TABLE 14-4 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: $\begin{array}{ll} & \text { Regression Stuistics } \\ \hline \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } &50 \\ \hline \end{array}$ ANOVA $\begin{array}{lrrrrr} \hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\ \hline \text {Regression} & & 3605.7736 & 1201.9245 & &0.0000 \\ \text {Residual} & & 1214.2264 & 26.3962 & \\ Total & 49 & 4820.0000 & & & \\ \hline \end{array}$ $\begin{array}{lcccc} \hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\ \hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\ \hline \end{array}$ -Referring to Table 14-4, which of the following values for the level of significance is the smallest for which every explanatory variable is significant individually?

A) 0.05 B) 0.15 C) 0.025 D) 0.01 A) 0.05 B) 0.15 C) 0.025 D) 0.01

TABLE 14-17 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 (Attitude 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: $\begin{array}{lccccccrr} & & & & \text { Odds } & \text { 95 \% CI } \\ \text {Predictor }& \text {Coef }&\text { SE Coef }&\text { Z }& \text {P} &\text { Ratio} &\text { Lower} & \text {Upper }\\ \text {Constant }& -70.49 & 47.22 & -1.49 & 0.135 & & & \\ \text {Income }& 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\ \text {Lawn Size} & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\ \text {Attitude} & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\ \text {Teenager} & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\ \text {Age} & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45 \end{array}$ Log-Likelihood = -4.890 Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000 Goodness-of-Fit Tests $ \begin{array}{lrrr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000\end{array} $ -Referring to Table 14-17, what are the degrees of freedom for the chi-square distribution when testing whether the model is a good-fitting model?

The answer of TABLE 14-17 The marketing manager for...

TABLE 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output: $\text {SUMMARY OUTPUT}$ $\begin{array}{ll} \hline \text { Regression Statistics } \\ \hline \text { Multiple R }& 0.916 \\ \text { R Square} & 0.839 \\ \text { Adjusted R Square} & 0.732 \\ \text { Standard Error }& 0.24685 \\ \text { Observations} & 6 \\ \hline \end{array}$ ANOVA $\begin{array}{lccclc} \hline & \text {d f }& \text { SS }& \text { M S } & \text { F } & \text {Significance F } \\ \hline \text { Regression} & 2 & 0.95219 & 0.47610 & 7.813 & 0.0646 \\ \text {Residual} & 3 & 0.18281 & 0.06094 & & \\ \text {Total} & 5 & 1.13500 & & & \\ \hline \end{array}$ $\begin{array}{lrcrr} \hline & \text {Coefficients }& \text {Standard Error} & \text {t Stat } & \text { p -value} \\ \hline \text { Intercept }& 4.593897 & 1.13374542 & 4.052 & 0.0271 \\ \text {Units }& -0.247270 & 0.06268485 & -3.945 & 0.0290 \\ \text {SAT Total }& 0.001443 & 0.00101241 & 1.425 & 0.2494 \\ \hline \end{array}$ -Referring to Table 14-7, the department head wants to use a t test to test for the significance of the coefficient of X1. The p-value of the test is_____ .

The answer of TABLE 14-7 The department head of the...

TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. \[\begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l r } \hline \text { Multiple R } & 0.830 \\ \text { R Square } & 0.689 \\ \text { Adjusted R Square } & 0.662 \\ \text { Standard Error } & 17501.643 \\ \text { Observations } & 26 \end{array} \end{array}\] ANOVA $\begin{array}{lcrrrr} \hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\ \hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\ \text {Residual }& 23 & 7045072780 & 306307512 & & \\ \text {Total }& 25 & 22624849820 & & & \\ \hline \end{array}$ \[\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\ \hline \end{array}\] -Referring to Table 14-5, what is the p-value for Wages?

A) 0.05 B) 0.0001 C) 0.01 D) none of the above A) 0.05 B) 0.0001 C) 0.01 D) none of the above

TABLE 14-1 A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (XS1U1B11S1U1B0) and how he/she scored on a business aptitude test (XS1U1B12S1U1B0). A random sample of 8 employees provides the following: \[\begin{array} { c r r r } \text { Employee } & Y & X _ { 1 } & X _ { 2 } \\ \hline 1 & 100 & 10 & 7 \\ 2 & 90 & 3 & 10 \\ 3 & 80 & 8 & 9 \\ 4 & 70 & 5 & 4 \\ 5 & 60 & 5 & 8 \\ 6 & 50 & 7 & 5 \\ 7 & 40 & 1 & 4 \\ 8 & 30 & 1 & 1 \end{array}\] -Referring to Table 14-1, for these data, what is the value for the regression constant, b0?

