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Statistics for Managers Study Set 1
Exam 17: Getting Ready to Analyze Data
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Question 1
Multiple Choice
SCENARIO 17-1 A real estate builder wishes to determine how house size (House) is influenced by family income (Income) , family size (Size) , and education of the head of household (School) . House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT Regression Statistics
Ā MultipleĀ RĀ
0.865
Ā RĀ SquareĀ
0.748
Ā AdjustedĀ RĀ SquareĀ
0.726
Ā StandardĀ ErrorĀ
5.195
Ā ObservationsĀ
50
\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}
Ā MultipleĀ RĀ
Ā RĀ SquareĀ
Ā AdjustedĀ RĀ SquareĀ
Ā StandardĀ ErrorĀ
Ā ObservationsĀ
ā
0.865
0.748
0.726
5.195
50
ā
ANOVA
d
f
Ā SSĀ
Ā MSĀ
F
Ā SignifĀ
F
Ā RegressionĀ
3605.7736
1201.9245
0.0000
Ā ResidualĀ
1214.2264
26.3962
Ā TotalĀ
49
4820.0000
\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}
Ā RegressionĀ
Ā ResidualĀ
Ā TotalĀ
ā
df
49
ā
Ā SSĀ
3605.7736
1214.2264
4820.0000
ā
Ā MSĀ
1201.9245
26.3962
ā
F
ā
Ā SignifĀ
F
0.0000
ā
Ā CoeffĀ
Ā StdErrorĀ
t
Ā StatĀ
P
-valueĀ
Ā InterceptĀ
ā
1.6335
5.8078
ā
0.281
0.7798
Ā IncomeĀ
0.4485
0.1137
3.9545
0.0003
Ā SizeĀ
4.2615
0.8062
5.286
0.0001
Ā SchoolĀ
ā
0.6517
0.4319
ā
1.509
0.1383
\begin{array} { l c l c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}
Ā InterceptĀ
Ā IncomeĀ
Ā SizeĀ
Ā SchoolĀ
ā
Ā CoeffĀ
ā
1.6335
0.4485
4.2615
ā
0.6517
ā
Ā StdErrorĀ
5.8078
0.1137
0.8062
0.4319
ā
t
Ā StatĀ
ā
0.281
3.9545
5.286
ā
1.509
ā
P
-valueĀ
0.7798
0.0003
0.0001
0.1383
ā
-Referring to Scenario 17-1, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?
Question 2
True/False
Double-clicking a cell in a PivotTable causes Excel to drill down and display the underlying data in a new worksheet.
Question 3
Short Answer
SCENARIO 17-8 The superintendent of a school district wanted to predict the percentage of students passing a sixth- grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily mean of the percentage of students attending class (% Attendance), mean teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with
Y
=
%
Y = \%
Y
=
%
Passing as the dependent variable,
X
1
=
%
X _ { 1 } = \%
X
1
ā
=
%
Attendance,
X
2
=
X _ { 2 } =
X
2
ā
=
Salaries and
X
3
=
X _ { 3 } =
X
3
ā
=
Spending:
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
0.7930
Ā RĀ SquareĀ
0.6288
Ā AdjustedĀ RĀ
0.6029
Ā SquareĀ
Ā StandardĀ
10.4570
Ā ErrorĀ
Ā ObservationsĀ
47
\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7930 \\\text { R Square } & 0.6288 \\\text { Adjusted R } & 0.6029 \\\text { Square } & \\\text { Standard } & 10.4570 \\\text { Error } & \\\text { Observations } & 47 \\\hline\end{array}
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
Ā RĀ SquareĀ
Ā AdjustedĀ RĀ
Ā SquareĀ
Ā StandardĀ
Ā ErrorĀ
Ā ObservationsĀ
ā
0.7930
0.6288
0.6029
10.4570
47
ā
ā
ANOVA
Ā CoefficientsĀ
Ā StandardĀ
Ā ErrorĀ
Ā tĀ StatĀ
Ā P-valueĀ
Ā LowerĀ 95%Ā
Ā UpperĀ 95%Ā
Ā InterceptĀ
ā
753.4225
101.1149
ā
7.4511
0.0000
ā
957.3401
ā
549.5050
Ā %Ā AttendanceĀ
8.5014
1.0771
7.8929
0.0000
6.3292
10.6735
Ā SalaryĀ
0.000000685
0.0006
0.0011
0.9991
ā
0.0013
0.0013
Ā SpendingĀ
0.0060
0.0046
1.2879
0.2047
ā
0.0034
0.0153
\begin{array}{lrrrrrr}\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \\\text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\\text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}
Ā InterceptĀ
Ā %Ā AttendanceĀ
Ā SalaryĀ
Ā SpendingĀ
ā
Ā CoefficientsĀ
ā
753.4225
8.5014
0.000000685
0.0060
ā
Ā StandardĀ
Ā ErrorĀ
ā
101.1149
1.0771
0.0006
0.0046
ā
Ā tĀ StatĀ
ā
7.4511
7.8929
0.0011
1.2879
ā
Ā P-valueĀ
0.0000
0.0000
0.9991
0.2047
ā
Ā LowerĀ 95%Ā
ā
957.3401
6.3292
ā
0.0013
ā
0.0034
ā
Ā UpperĀ 95%Ā
ā
549.5050
10.6735
0.0013
0.0153
ā
ā
-Referring to Scenario 17-8, what is the value of the test statistic when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, taking into account the effect of all the other independent variables?
