TABLE 14-19 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: Logistic Regression Table $\begin{array}{lrrrrrrr} & & & & & \text { Odds } & {95 \% \text { CI }} \\ \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { Z } & \text { P } & \text { Ratio } & \text { Lower } & \text { Upper } \\ \text { Constant } & -70.49 & 47.22 & -1.49 & 0.135 & & & \\ \text { Income } & 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\ \text { LawnSiz } & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\ \text { Attitude } & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\ \text { Teenager } & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\ \text { Age } & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45 \end{array}$ Log-Likelihood $= - 4.890$ Test that all slopes are zero: $\mathrm { G } = 31.808 , \mathrm { DF } = 5 , p$-value $= 0.000$ Goodness-of-Fit Tests $\begin{array} { l c r c } \text { Method } & \text { Chi-Square } & \text { DF } & \mathrm { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000 \end{array}$ -Referring to Table 14-19, which of the following is the correct interpretation for the Income slope coefficient?

A) Holding constant the effect of the other variables, the estimated number of lawn service purchased increases by 0.2868 for each increase of one thousand dollars in family income. B) Holding constant the effect of the other variables, the estimated average number of lawn service purchased increases by 0.2868 for each increase of one thousand dollars in family income. C) Holding constant the effect of the other variables, the estimated probability of purchasing a lawn service increases by 0.2868 for each increase of one thousand dollars in family income. D) Holding constant the effect of the other variables, the estimated natural logarithm of the odds ratio of purchasing a lawn service increases by 0.2868 for each increase of one thousand dollars in family income. A) Holding constant the effect of the other variables, the estimated number of lawn service purchased increases by 0.2868 for each increase of one thousand dollars in family income. B) Holding constant the effect of the other variables, the estimated average number of lawn service purchased increases by 0.2868 for each increase of one thousand dollars in family income. C) Holding constant the effect of the other variables, the estimated probability of purchasing a lawn service increases by 0.2868 for each increase of one thousand dollars in family income. D) Holding constant the effect of the other variables, the estimated natural logarithm of the odds ratio of purchasing a lawn service increases by 0.2868 for each increase of one thousand dollars in family income.

TABLE 14-19 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: Logistic Regression Table $\begin{array}{lrrrrrrr} & & & & & \text { Odds } & {95 \% \text { CI }} \\ \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { Z } & \text { P } & \text { Ratio } & \text { Lower } & \text { Upper } \\ \text { Constant } & -70.49 & 47.22 & -1.49 & 0.135 & & & \\ \text { Income } & 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\ \text { LawnSiz } & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\ \text { Attitude } & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\ \text { Teenager } & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\ \text { Age } & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45 \end{array}$ Log-Likelihood $= - 4.890$ Test that all slopes are zero: $\mathrm { G } = 31.808 , \mathrm { DF } = 5 , p$-value $= 0.000$ Goodness-of-Fit Tests $\begin{array} { l c r c } \text { Method } & \text { Chi-Square } & \text { DF } & \mathrm { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000 \end{array}$ -Referring to Table 14-19, what is the p-value of the test statistic when testing whether Age makes a significant contribution to the model in the presence of the other independent variables?

The answer of TABLE 14-19 The marketing manager for a nationally...

TABLE 14-19 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: Logistic Regression Table $\begin{array}{lrrrrrrr} & & & & & \text { Odds } & {95 \% \text { CI }} \\ \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { Z } & \text { P } & \text { Ratio } & \text { Lower } & \text { Upper } \\ \text { Constant } & -70.49 & 47.22 & -1.49 & 0.135 & & & \\ \text { Income } & 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\ \text { LawnSiz } & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\ \text { Attitude } & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\ \text { Teenager } & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\ \text { Age } & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45 \end{array}$ Log-Likelihood $= - 4.890$ Test that all slopes are zero: $\mathrm { G } = 31.808 , \mathrm { DF } = 5 , p$-value $= 0.000$ Goodness-of-Fit Tests $\begin{array} { l c r c } \text { Method } & \text { Chi-Square } & \text { DF } & \mathrm { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000 \end{array}$ -Referring to Table 14-19, what should be the decision ('reject' or 'do not reject')on the null hypothesis when testing whether Attitude makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance?

The answer of TABLE 14-19 The marketing manager for a nationally...

