
= number of family members
3
x
= number of children under 10 years of age
The computer output is shown below.
page-pf9
THE REGRESSION EQUATION IS
=y
321 26.093.0091.074.1 xxx +++
Predictor
Coef
StDev
T
Constant
1.74
0.630
2.762
1
x
0.091
0.025
3.640
2
x
0.93
0.290
3.207
3
x
0.26
0.180
1.444
S = 2.06 R-Sq = 59.6%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
288
96
22.647
Error
46
195
4.239
Total
49
483
Test at the 5% significance level to determine whether annual household income and annual family
clothes expenditure are positively linearly related.
21. An economist wanted to develop a multiple regression model to enable him to predict the annual
family expenditure on clothes. After some consideration, he developed the multiple regression model:
++++= 3322110 xxxy
.
Where:
y = annual family clothes expenditure (in $1000s)
1
x
= annual household income (in $1000s)
2
x
= number of family members
3
x
= number of children under 10 years of age
The computer output is shown below.
THE REGRESSION EQUATION IS
=y
321 26.093.0091.074.1 xxx +++
Predictor
Coef
StDev
T
Constant
1.74
0.630
2.762
1
x
0.091
0.025
3.640
2
x
0.93
0.290
3.207
3
x
0.26
0.180
1.444
page-pfa
S = 2.06 R-Sq = 59.6%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
288
96
22.647
Error
46
195
4.239
Total
49
483
Test at the 1% significance level to determine whether the number of family members and annual
family clothes expenditure are linearly related.
22. An economist wanted to develop a multiple regression model to enable him to predict the annual
family expenditure on clothes. After some consideration, he developed the multiple regression model:
++++= 3322110 xxxy
.
Where:
y = annual family clothes expenditure (in $1000s)
1
x
= annual household income (in $1000s)
2
x
= number of family members
3
x
= number of children under 10 years of age
The computer output is shown below.
THE REGRESSION EQUATION IS
=y
321 26.093.0091.074.1 xxx +++
Predictor
Coef
StDev
T
Constant
1.74
0.630
2.762
1
x
0.091
0.025
3.640
2
x
0.93
0.290
3.207
3
x
0.26
0.180
1.444
S = 2.06 R-Sq = 59.6%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
288
96
22.647
Error
46
195
4.239
Total
49
483
What is the coefficient of determination? What does this statistic tell you?
page-pfb
23. An economist wanted to develop a multiple regression model to enable him to predict the annual
family expenditure on clothes. After some consideration, he developed the multiple regression model:
++++= 3322110 xxxy
.
Where:
y = annual family clothes expenditure (in $1000s)
1
x
= annual household income (in $1000s)
2
x
= number of family members
3
x
= number of children under 10 years of age
The computer output is shown below.
THE REGRESSION EQUATION IS
=y
321 26.093.0091.074.1 xxx +++
Predictor
Coef
StDev
T
Constant
1.74
0.630
2.762
1
x
0.091
0.025
3.640
2
x
0.93
0.290
3.207
3
x
0.26
0.180
1.444
S = 2.06 R-Sq = 59.6%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
288
96
22.647
Error
46
195
4.239
Total
49
483
Interpret the coefficient
2
b
.
24. A statistics professor investigated some of the factors that affect an individual student’s final grade in
his or her course. He proposed the multiple regression model:
++++= 3322110 xxxy
.
page-pfc
Where:
y = final mark (out of 100).
1
x
= number of lectures skipped.
2
x
= number of late assignments.
3
x
= mid-term test mark (out of 100).
The professor recorded the data for 50 randomly selected students. The computer output is shown
below.
THE REGRESSION EQUATION IS
ö
y
=
321 63.17.118.36.41 xxx +−−
Predictor
Coef
StDev
Constant
41.6
17.8
1
x
–3.18
1.66
2
x
–1.17
1.13
3
x
0.63
0.13
S = 13.74 R-Sq = 30.0%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
3716
1238.667
6.558
Error
46
8688
188.870
Total
49
12404
What is the coefficient of determination? What does this statistic tell you?
25. A statistics professor investigated some of the factors that affect an individual student’s final grade in
his or her course. He proposed the multiple regression model:
++++= 3322110 xxxy
.
Where:
y = final mark (out of 100).
1
x
= number of lectures skipped.
2
x
= number of late assignments.