Question 4
True/False
SCENARIO 17-8 The superintendent of a school district wanted to predict the percentage of students passing a sixth- grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily mean of the percentage of students attending class (% Attendance), mean teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with
Y
=
%
Y = \%
Y
=
%
Passing as the dependent variable,
X
1
=
%
X _ { 1 } = \%
X
1
ā
=
%
Attendance,
X
2
=
X _ { 2 } =
X
2
ā
=
Salaries and
X
3
=
X _ { 3 } =
X
3
ā
=
Spending:
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
0.7930
Ā RĀ SquareĀ
0.6288
Ā AdjustedĀ RĀ
0.6029
Ā SquareĀ
Ā StandardĀ
10.4570
Ā ErrorĀ
Ā ObservationsĀ
47
\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7930 \\\text { R Square } & 0.6288 \\\text { Adjusted R } & 0.6029 \\\text { Square } & \\\text { Standard } & 10.4570 \\\text { Error } & \\\text { Observations } & 47 \\\hline\end{array}
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
Ā RĀ SquareĀ
Ā AdjustedĀ RĀ
Ā SquareĀ
Ā StandardĀ
Ā ErrorĀ
Ā ObservationsĀ
ā
0.7930
0.6288
0.6029
10.4570
47
ā
ā
ANOVA
Ā CoefficientsĀ
Ā StandardĀ
Ā ErrorĀ
Ā tĀ StatĀ
Ā P-valueĀ
Ā LowerĀ 95%Ā
Ā UpperĀ 95%Ā
Ā InterceptĀ
ā
753.4225
101.1149
ā
7.4511
0.0000
ā
957.3401
ā
549.5050
Ā %Ā AttendanceĀ
8.5014
1.0771
7.8929
0.0000
6.3292
10.6735
Ā SalaryĀ
0.000000685
0.0006
0.0011
0.9991
ā
0.0013
0.0013
Ā SpendingĀ
0.0060
0.0046
1.2879
0.2047
ā
0.0034
0.0153
\begin{array}{lrrrrrr}\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \\\text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\\text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}
Ā InterceptĀ
Ā %Ā AttendanceĀ
Ā SalaryĀ
Ā SpendingĀ
ā
Ā CoefficientsĀ
ā
753.4225
8.5014
0.000000685
0.0060
ā
Ā StandardĀ
Ā ErrorĀ
ā
101.1149
1.0771
0.0006
0.0046
ā
Ā tĀ StatĀ
ā
7.4511
7.8929
0.0011
1.2879
ā
Ā P-valueĀ
0.0000
0.0000
0.9991
0.2047
ā
Ā LowerĀ 95%Ā
ā
957.3401
6.3292
ā
0.0013
ā
0.0034
ā
Ā UpperĀ 95%Ā
ā
549.5050
10.6735
0.0013
0.0153
ā
ā
-Referring to Scenario 17-8, the null hypothesis
H
0
:
β
1
=
β
2
=
β
3
=
0
H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0
H
0
ā
:
β
1
ā
=
β
2
ā
=
β
3
ā
=
0
implies that percentage of students passing the proficiency test is not affected by any of the explanatory variables.