A) 4.698 B) 21.293 C) 3.103 D) 0.998 A) 4.698 B) 21.293 C) 3.103 D) 0.998

TABLE 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 4 variables: age (XS1U1B11S1U1B0S1U1B1 S1U1B0= Age), experience in the field (XS1U1B12S1U1B0S1U1B1 S1U1B0= Exper), number of degrees (XS1U1B13S1U1B0S1U1B1 S1U1B0= Degrees), and number of previous jobs in the field (XS1U1B14S1U1B0S1U1B1 S1U1B0= Prevjobs). He took a sample of 20 employees and obtained the following Microsoft Excel output: $\text {SUMMARY OUTPUT}$ $\begin{array}{ll} \hline \text { Regression Statistics } \\ \hline \text { Multiple R }& 0.992 \\ \text { R Square} & 0.984 \\ \text { Adjusted R Square} & 0.979 \\ \text { Standard Error }& 2.26743 \\ \text { Observations} & 20 \\ \hline \end{array}$ ANOVA $\begin{array}{lccclc} \hline & \text {d f }& \text { SS }& \text { M S } & \text { F } & \text {Significance F } \\ \hline \text { Regression} & 4 & 4609.83164& 1152.45791 & 224.160& 0.0001 \\ \text {Residual} &15& 77.11836 & 5.14122& & \\ \text {Total} & 19 & 4686.95000 & & & \\ \hline \end{array}$ $\begin{array}{lrrrr} \hline & \text {Coefficients} &\text { Standard Error} & \text { t Stat } & \text { p -value} \\ \hline \text { Intercept }& -9.611198 & 2.77988638 & -3.457 & 0.0035 \\ \text { Age }& 1.327695 & 0.11491930 & 11.553 & 0.0001 \\ \text { Exper }& -0.106705 & 0.14265559 & -0.748 & 0.4660 \\ \text { Degrees} & 7.311332 & 0.80324187 & 9.102 & 0.0001 \\ \text { Prevjobs }& -0.504168 & 0.44771573 & -1.126 & 0.2778 \\ \hline \end{array}$ -Referring to Table 14-8, the predicted salary for a 35-year-old person with 10 years of experience, 3 degrees, and 1 previous job is_____ .

The answer of TABLE 14-8 A financial analyst wanted to...

TABLE 14-4 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: $\begin{array}{ll} & \text { Regression Stuistics } \\ \hline \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } &50 \\ \hline \end{array}$ ANOVA $\begin{array}{lrrrrr} \hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\ \hline \text {Regression} & & 3605.7736 & 1201.9245 & &0.0000 \\ \text {Residual} & & 1214.2264 & 26.3962 & \\ Total & 49 & 4820.0000 & & & \\ \hline \end{array}$ $\begin{array}{lcccc} \hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\ \hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\ \hline \end{array}$ -Referring to Table 14-4, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of Income in the regression model?

A) Income is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01. B) Income is significant in explaining house size and should be included in the model because its p-value is more than 0.01. C) Income is significant in explaining house size and should be included in the model because its p-value is less than 0.01. D) Income is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01. A) Income is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01. B) Income is significant in explaining house size and should be included in the model because its p-value is more than 0.01. C) Income is significant in explaining house size and should be included in the model because its p-value is less than 0.01. D) Income is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.

TABLE 14-16 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 average of the percentage of students attending class (% Attendance), average 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 = % Passing as the dependent variable, XS1U1B11S1U1B0S1U1B1 S1U1B0= % Attendance, XS1U1B12S1U1B0S1U1B1 S1U1B0= Salaries and XS1U1B13 S1U1B0= Spending: $\begin{array}{lr} \hline\text {Regression Statistics } \\ \hline \text {Multiple R }& 0.7930 \\ \text {R Square} & 0.6288 \\ \text {Adjusted R Square} & 0.6029 \\ \text {Standard Error }& 10.4570 \\ \text {Observations }& 47 \\ \hline \end{array}$ ANOVA $\begin{array}{lccccc} \hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\ \hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\ \text { Residual} & 43 & 4702.02 & 109.35 & & \\ \text { Total }& 46 & 12667.11 & & & \\ \hline \end{array}$ $\begin{array}{lrrrrrr} \hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\ \hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\ \%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\ \text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\ \text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\ \hline \end{array}$ -Referring to Table 14-16, which of the following is the correct null hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test?