TABLE 14-17 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 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. The coefficients of partial determination ( 2 Yj. (Allvariables except $ j $ ) ) of each of the 6 predictors are, respectively, 0.2807, 0.0386, 0.0317, 0.0141, 0.0958, and 0.1201. $\begin{array}{|lr|} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.7035 \\ \hline \text { R Square } & 0.4949 \\ \hline \text { Adjusted R } & 0.4030 \\ \text { Square } & \\ \text { Standard } & 18.4861 \\ \text { Error } & 40 \\ \hline \text { Observations } & \\ \hline \end{array}$ $\text { ANOVA }$ $\begin{array} { | l | r | r | r | r | r | } \hline & { \text { df } } & \text { SS } & \text { MS } &F& \text { significance F } \\ \hline \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 \\ \hline \text { Residual } & 33 & 11277.2586 & 341.7351 & & \\ \hline \text { Total } & 39 & 22325.9 & & & \\ \hline \end{array}$ $\begin{array}{|l|r|r|r|r|r|r|} \hline & \text { Coefficients } & \text { Standard Error } & {t \text { Stat }} & {\text { P-value }} & {\text { Lower 95\% }} &{\text { Upper 95\% }} \\ \hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & -14.5067 & 79.8257 \\ \hline \text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\ \hline \text { Edu } & -1.3537 & 1.1766 & -1.1504 & 0.2582 & -3.7476 & 1.0402 \\ \hline \text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & -0.5914 & 1.8257 \\ \hline \text { Married } & -5.2189 & 7.6068 & -0.6861 & 0.4974 & -20.6950 & 10.2571 \\ \hline \text { Head } & -14.2978 & 7.6479 & -1.8695 & 0.0704 & -29.8575 & 1.2618 \\ \hline \text { Manager } & -24.8203 & 11.6932 & -2.1226 & 0.0414 & -48.6102 & -1.0303 \\ \hline \end{array}$ Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: $\begin{array}{|l|r|} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.6391 \\ \hline \text { R Square } & 0.4085 \\ \hline \text { Adjusted R } & 0.3765 \\ \text { Square } & \\ \hline \text { Standard Error } & 18.8929 \\ \hline \text { Observations } & 40 \\ \hline \end{array}$ $\text { ANOVA }$ $\begin{array} { | l | r | r | r | r | r | } \hline & { \text { df } } & { \text { SS } } & { \text { MS } } & F & \text { Significance } F \\ \hline \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\ \hline \text { Residual } & 37 & 13206.8103 & 356.9408 & & \\ \hline \text { Total } & 39 & 22325.9 & & & \\ \hline \end{array}$ $\begin{array}{lrrrr} \hline & \text { Coefficients } & \text { Standard Error } & {t \text { Stat }} & {P \text {-value }} \\ \hline \text { Intercept } & -0.2143 & 11.5796 & -0.0185 & 0.9853 \\ \hline \text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 \\ \hline \text { Manager } & -22.5761 & 11.3488 & -1.9893 & 0.0541 \\ \hline \end{array}$ -Referring to Table 14-17 Model 1, what are the numerator and denominator degrees of freedom, respectively, for the test statistic to determine whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables?

The answer of TABLE 14-17 Given below are results from the...

TABLE 14-15 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 = % Passing as the dependent variable, X₁ = % Attendance, X₂= Salaries and X₃= Spending: $\begin{array}{l|r} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.7930 \\ \hline \text { R Square } & 0.6288 \\ \hline \text { Adjusted R } & 0.6029 \\ \text { Square } & \\ \text { Standard } & 10.4570 \\ \text { Error } & \\ \hline \text { Observations } & 47 \\ \hline \end{array}$ $\text { ANOVA }$ $\begin{array} { l | r | r | r | r | r | } \hline & { \text { df } } & { \text { SS } } & \text { MS } & \text { Significance } \\ & & & & & F \\ \hline \text { Regression } & 3 & 7965.08 & 2655.03 & 24.2802 & 0.0000 \\ \hline \text { Residual } & 43 & 4702.02 & 109.35 & & \\ \hline \text { Total } & 46 & 12667.11 & & & \\ \hline \end{array}$ $\begin{array} { | l | r | r | r | r | r | r | } \hline & \text { Coefficients } & \begin{array} { c } \text { Standard } \\ \text { Error } \end{array} & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & - 753.4225 & 101.1149 & - 7.4511 & 0.0000 & - 957.3401 & - 549.5050 \\ \hline \text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\ \hline \text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & - 0.0013 & 0.0013 \\ \hline \text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & - 0.0034 & 0.0153 \\ \hline \end{array}$ -Referring to Table 14-15, what is the p-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?