Question 5
Multiple Choice
SCENARIO 17-1 A real estate builder wishes to determine how house size (House) is influenced by family income (Income) , family size (Size) , and education of the head of household (School) . House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT Regression Statistics
Ā MultipleĀ RĀ
0.865
Ā RĀ SquareĀ
0.748
Ā AdjustedĀ RĀ SquareĀ
0.726
Ā StandardĀ ErrorĀ
5.195
Ā ObservationsĀ
50
\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}
Ā MultipleĀ RĀ
Ā RĀ SquareĀ
Ā AdjustedĀ RĀ SquareĀ
Ā StandardĀ ErrorĀ
Ā ObservationsĀ
ā
0.865
0.748
0.726
5.195
50
ā
ANOVA
d
f
Ā SSĀ
Ā MSĀ
F
Ā SignifĀ
F
Ā RegressionĀ
3605.7736
1201.9245
0.0000
Ā ResidualĀ
1214.2264
26.3962
Ā TotalĀ
49
4820.0000
\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}
Ā RegressionĀ
Ā ResidualĀ
Ā TotalĀ
ā
df
49
ā
Ā SSĀ
3605.7736
1214.2264
4820.0000
ā
Ā MSĀ
1201.9245
26.3962
ā
F
ā
Ā SignifĀ
F
0.0000
ā
Ā CoeffĀ
Ā StdErrorĀ
t
Ā StatĀ
P
-valueĀ
Ā InterceptĀ
ā
1.6335
5.8078
ā
0.281
0.7798
Ā IncomeĀ
0.4485
0.1137
3.9545
0.0003
Ā SizeĀ
4.2615
0.8062
5.286
0.0001
Ā SchoolĀ
ā
0.6517
0.4319
ā
1.509
0.1383
\begin{array} { l c l c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}
Ā InterceptĀ
Ā IncomeĀ
Ā SizeĀ
Ā SchoolĀ
ā
Ā CoeffĀ
ā
1.6335
0.4485
4.2615
ā
0.6517
ā
Ā StdErrorĀ
5.8078
0.1137
0.8062
0.4319
ā
t
Ā StatĀ
ā
0.281
3.9545
5.286
ā
1.509
ā
P
-valueĀ
0.7798
0.0003
0.0001
0.1383
ā
-Referring to Scenario 17-1, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?
Question 6
Short Answer
SCENARIO 17-12 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Atitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below:
-Referring to Scenario 17-12, what should be the decision ('reject' or 'do not reject') on the null hypothesis when testing whether LawnSize makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance?
Question 7
Multiple Choice
SCENARIO 17-1 A real estate builder wishes to determine how house size (House) is influenced by family income (Income) , family size (Size) , and education of the head of household (School) . House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT Regression Statistics
Ā MultipleĀ RĀ
0.865
Ā RĀ SquareĀ
0.748
Ā AdjustedĀ RĀ SquareĀ
0.726
Ā StandardĀ ErrorĀ
5.195
Ā ObservationsĀ
50
\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}
Ā MultipleĀ RĀ
Ā RĀ SquareĀ
Ā AdjustedĀ RĀ SquareĀ
Ā StandardĀ ErrorĀ
Ā ObservationsĀ
ā
0.865
0.748
0.726
5.195
50
ā
ANOVA
d
f
Ā SSĀ
Ā MSĀ
F
Ā SignifĀ
F
Ā RegressionĀ
3605.7736
1201.9245
0.0000
Ā ResidualĀ
1214.2264
26.3962
Ā TotalĀ
49
4820.0000
\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}
Ā RegressionĀ
Ā ResidualĀ
Ā TotalĀ
ā
df
49
ā
Ā SSĀ
3605.7736
1214.2264
4820.0000
ā
Ā MSĀ
1201.9245
26.3962
ā
F
ā
Ā SignifĀ
F
0.0000
ā
Ā CoeffĀ
Ā StdErrorĀ
t
Ā StatĀ
P
-valueĀ
Ā InterceptĀ
ā
1.6335
5.8078
ā
0.281
0.7798
Ā IncomeĀ
0.4485
0.1137
3.9545
0.0003
Ā SizeĀ
4.2615
0.8062
5.286
0.0001
Ā SchoolĀ
ā
0.6517
0.4319
ā
1.509
0.1383
\begin{array} { l c l c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}
Ā InterceptĀ
Ā IncomeĀ
Ā SizeĀ
Ā SchoolĀ
ā
Ā CoeffĀ
ā
1.6335
0.4485
4.2615
ā
0.6517
ā
Ā StdErrorĀ
5.8078
0.1137
0.8062
0.4319
ā
t
Ā StatĀ
ā
0.281
3.9545
5.286
ā
1.509
ā
P
-valueĀ
0.7798
0.0003
0.0001
0.1383
ā
-Referring to Scenario 17-1, what minimum annual income would an individual with a family size of 9 and 10 years of education need to attain a predicted 5,000 square foot home (House = 50) ?
Question 8
Multiple Choice
The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is related to the type of community (urban, rural, Suburban) in which an applicant resides. Which of the following tests will be the most Appropriate?