A) $ H_{0}: \beta_{2}=0 $ B) $ H_{0}: \beta_{3}=0 $ C) $ H_{0}: \beta_{0}=0 $ D) $ H_{0}: \beta_{1}=0 $ A) $ H_{0}: \beta_{2}=0 $ B) $ H_{0}: \beta_{3}=0 $ C) $ H_{0}: \beta_{0}=0 $ D) $ H_{0}: \beta_{1}=0 $

TABLE 14-17 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 (Attitude 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: $\begin{array}{lccccccrr} & & & & \text { Odds } & \text { 95 \% CI } \\ \text {Predictor }& \text {Coef }&\text { SE Coef }&\text { Z }& \text {P} &\text { Ratio} &\text { Lower} & \text {Upper }\\ \text {Constant }& -70.49 & 47.22 & -1.49 & 0.135 & & & \\ \text {Income }& 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\ \text {Lawn Size} & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\ \text {Attitude} & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\ \text {Teenager} & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\ \text {Age} & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45 \end{array}$ Log-Likelihood = -4.890 Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000 Goodness-of-Fit Tests $ \begin{array}{lrrr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000\end{array} $ -Referring to Table 14-17, what is the p-value of the test statistic when testing whether Attitude makes a significant contribution to the model in the presence of the other independent variables?

The answer of TABLE 14-17 The marketing manager for a nationally...

TABLE 14-17 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 (Attitude 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: $\begin{array}{lccccccrr} & & & & \text { Odds } & \text { 95 \% CI } \\ \text {Predictor }& \text {Coef }&\text { SE Coef }&\text { Z }& \text {P} &\text { Ratio} &\text { Lower} & \text {Upper }\\ \text {Constant }& -70.49 & 47.22 & -1.49 & 0.135 & & & \\ \text {Income }& 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\ \text {Lawn Size} & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\ \text {Attitude} & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\ \text {Teenager} & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\ \text {Age} & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45 \end{array}$ Log-Likelihood = -4.890 Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000 Goodness-of-Fit Tests $ \begin{array}{lrrr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000\end{array} $ -Referring to Table 14-14, the predicted demand in Los Angeles when the mortgage rate is 8% is_______ .

The answer of TABLE 14-17 The marketing manager for...

TABLE 14-4 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: $\begin{array}{ll} & \text { Regression Stuistics } \\ \hline \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } &50 \\ \hline \end{array}$ ANOVA $\begin{array}{lrrrrr} \hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\ \hline \text {Regression} & & 3605.7736 & 1201.9245 & &0.0000 \\ \text {Residual} & & 1214.2264 & 26.3962 & \\ Total & 49 & 4820.0000 & & & \\ \hline \end{array}$ $\begin{array}{lcccc} \hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\ \hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\ \hline \end{array}$ -Referring to Table 14-4, suppose the builder wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?

A) 5.286 B) - 1.509 C) 5.195 D) 3.945 A) 5.286 B) - 1.509 C) 5.195 D) 3.945

Exam 14: Introduction to Multiple Regression

TABLE 14-4 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: Regression Stuistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA d f S S M S F Significance F Regression 3605.7736 1201.9245 0.0000 Residual 1214.2264 26.3962 Total 49 4820.0000 Coefficients Standard Error t Stat p -value Intercept -1.6335 5.8078 -0.281 0.7798 Income 0.4485 0.1137 3.9545 0.0003 Size 4.2615 0.8062 5.286 0.0001 School -0.6517 0.4319 -1.509 0.1383 -Referring to Table 14-4, which of the following values for the level of significance is the smallest for which every explanatory variable is significant individually?