3
x
= mid-term test mark (out of 100).
The professor recorded the data for 50 randomly selected students. The computer output is shown
below.
page-pfd
THE REGRESSION EQUATION IS
ö
y
=
321 63.17.118.36.41 xxx +−−
Predictor
Coef
StDev
Constant
41.6
17.8
1
x
–3.18
1.66
2
x
–1.17
1.13
3
x
0.63
0.13
S = 13.74 R-Sq = 30.0%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
3716
1238.667
6.558
Error
46
8688
188.870
Total
49
12404
Do these data provide enough evidence to conclude at the 5% significance level that the model is
useful in predicting the final mark?
26. A statistics professor investigated some of the factors that affect an individual student’s final grade in
his or her course. He proposed the multiple regression model:
++++= 3322110 xxxy
.
Where:
y = final mark (out of 100).
1
x
= number of lectures skipped.
2
x
= number of late assignments.
3
x
= mid-term test mark (out of 100).
The professor recorded the data for 50 randomly selected students. The computer output is shown
below.
page-pfe
THE REGRESSION EQUATION IS
ö
y
=
321 63.17.118.36.41 xxx +−−
Predictor
Coef
StDev
Constant
41.6
17.8
1
x
–3.18
1.66
2
x
–1.17
1.13
3
x
0.63
0.13
S = 13.74 R-Sq = 30.0%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
3716
1238.667
6.558
Error
46
8688
188.870
Total
49
12404
Do these data provide enough evidence to conclude at the 5% significance level that the final mark and
the number of skipped lectures are linearly related?
27. A statistics professor investigated some of the factors that affect an individual student’s final grade in
his or her course. He proposed the multiple regression model:
++++= 3322110 xxxy
.
Where:
y = final mark (out of 100).
1
x
= number of lectures skipped.
2
x
= number of late assignments.
3
x
= mid-term test mark (out of 100).
The professor recorded the data for 50 randomly selected students. The computer output is shown
below.
page-pff
THE REGRESSION EQUATION IS
ö
y
=
321 63.17.118.36.41 xxx +−−
Predictor
Coef
StDev
Constant
41.6
17.8
1
x
–3.18
1.66
2
x
–1.17
1.13
3
x
0.63
0.13
S = 13.74 R-Sq = 30.0%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
3716
1238.667
6.558
Error
46
8688
188.870
Total
49
12404
Do these data provide enough evidence at the 5% significance level to conclude that the final mark and
the number of late assignments are negatively linearly related?
28. A statistics professor investigated some of the factors that affect an individual student’s final grade in
his or her course. He proposed the multiple regression model:
++++= 3322110 xxxy
.
Where:
y = final mark (out of 100).
1
x
= number of lectures skipped.
2
x
= number of late assignments.
3
x
= mid-term test mark (out of 100).
The professor recorded the data for 50 randomly selected students. The computer output is shown
below.
page-pf10
THE REGRESSION EQUATION IS
ö
y
=
321 63.17.118.36.41 xxx +−−
Predictor
Coef
StDev
Constant
41.6
17.8
1
x
–3.18
1.66
2
x
–1.17
1.13
3
x
0.63
0.13
S = 13.74 R-Sq = 30.0%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
3716
1238.667
6.558
Error
46
8688
188.870
Total
49
12404
Do these data provide enough evidence at the 1% significance level to conclude that the final mark and
the mid-term mark are positively linearly related?
29. A statistics professor investigated some of the factors that affect an individual student’s final grade in
his or her course. He proposed the multiple regression model:
++++= 3322110 xxxy
.
Where:
y = final mark (out of 100).
1
x
= number of lectures skipped.
2
x
= number of late assignments.
3
x
= mid-term test mark (out of 100).
The professor recorded the data for 50 randomly selected students. The computer output is shown
below.
page-pf11
THE REGRESSION EQUATION IS
ö
y
=
321 63.17.118.36.41 xxx +−−
Predictor
Coef
StDev
Constant
41.6
17.8
1
x
–3.18
1.66
2
x
–1.17
1.13
3
x
0.63
0.13
S = 13.74 R-Sq = 30.0%.
ANALYSIS OF VARIANCE
Source of Variation
df
SS
MS
F
Regression
3
3716
1238.667
6.558
Error
46
8688
188.870
Total
49
12404
Interpret the coefficients
1
b
and
3
b
.

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