Question 9
Short Answer
SCENARIO 17-5 You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in EXCEL and obtained the following information:
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
0.63
Ā RĀ SquareĀ
0.40
Ā AdjustedĀ RĀ SquareĀ
0.23
Ā StandardĀ ErrorĀ
50.00
Ā ObservationsĀ
15.00
Ā ANOVAĀ
d
f
Ā SSĀ
Ā MSĀ
Ā FĀ
Ā SignificanceĀ
F
Ā RegressionĀ
3
5994.24
2.40
0.12
Ā ResidualĀ
11
27496.82
Ā TotalĀ
45479.54
Ā CoefficientsĀ
Ā StandardĀ
Ā ErrorĀ
Ā tĀ StatĀ
Ā P-valueĀ
Ā LowerĀ 99.0%Ā
Ā UpperĀ 99.0%Ā
Ā InterceptĀ
123.80
48.71
2.54
0.03
ā
27.47
275.07
Ā AGEĀ
ā
0.82
0.87
ā
0.95
0.36
ā
3.51
1.87
Ā TICKETSĀ
21.25
10.66
1.99
0.07
ā
11.86
54.37
Ā DENSITYĀ
ā
3.14
6.46
ā
0.49
0.64
ā
23.19
16.91
\begin{array}{l}\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.63 \\\text { R Square } & 0.40 \\\text { Adjusted R Square } & 0.23 \\\text { Standard Error } & 50.00 \\\text { Observations } & 15.00 \\\hline\end{array}\\\\\text { ANOVA }\\\begin{array}{lrcccr}\hline & d f &{\text { SS }} & \text { MS } & \text { F }&{\text { Significance } F} \\\hline \text { Regression } & 3 & & 5994.24 & 2.40 & 0.12 \\\text { Residual } & 11 & 27496.82 & & & \\\text { Total } & & 45479.54 & & & \\\hline\end{array}\\\\\begin{array}{lrrrrrr}\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 99.0\% } & \text { Upper 99.0\% } \\\hline \text { Intercept } & 123.80 & 48.71 & 2.54 & 0.03 & -27.47 & 275.07 \\\text { AGE } & -0.82 & 0.87 & -0.95 & 0.36 & -3.51 & 1.87 \\\text { TICKETS } & 21.25 & 10.66 & 1.99 & 0.07 & -11.86 & 54.37 \\\text { DENSITY } & -3.14 & 6.46 & -0.49 & 0.64 & -23.19 & 16.91 \\\hline\end{array}\end{array}
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
Ā RĀ SquareĀ
Ā AdjustedĀ RĀ SquareĀ
Ā StandardĀ ErrorĀ
Ā ObservationsĀ
ā
0.63
0.40
0.23
50.00
15.00
ā
ā
Ā ANOVAĀ
Ā RegressionĀ
Ā ResidualĀ
Ā TotalĀ
ā
df
3
11
ā
Ā SSĀ
27496.82
45479.54
ā
Ā MSĀ
5994.24
ā
Ā FĀ
2.40
ā
Ā SignificanceĀ
F
0.12
ā
ā
Ā InterceptĀ
Ā AGEĀ
Ā TICKETSĀ
Ā DENSITYĀ
ā
Ā CoefficientsĀ
123.80
ā
0.82
21.25
ā
3.14
ā
Ā StandardĀ
Ā ErrorĀ
ā
48.71
0.87
10.66
6.46
ā
Ā tĀ StatĀ
2.54
ā
0.95
1.99
ā
0.49
ā
Ā P-valueĀ
0.03
0.36
0.07
0.64
ā
Ā LowerĀ 99.0%Ā
ā
27.47
ā
3.51
ā
11.86
ā
23.19
ā
Ā UpperĀ 99.0%Ā
275.07
1.87
54.37
16.91
ā
ā
ā
AGE -0.82 0.87 -0.95 0.36 -3.51 1.87 TICKETS 21.25 10.66 1.99 0.07 -11.86 54.37 DENSITY -3.14 6.46 -0.49 0.64 -23.19 16.91 -Referring to Scenario 17-5, the total degrees of freedom that are missing in the ANOVA table should be ______.