(Multiple Choice)

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(98)

Question 141

TABLE 14-17 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 (Attitude 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: Odds 95 \% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -70.49 47.22 -1.49 0.135 Income 0.2868 0.1523 1.88 0.060 1.33 0.99 1.80 Lawn Size 1.0647 0.7472 1.42 0.154 2.90 0.67 12.54 Attitude -12.744 9.455 -1.35 0.178 0.00 0.00 326.06 Teenager -0.200 1.061 -0.19 0.850 0.82 0.10 6.56 Age 1.0792 0.8783 1.23 0.219 2.94 0.53 16.45 Log-Likelihood = -4.890 Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000 Goodness-of-Fit Tests Method Chi-Square DF P Pearson 9.313 24 0.997 Deviance 9.780 24 0.995 Hosmer-Lemeshow 0.571 8 1.000 -Referring to Table 14-17, what are the degrees of freedom for the chi-square distribution when testing whether the model is a good-fitting model?

(Short Answer)

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Question 142

TABLE 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output: $\text {SUMMARY OUTPUT}$ Regression Statistics Multiple R 0.916 R Square 0.839 Adjusted R Square 0.732 Standard Error 0.24685 Observations 6 ANOVA d f SS M S F Significance F Regression 2 0.95219 0.47610 7.813 0.0646 Residual 3 0.18281 0.06094 Total 5 1.13500 Coefficients Standard Error t Stat p -value Intercept 4.593897 1.13374542 4.052 0.0271 Units -0.247270 0.06268485 -3.945 0.0290 SAT Total 0.001443 0.00101241 1.425 0.2494 -Referring to Table 14-7, the department head wants to use a t test to test for the significance of the coefficient of X1. The p-value of the test is_____ .

(Short Answer)

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Question 143

TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. Regression Statistics Multiple R 0.830 R Square 0.689 Adjusted R Square 0.662 Standard Error 17501.643 Observations 26 ANOVA d f S S M S F Significance F Regression 2 15579777040 7789888520 25.432 0.0001 Residual 23 7045072780 306307512 Total 25 22624849820 Coefficients Standard Error t Stat p-value Intercept 15800.0000 6038.2999 2.617 0.0154 C apital 0.1245 0.2045 0.609 0.5485 W ages 7.0762 1.4729 4.804 0.0001 -Referring to Table 14-5, what is the p-value for Wages?

(Multiple Choice)

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Question 144

In a multiple regression model, the value of the coefficient of multiple determination

(Multiple Choice)

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Question 145

TABLE 14-9 You decide to predict gasoline prices in different cities and towns in the United States for your term project. Your dependent variable is price of gasoline per gallon and your explanatory variables are per capita income, the number of firms that manufacture automobile parts in and around the city, the number of new business starts in the last year, population density of the city, percentage of local taxes on gasoline, and the number of people using public transportation. You collected data of 32 cities and obtained a regression sum of squares SSR= 122.8821. Your computed value of standard error of the estimate is 1.9549. -Referring to Table 14-9, what is the value of adjusted r²?

(Multiple Choice)

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Question 146

TABLE 14-1 A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X₁) and how he/she scored on a business aptitude test (X₂). A random sample of 8 employees provides the following: Employee Y 1 100 10 7 2 90 3 10 3 80 8 9 4 70 5 4 5 60 5 8 6 50 7 5 7 40 1 4 8 30 1 1 -Referring to Table 14-1, for these data, what is the value for the regression constant, b0?

(Multiple Choice)

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Question 147

TABLE 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 4 variables: age (X₁= Age), experience in the field (X₂= Exper), number of degrees (X₃= Degrees), and number of previous jobs in the field (X₄= Prevjobs). He took a sample of 20 employees and obtained the following Microsoft Excel output: $\text {SUMMARY OUTPUT}$ Regression Statistics Multiple R 0.992 R Square 0.984 Adjusted R Square 0.979 Standard Error 2.26743 Observations 20 ANOVA d f SS M S F Significance F Regression 4 4609.83164 1152.45791 224.160 0.0001 Residual 15 77.11836 5.14122 Total 19 4686.95000 Coefficients Standard Error t Stat p -value Intercept -9.611198 2.77988638 -3.457 0.0035 Age 1.327695 0.11491930 11.553 0.0001 Exper -0.106705 0.14265559 -0.748 0.4660 Degrees 7.311332 0.80324187 9.102 0.0001 Prevjobs -0.504168 0.44771573 -1.126 0.2778 -Referring to Table 14-8, the predicted salary for a 35-year-old person with 10 years of experience, 3 degrees, and 1 previous job is_____ .