The answer of TABLE 14-15 The superintendent of a school district...

TABLE 14-15 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 = % Passing as the dependent variable, X₁ = % Attendance, X₂= Salaries and X₃= Spending: $\begin{array}{l|r} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.7930 \\ \hline \text { R Square } & 0.6288 \\ \hline \text { Adjusted R } & 0.6029 \\ \text { Square } & \\ \text { Standard } & 10.4570 \\ \text { Error } & \\ \hline \text { Observations } & 47 \\ \hline \end{array}$ $\text { ANOVA }$ $\begin{array} { l | r | r | r | r | r | } \hline & { \text { df } } & { \text { SS } } & \text { MS } & \text { Significance } \\ & & & & & F \\ \hline \text { Regression } & 3 & 7965.08 & 2655.03 & 24.2802 & 0.0000 \\ \hline \text { Residual } & 43 & 4702.02 & 109.35 & & \\ \hline \text { Total } & 46 & 12667.11 & & & \\ \hline \end{array}$ $\begin{array} { | l | r | r | r | r | r | r | } \hline & \text { Coefficients } & \begin{array} { c } \text { Standard } \\ \text { Error } \end{array} & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & - 753.4225 & 101.1149 & - 7.4511 & 0.0000 & - 957.3401 & - 549.5050 \\ \hline \text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\ \hline \text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & - 0.0013 & 0.0013 \\ \hline \text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & - 0.0034 & 0.0153 \\ \hline \end{array}$ -Referring to Table 14-15, what is the value of the test statistic to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

The answer of TABLE 14-15 The superintendent of a school district...

TABLE 14-15 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 = % Passing as the dependent variable, X₁ = % Attendance, X₂= Salaries and X₃= Spending: $\begin{array}{l|r} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.7930 \\ \hline \text { R Square } & 0.6288 \\ \hline \text { Adjusted R } & 0.6029 \\ \text { Square } & \\ \text { Standard } & 10.4570 \\ \text { Error } & \\ \hline \text { Observations } & 47 \\ \hline \end{array}$ $\text { ANOVA }$ $\begin{array} { l | r | r | r | r | r | } \hline & { \text { df } } & { \text { SS } } & \text { MS } & \text { Significance } \\ & & & & & F \\ \hline \text { Regression } & 3 & 7965.08 & 2655.03 & 24.2802 & 0.0000 \\ \hline \text { Residual } & 43 & 4702.02 & 109.35 & & \\ \hline \text { Total } & 46 & 12667.11 & & & \\ \hline \end{array}$ $\begin{array} { | l | r | r | r | r | r | r | } \hline & \text { Coefficients } & \begin{array} { c } \text { Standard } \\ \text { Error } \end{array} & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & - 753.4225 & 101.1149 & - 7.4511 & 0.0000 & - 957.3401 & - 549.5050 \\ \hline \text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\ \hline \text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & - 0.0013 & 0.0013 \\ \hline \text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & - 0.0034 & 0.0153 \\ \hline \end{array}$ -Referring to Table 14-15, which of the following is a correct statement?

A) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, mean teacher salary, and instructional spending per pupil. B) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, mean teacher salary, and instructional spending per pupil after adjusting for the number of predictors and sample size. C) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class holding constant the effect of mean teacher salary, and instructional spending per pupil. D) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class after adjusting for the effect of mean teacher salary, and instructional spending per pupil. A) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, mean teacher salary, and instructional spending per pupil. B) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, mean teacher salary, and instructional spending per pupil after adjusting for the number of predictors and sample size. C) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class holding constant the effect of mean teacher salary, and instructional spending per pupil. D) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class after adjusting for the effect of mean teacher salary, and instructional spending per pupil.

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. SUMMARY OUTPUT $\begin{array}{l} \text { Regression Statistics }\\ \begin{array}{ll} \text { Multiple R } & 0.830 \\ \text { R Square } & 0.689 \\ \text { Adjusted R Square } & 0.662 \\ \text { Standard Error } & 17501.643 \\ \text { Observations } & 26 \end{array} \end{array}$ ANOVA $\begin{array}{lrcccr} & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\ \text { Residual } & 23 & 7045072780 & 306307512 & & \\ \text { Total } & 25 & 22624849820 & & & \end{array}$ $\begin{array} { l r r r r } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$ -Referring to Table 14-5, one company in the sample had sales of $20 billion (Sales = 20,000). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars)for this data point?