Question 10
True/False
SCENARIO 17-8 The superintendent of a school district wanted to predict the percentage of students passing a sixth- grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily mean of the percentage of students attending class (% Attendance), mean teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with
Y
=
%
Y = \%
Y
=
%
Passing as the dependent variable,
X
1
=
%
X _ { 1 } = \%
X
1
ā
=
%
Attendance,
X
2
=
X _ { 2 } =
X
2
ā
=
Salaries and
X
3
=
X _ { 3 } =
X
3
ā
=
Spending:
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
0.7930
Ā RĀ SquareĀ
0.6288
Ā AdjustedĀ RĀ
0.6029
Ā SquareĀ
Ā StandardĀ
10.4570
Ā ErrorĀ
Ā ObservationsĀ
47
\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7930 \\\text { R Square } & 0.6288 \\\text { Adjusted R } & 0.6029 \\\text { Square } & \\\text { Standard } & 10.4570 \\\text { Error } & \\\text { Observations } & 47 \\\hline\end{array}
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
Ā RĀ SquareĀ
Ā AdjustedĀ RĀ
Ā SquareĀ
Ā StandardĀ
Ā ErrorĀ
Ā ObservationsĀ
ā
0.7930
0.6288
0.6029
10.4570
47
ā
ā
ANOVA
Ā CoefficientsĀ
Ā StandardĀ
Ā ErrorĀ
Ā tĀ StatĀ
Ā P-valueĀ
Ā LowerĀ 95%Ā
Ā UpperĀ 95%Ā
Ā InterceptĀ
ā
753.4225
101.1149
ā
7.4511
0.0000
ā
957.3401
ā
549.5050
Ā %Ā AttendanceĀ
8.5014
1.0771
7.8929
0.0000
6.3292
10.6735
Ā SalaryĀ
0.000000685
0.0006
0.0011
0.9991
ā
0.0013
0.0013
Ā SpendingĀ
0.0060
0.0046
1.2879
0.2047
ā
0.0034
0.0153
\begin{array}{lrrrrrr}\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \\\text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\\text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}
Ā InterceptĀ
Ā %Ā AttendanceĀ
Ā SalaryĀ
Ā SpendingĀ
ā
Ā CoefficientsĀ
ā
753.4225
8.5014
0.000000685
0.0060
ā
Ā StandardĀ
Ā ErrorĀ
ā
101.1149
1.0771
0.0006
0.0046
ā
Ā tĀ StatĀ
ā
7.4511
7.8929
0.0011
1.2879
ā
Ā P-valueĀ
0.0000
0.0000
0.9991
0.2047
ā
Ā LowerĀ 95%Ā
ā
957.3401
6.3292
ā
0.0013
ā
0.0034
ā
Ā UpperĀ 95%Ā
ā
549.5050
10.6735
0.0013
0.0153
ā
ā
-Referring to Scenario 17-8, you can conclude that mean teacher salary individually has no impact on the mean percentage of students passing the proficiency test, taking into account the effect of all the other independent variables, at a 1% level of significance based solely on the 95% confidence interval estimate for
β
2
\beta _ { 2 }
β
2
ā
.
Question 11
True/False
SCENARIO 17-10 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married:
1
=
1 =
1
=
married,
0
=
0 =
0
=
otherwise), a dummy variable for head of household (Head:
1
=
1 =
1
=
yes,
0
=
0 =
0
=
no) and a dummy variable for management position (Manager:
1
=
1 =
1
=
yes,
0
=
0 =
0
=
no). We shall call this Model 1. The coefficient of partial determination (
R
y
2
R _ { \mathrm { y } } ^ { 2 }
R
y
2
ā
(All raiables excopt
j
j
j
) ) of each of the 6 predictors are, respectively,
0.2807
0.2807
0.2807
,
0.0386
,
0.0317
,
0.0141
,
0.0958
0.0386,0.0317,0.0141,0.0958
0.0386
,
0.0317
,
0.0141
,
0.0958
, and
0.1201
0.1201
0.1201
.
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
0.7035
Ā RĀ SquareĀ
0.4949
Ā AdjustedĀ RĀ
0.4030
Ā SquareĀ
Ā StandardĀ
18.4861
Ā ErrorĀ
Ā ObservationsĀ
40