(Short Answer)

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Question 148

TABLE 14-4 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: Regression Stuistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA d f S S M S F Significance F Regression 3605.7736 1201.9245 0.0000 Residual 1214.2264 26.3962 Total 49 4820.0000 Coefficients Standard Error t Stat p -value Intercept -1.6335 5.8078 -0.281 0.7798 Income 0.4485 0.1137 3.9545 0.0003 Size 4.2615 0.8062 5.286 0.0001 School -0.6517 0.4319 -1.509 0.1383 -Referring to Table 14-4, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of Income in the regression model?

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Question 149

TABLE 14-16 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 average of the percentage of students attending class (% Attendance), average 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 = % Passing as the dependent variable, X₁= % Attendance, X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R Square 0.6029 Standard Error 10.4570 Observations 47 ANOVA d f SS MS F Significance F Regression 3 7965.08 2655.03 24.2802 2.3853-09 Residual 43 4702.02 109.35 Total 46 12667.11 Coeffs Stnd Err t Stat p -value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 2.88-09 -957.3401 -549.5050 \% Attend 8.5014 1.0771 7.8929 6.73-10 6.3292 10.6735 Salary 6.85-07 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Table 14-16, which of the following is the correct null hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test?

(Multiple Choice)

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Question 150

TABLE 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 4 variables: age (X₁= Age), experience in the field (X₂= Exper), number of degrees (X₃= Degrees), and number of previous jobs in the field (X₄= Prevjobs). He took a sample of 20 employees and obtained the following Microsoft Excel output: $\text {SUMMARY OUTPUT}$ Regression Statistics Multiple R 0.992 R Square 0.984 Adjusted R Square 0.979 Standard Error 2.26743 Observations 20 ANOVA d f SS M S F Significance F Regression 4 4609.83164 1152.45791 224.160 0.0001 Residual 15 77.11836 5.14122 Total 19 4686.95000 Coefficients Standard Error t Stat p -value Intercept -9.611198 2.77988638 -3.457 0.0035 Age 1.327695 0.11491930 11.553 0.0001 Exper -0.106705 0.14265559 -0.748 0.4660 Degrees 7.311332 0.80324187 9.102 0.0001 Prevjobs -0.504168 0.44771573 -1.126 0.2778 -Referring to Table 14-8, the analyst wants to use a t test to test for the significance of the coefficient of X₃. The value of the test statistic is_____ .

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Question 151

TABLE 14-17 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 (Attitude 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: Odds 95 \% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -70.49 47.22 -1.49 0.135 Income 0.2868 0.1523 1.88 0.060 1.33 0.99 1.80 Lawn Size 1.0647 0.7472 1.42 0.154 2.90 0.67 12.54 Attitude -12.744 9.455 -1.35 0.178 0.00 0.00 326.06 Teenager -0.200 1.061 -0.19 0.850 0.82 0.10 6.56 Age 1.0792 0.8783 1.23 0.219 2.94 0.53 16.45 Log-Likelihood = -4.890 Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000 Goodness-of-Fit Tests Method Chi-Square DF P Pearson 9.313 24 0.997 Deviance 9.780 24 0.995 Hosmer-Lemeshow 0.571 8 1.000 -Referring to Table 14-17, what is the p-value of the test statistic when testing whether Attitude makes a significant contribution to the model in the presence of the other independent variables?

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Question 152

TABLE 14-16 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 average of the percentage of students attending class (% Attendance), average 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 = % Passing as the dependent variable, X₁= % Attendance, X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R Square 0.6029 Standard Error 10.4570 Observations 47 ANOVA d f SS MS F Significance F Regression 3 7965.08 2655.03 24.2802 2.3853-09 Residual 43 4702.02 109.35 Total 46 12667.11 Coeffs Stnd Err t Stat p -value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 2.88-09 -957.3401 -549.5050 \% Attend 8.5014 1.0771 7.8929 6.73-10 6.3292 10.6735 Salary 6.85-07 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Table 14-16, the null hypothesis H₀ : ?₁ = ?₂ = ?₃ = 0 implies that percentage of students passing the proficiency test is not affected by some of the explanatory variables.