\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7035 \\\text { R Square } & 0.4949 \\\text { Adjusted R } & 0.4030 \\\text { Square } & \\\text { Standard } & 18.4861 \\\text { Error } & \\\text { Observations } & 40 \\\hline\end{array}
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
Ā RĀ SquareĀ
Ā AdjustedĀ RĀ
Ā SquareĀ
Ā StandardĀ
Ā ErrorĀ
Ā ObservationsĀ
ā
0.7035
0.4949
0.4030
18.4861
40
ā
ā
Ā ANOVAĀ
\text { ANOVA }
Ā ANOVAĀ
Ā CoefficientsĀ
Ā StandardĀ ErrorĀ
t
Ā StatĀ
Ā P-valueĀ
Ā LowerĀ 95%Ā
Ā UpperĀ 95%Ā
Ā InterceptĀ
32.6595
23.18302
1.4088
0.1683
ā
14.5067
79.8257
Ā AgeĀ
1.2915
0.3599
3.5883
0.0011
0.5592
2.0238
Ā EduĀ
ā
1.3537
1.1766
ā
1.1504
0.2582
ā
3.7476
1.0402
Ā JobĀ YrĀ
0.6171
0.5940
1.0389
0.3064
ā
0.5914
1.8257
Ā MarriedĀ
ā
5.2189
7.6068
ā
0.6861
0.4974
ā
20.6950
10.2571
Ā HeadĀ
ā
14.2978
7.6479
ā
1.8695
0.0704
ā
29.8575
1.2618
Ā ManagerĀ
ā
24.8203
11.6932
ā
2.1226
0.0414
ā
48.6102
ā
1.0303
\begin{array}{l}\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \\\hline\end{array}\end{array}
Ā InterceptĀ
Ā AgeĀ
Ā EduĀ
Ā JobĀ YrĀ
Ā MarriedĀ
Ā HeadĀ
Ā ManagerĀ
ā
Ā CoefficientsĀ
32.6595
1.2915
ā
1.3537
0.6171
ā
5.2189
ā
14.2978
ā
24.8203
ā
Ā StandardĀ ErrorĀ
23.18302
0.3599
1.1766
0.5940
7.6068
7.6479
11.6932
ā
t
Ā StatĀ
1.4088
3.5883
ā
1.1504
1.0389
ā
0.6861
ā
1.8695
ā
2.1226
ā
Ā P-valueĀ
0.1683
0.0011
0.2582
0.3064
0.4974
0.0704
0.0414
ā
Ā LowerĀ 95%Ā
ā
14.5067
0.5592
ā
3.7476
ā
0.5914
ā
20.6950
ā
29.8575
ā
48.6102
ā
Ā UpperĀ 95%Ā
79.8257
2.0238
1.0402
1.8257
10.2571
1.2618
ā
1.0303
ā
ā
ā
-Referring to Scenario 17-10 Model 1, the null hypothesis should be rejected at a 10% level of significance when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff.
Question 12
Multiple Choice
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the Proficiency test (% Passing) , daily mean of the percentage of students attending class (% Attendance) , mean teacher salary in dollars (Salaries) , and instructional spending per pupil in Dollars (Spending) of 47 schools in the state. She believed that holding everything else constant, Instructional spending per pupil had a positive but decreasing impact on percentage. Which of The following would be the most appropriate analysis to perform?
Question 13
Short Answer
SCENARIO 17-10 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married:
1
=
1 =
1
=
married,
0
=
0 =
0
=
otherwise), a dummy variable for head of household (Head:
1
=
1 =
1
=
yes,
0
=
0 =
0
=
no) and a dummy variable for management position (Manager:
1
=
1 =
1
=
yes,
0
=
0 =
0
=
no). We shall call this Model 1. The coefficient of partial determination (
R
y
2
R _ { \mathrm { y } } ^ { 2 }
R
y
2
ā
(All raiables excopt
j
j
j
) ) of each of the 6 predictors are, respectively,
0.2807
0.2807
0.2807
,
0.0386
,
0.0317
,
0.0141
,
0.0958
0.0386,0.0317,0.0141,0.0958
0.0386
,
0.0317
,
0.0141
,
0.0958
, and
0.1201
0.1201
0.1201
.
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
0.7035
Ā RĀ SquareĀ
0.4949
Ā AdjustedĀ RĀ
0.4030
Ā SquareĀ
Ā StandardĀ
18.4861
Ā ErrorĀ
Ā ObservationsĀ
40
\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7035 \\\text { R Square } & 0.4949 \\\text { Adjusted R } & 0.4030 \\\text { Square } & \\\text { Standard } & 18.4861 \\\text { Error } & \\\text { Observations } & 40 \\\hline\end{array}
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
Ā RĀ SquareĀ
Ā AdjustedĀ RĀ
Ā SquareĀ
Ā StandardĀ
Ā ErrorĀ
Ā ObservationsĀ
ā
0.7035
0.4949
0.4030
18.4861
40
ā
ā
Ā ANOVAĀ
\text { ANOVA }
Ā ANOVAĀ
Ā CoefficientsĀ
Ā StandardĀ ErrorĀ
t
Ā StatĀ
Ā P-valueĀ
Ā LowerĀ 95%Ā
Ā UpperĀ 95%Ā
Ā InterceptĀ
32.6595
23.18302
1.4088
0.1683
ā
14.5067
79.8257
Ā AgeĀ
1.2915
0.3599
3.5883
0.0011
0.5592
2.0238
Ā EduĀ
ā
1.3537
1.1766
ā
1.1504
0.2582
ā
3.7476
1.0402
Ā JobĀ YrĀ
0.6171
0.5940
1.0389
0.3064
ā
0.5914
1.8257
Ā MarriedĀ
ā
5.2189
7.6068
ā
0.6861
0.4974
ā
20.6950
10.2571
Ā HeadĀ
ā
14.2978
7.6479
ā
1.8695
0.0704
ā
29.8575
1.2618
Ā ManagerĀ
ā
24.8203
11.6932
ā
2.1226
0.0414
ā
48.6102
ā
1.0303
\begin{array}{l}\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \\\hline\end{array}\end{array}
Ā InterceptĀ
Ā AgeĀ
Ā EduĀ
Ā JobĀ YrĀ
Ā MarriedĀ
Ā HeadĀ
Ā ManagerĀ
ā
Ā CoefficientsĀ
32.6595
1.2915
ā
1.3537
0.6171
ā
5.2189
ā
14.2978
ā
24.8203
ā
Ā StandardĀ ErrorĀ
23.18302
0.3599
1.1766
0.5940
7.6068
7.6479
11.6932
ā
t
Ā StatĀ
1.4088
3.5883
ā
1.1504
1.0389
ā
0.6861
ā
1.8695
ā
2.1226
ā
Ā P-valueĀ
0.1683
0.0011
0.2582
0.3064
0.4974
0.0704
0.0414
ā
Ā LowerĀ 95%Ā
ā
14.5067
0.5592
ā
3.7476
ā
0.5914
ā
20.6950
ā
29.8575
ā
48.6102
ā
Ā UpperĀ 95%Ā
79.8257
2.0238
1.0402
1.8257
10.2571
1.2618
ā
1.0303
ā
ā
ā
-Referring to Scenario 17-10 Model 1, which of the following is the correct alternative hypothesis to test whether age has any effect on the number of weeks a worker is unemployed Due to a layoff while holding constant the effect of all the other independent variables? a)
H
1
:
β
0
ā
0
H _ { 1 } : \beta _ { 0 } \neq 0
H
1
ā
:
β
0
ā
ī
=
0
b)
H
1
:
β
1
ā
0
H _ { 1 } : \beta _ { 1 } \neq 0
H
1
ā
:
β
1
ā
ī
=
0
c)
H
1
:
β
2
ā
0
H _ { 1 } : \beta _ { 2 } \neq 0
H
1
ā
:
β
2
ā
ī
=
0
d)
H
1
:
β
3
ā
0
H _ { 1 } : \beta _ { 3 } \neq 0
H
1
ā
:
β
3
ā
ī
=
0
Question 14
Multiple Choice
An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the mean daily revenue was $675 with a standard deviation of $75. A Sample of 30 days reveals a daily mean revenue of $625 and a standard deviation of $70. Which Of the following tests will be the most appropriate?
Question 15
Multiple Choice
Which of the following is NOT one of the categories of predictive analytics methods?
Question 16
True/False
SCENARIO 17-12 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Atitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below:
-Referring to Scenario 17-12, there is not enough evidence to conclude that Teenager makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance.
Question 17
True/False
SCENARIO 17-10 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married:
1
=
1 =
1
=
married,
0
=
0 =
0
=
otherwise), a dummy variable for head of household (Head:
1
=
1 =
1
=
yes,
0
=
0 =
0
=
no) and a dummy variable for management position (Manager:
1
=
1 =
1
=
yes,
0
=
0 =
0
=
no). We shall call this Model 1. The coefficient of partial determination (
R
y
2
R _ { \mathrm { y } } ^ { 2 }
R
y
2
ā
(All raiables excopt
j
j
j
) ) of each of the 6 predictors are, respectively,
0.2807
0.2807
0.2807
,
0.0386
,
0.0317
,
0.0141
,
0.0958
0.0386,0.0317,0.0141,0.0958
0.0386
,
0.0317
,
0.0141
,
0.0958
, and
0.1201
0.1201
0.1201
.