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Question 153

TABLE 14-16 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 average of the percentage of students attending class (% Attendance), average 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 = % Passing as the dependent variable, X₁= % Attendance, X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R Square 0.6029 Standard Error 10.4570 Observations 47 ANOVA d f SS MS F Significance F Regression 3 7965.08 2655.03 24.2802 2.3853-09 Residual 43 4702.02 109.35 Total 46 12667.11 Coeffs Stnd Err t Stat p -value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 2.88-09 -957.3401 -549.5050 \% Attend 8.5014 1.0771 7.8929 6.73-10 6.3292 10.6735 Salary 6.85-07 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Table 14-16, we can conclude that instructional spending per pupil has no impact on average percentage of students passing the proficiency test at a 1% level of significance based solely on the 95% confidence interval estimate for þ3.

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Question 154

TABLE 14-17 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 (Attitude 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: Odds 95 \% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -70.49 47.22 -1.49 0.135 Income 0.2868 0.1523 1.88 0.060 1.33 0.99 1.80 Lawn Size 1.0647 0.7472 1.42 0.154 2.90 0.67 12.54 Attitude -12.744 9.455 -1.35 0.178 0.00 0.00 326.06 Teenager -0.200 1.061 -0.19 0.850 0.82 0.10 6.56 Age 1.0792 0.8783 1.23 0.219 2.94 0.53 16.45 Log-Likelihood = -4.890 Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000 Goodness-of-Fit Tests Method Chi-Square DF P Pearson 9.313 24 0.997 Deviance 9.780 24 0.995 Hosmer-Lemeshow 0.571 8 1.000 -Referring to Table 14-14, the predicted demand in Los Angeles when the mortgage rate is 8% is_______ .

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Question 155

When a dummy variable is included in a multiple regression model, the interpretation of the estimated slope coefficient does not make any sense anymore.

(True/False)

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Question 156

When an explanatory variable is dropped from a multiple regression model, the coefficient of multiple determination can increase.

(True/False)

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Question 157

TABLE 14-4 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: Regression Stuistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA d f S S M S F Significance F Regression 3605.7736 1201.9245 0.0000 Residual 1214.2264 26.3962 Total 49 4820.0000 Coefficients Standard Error t Stat p -value Intercept -1.6335 5.8078 -0.281 0.7798 Income 0.4485 0.1137 3.9545 0.0003 Size 4.2615 0.8062 5.286 0.0001 School -0.6517 0.4319 -1.509 0.1383 -Referring to Table 14-4, suppose the builder wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?

(Multiple Choice)

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Question 158

TABLE 14-13 As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area. Data were collected for the price per hour of parking, blocks to the quadrangle, and one of the three jurisdictions: on campus, in downtown and off campus, or outside of downtown and off campus. The population regression model hypothesized is $Y_{i}=\alpha+\beta_{1} X_{1 i}+\beta_{2} X_{2 i}+\beta_{3} X_{3 i}+\varepsilon$ where Y is the meter price; ^X1 ^{is the number of blocks to the quad;} ^X2 ^{is a dummy variable that takes the value 1 if the meter} is located in downtown and off campus and the value 0 otherwise; ^X3 ^{is a dummy variable that takes the value 1 if the meter} is located outside of downtown and off campus, and the value 0 otherwise. The following Excel results are obtained. Regression Statistics Multiple R 0.9659 R Square 0.9331 Adjusted R Square 0.9294 Standard Error 0.0327 Observations 58 ANOVA d f SS M S F Significance F Regression 3 0.8094 0.2698 251.1995 1.0964-31 Residual 54 0.0580 0.0010 Total 57 0.8675 Coefficients Standard Error t Stat p-value Intercept 0.5118 0.0136 37.4675 2.4904 -0.0045 0.0034 -1.3276 0.1898 -0.2392 0.0123 -19.3942 5.3581-26 -0.0002 0.0123 -0.0214 0.9829 -Referring to Table 14-13, if one is already outside of downtown and off campus but decides to park 3 more blocks from the quad, the estimated average parking meter rate will

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Question 159

A dummy variable is used as an independent variable in a regression model when

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Question 160

In a multiple regression model, the value of the coefficient of multiple determination

When a dummy variable is included in a multiple regression model, the interpretation of the estimated slope coefficient does not make any sense anymore.

When an explanatory variable is dropped from a multiple regression model, the coefficient of multiple determination can increase.

A dummy variable is used as an independent variable in a regression model when

Introduction and Data Collection

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Numerical Descriptive Measures

Basic Probability

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Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

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