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
0.7035
Ā RĀ SquareĀ
0.4949
Ā AdjustedĀ RĀ
0.4030
Ā SquareĀ
Ā StandardĀ
18.4861
Ā ErrorĀ
Ā ObservationsĀ
40
\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7035 \\\text { R Square } & 0.4949 \\\text { Adjusted R } & 0.4030 \\\text { Square } & \\\text { Standard } & 18.4861 \\\text { Error } & \\\text { Observations } & 40 \\\hline\end{array}
Ā RegressionĀ StatisticsĀ
Ā MultipleĀ RĀ
Ā RĀ SquareĀ
Ā AdjustedĀ RĀ
Ā SquareĀ
Ā StandardĀ
Ā ErrorĀ
Ā ObservationsĀ
ā
0.7035
0.4949
0.4030
18.4861
40
ā
ā
Ā ANOVAĀ
\text { ANOVA }
Ā ANOVAĀ
Ā CoefficientsĀ
Ā StandardĀ ErrorĀ
t
Ā StatĀ
Ā P-valueĀ
Ā LowerĀ 95%Ā
Ā UpperĀ 95%Ā
Ā InterceptĀ
32.6595
23.18302
1.4088
0.1683
ā
14.5067
79.8257
Ā AgeĀ
1.2915
0.3599
3.5883
0.0011
0.5592
2.0238
Ā EduĀ
ā
1.3537
1.1766
ā
1.1504
0.2582
ā
3.7476
1.0402
Ā JobĀ YrĀ
0.6171
0.5940
1.0389
0.3064
ā
0.5914
1.8257
Ā MarriedĀ
ā
5.2189
7.6068
ā
0.6861
0.4974
ā
20.6950
10.2571
Ā HeadĀ
ā
14.2978
7.6479
ā
1.8695
0.0704
ā
29.8575
1.2618
Ā ManagerĀ
ā
24.8203
11.6932
ā
2.1226
0.0414
ā
48.6102
ā
1.0303
\begin{array}{l}\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \\\hline\end{array}\end{array}
Ā InterceptĀ
Ā AgeĀ
Ā EduĀ
Ā JobĀ YrĀ
Ā MarriedĀ
Ā HeadĀ
Ā ManagerĀ
ā
Ā CoefficientsĀ
32.6595
1.2915
ā
1.3537
0.6171
ā
5.2189
ā
14.2978
ā
24.8203
ā
Ā StandardĀ ErrorĀ
23.18302
0.3599
1.1766
0.5940
7.6068
7.6479
11.6932
ā
t
Ā StatĀ
1.4088
3.5883
ā
1.1504
1.0389
ā
0.6861
ā
1.8695
ā
2.1226
ā
Ā P-valueĀ
0.1683
0.0011
0.2582
0.3064
0.4974
0.0704
0.0414
ā
Ā LowerĀ 95%Ā
ā
14.5067
0.5592
ā
3.7476
ā
0.5914
ā
20.6950
ā
29.8575
ā
48.6102
ā
Ā UpperĀ 95%Ā
79.8257
2.0238
1.0402
1.8257
10.2571
1.2618
ā
1.0303
ā
ā
ā
-Referring to Scenario 17-10 Model 1, the alternative hypothesis H1 : At least one of ?j ? 0 for j = 1, 2, 3, 4, 5, 6 implies that the number of weeks a worker is unemployed due to a layoff is affected by at least one of the explanatory variables.
Question 18
Multiple Choice
SCENARIO 17-1 A real estate builder wishes to determine how house size (House) is influenced by family income (Income) , family size (Size) , and education of the head of household (School) . House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT Regression Statistics
Ā MultipleĀ RĀ
0.865
Ā RĀ SquareĀ
0.748
Ā AdjustedĀ RĀ SquareĀ
0.726
Ā StandardĀ ErrorĀ
5.195
Ā ObservationsĀ
50
\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}
Ā MultipleĀ RĀ
Ā RĀ SquareĀ
Ā AdjustedĀ RĀ SquareĀ
Ā StandardĀ ErrorĀ
Ā ObservationsĀ
ā
0.865
0.748
0.726
5.195
50
ā
ANOVA
d
f
Ā SSĀ
Ā MSĀ
F
Ā SignifĀ
F
Ā RegressionĀ
3605.7736
1201.9245
0.0000
Ā ResidualĀ
1214.2264
26.3962
Ā TotalĀ
49
4820.0000
\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}
Ā RegressionĀ
Ā ResidualĀ
Ā TotalĀ
ā
df
49
ā
Ā SSĀ
3605.7736
1214.2264
4820.0000
ā
Ā MSĀ
1201.9245
26.3962
ā
F
ā
Ā SignifĀ
F
0.0000
ā
Ā CoeffĀ
Ā StdErrorĀ
t
Ā StatĀ
P
-valueĀ
Ā InterceptĀ
ā
1.6335
5.8078
ā
0.281
0.7798
Ā IncomeĀ
0.4485
0.1137
3.9545
0.0003
Ā SizeĀ
4.2615
0.8062
5.286
0.0001
Ā SchoolĀ
ā
0.6517
0.4319
ā
1.509
0.1383
\begin{array} { l c l c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}
Ā InterceptĀ
Ā IncomeĀ
Ā SizeĀ
Ā SchoolĀ
ā
Ā CoeffĀ
ā
1.6335
0.4485
4.2615
ā
0.6517
ā
Ā StdErrorĀ
5.8078
0.1137
0.8062
0.4319
ā
t
Ā StatĀ
ā
0.281
3.9545
5.286
ā
1.509
ā
P
-valueĀ
0.7798
0.0003
0.0001
0.1383
ā
-Referring to Scenario 17-1, what is the predicted house size (in hundreds of square feet) for an individual earning an annual income of $40,000, having a family size of 4, and going to school a Total of 13 years?
Question 19
True/False
Some business analytics involve starting with many variables, followed by filtering the data by exploring specific combinations of categorical values or numerical range. In Excel, this approach is mimicked by using a slicer.