A) 874.55 B) 622.87 C) -790.69 D) -983.56 A) 874.55 B) 622.87 C) -790.69 D) -983.56

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: SUMMARY OUTPUT Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$ ANOVA $\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$ $\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$ -Referring to Table 14-4, 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)?

A) $44.14 thousand B) $56.75 thousand C) $178.33 thousand D) $211.85 thousand A) $44.14 thousand B) $56.75 thousand C) $178.33 thousand D) $211.85 thousand

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: SUMMARY OUTPUT Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.992 \\ \text { R Square } & 0.984 \\ \text { Adjusted R Square } & 0.979 \\ \text { Standard Error } & 2.26743 \\ \text { Observations } & 20 \end{array}$ ANOVA $\begin{array} { l r r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & 4 & 4609.83164 & 1152.45791 & 224.160 & 0.0001 \\ \text { Residual } & 15 & 77.11836 & 5.14122 & & \\ \text { Total } & 19 & 4686.95000 & & & \end{array}$ $\begin{array} { l r c c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 9.611198 & 2.77988638 & - 3.457 & 0.0035 \\ \text { Age } & 1.327695 & 0.11491930 & 11.553 & 0.0001 \\ \text { Exper } & - 0.106705 & 0.14265559 & - 0.748 & 0.4660 \\ \text { Degrees } & 7.311332 & 0.80324187 & 9.102 & 0.0001 \\ \text { Prevjobs } & - 0.504168 & 0.44771573 & - 1.126 & 0.2778 \end{array}$ -Referring to Table 14-8, the estimate of the unit change in the mean of Y per unit change in X₄, taking into account the effects of the other 3 variables, is ________.

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

Exam 14: Introduction to Multiple Regression

TABLE 14-13 An econometrician is interested in evaluating the relationship of demand for building materials to mortgage rates in Los Angeles and San Francisco. He believes that the appropriate model is Y = 10 + 5X₁ + 8X₂ where X₁ = mortgage rate in % X₂ = 1 if SF, 0 if LA Y = demand in $100 per capita -Referring to Table 14-13, the predicted demand in Los Angeles when the mortgage rate is 8% is ________.

(Short Answer)

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(26)

Question 141

TABLE 14-19 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: Logistic Regression Table 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 LawnSiz 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: $\mathrm { G } = 31.808 , \mathrm { DF } = 5 , p$ -value $= 0.000$ Goodness-of-Fit Tests Method Chi-Square DF Pearson 9.313 24 0.997 Deviance 9.780 24 0.995 Hosmer-Lemeshow 0.571 8 1.000 -Referring to Table 14-19, which of the following is the correct interpretation for the Income slope coefficient?

(Multiple Choice)

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Question 142

TABLE 14-19 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: Logistic Regression Table 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 LawnSiz 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: $\mathrm { G } = 31.808 , \mathrm { DF } = 5 , p$ -value $= 0.000$ Goodness-of-Fit Tests Method Chi-Square DF Pearson 9.313 24 0.997 Deviance 9.780 24 0.995 Hosmer-Lemeshow 0.571 8 1.000 -Referring to Table 14-19, what is the p-value of the test statistic when testing whether Age makes a significant contribution to the model in the presence of the other independent variables?

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Question 143

TABLE 14-19 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: Logistic Regression Table 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 LawnSiz 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: $\mathrm { G } = 31.808 , \mathrm { DF } = 5 , p$ -value $= 0.000$ Goodness-of-Fit Tests Method Chi-Square DF Pearson 9.313 24 0.997 Deviance 9.780 24 0.995 Hosmer-Lemeshow 0.571 8 1.000 -Referring to Table 14-19, what should be the decision ('reject' or 'do not reject')on the null hypothesis when testing whether Attitude makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance?

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Question 144

TABLE 14-17 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 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. The coefficients of partial determination ( 2 Yj. (Allvariables except $j$ ) ) of each of the 6 predictors are, respectively, 0.2807, 0.0386, 0.0317, 0.0141, 0.0958, and 0.1201. Regression Statistics Multiple R 0.7035 R Square 0.4949 Adjusted R 0.4030 Square Standard 18.4861 Error 40 Observations $\text { ANOVA }$ df SS MS F significance F Regression 6 11048.6415 1841.4402 5.3885 0.00057 Residual 33 11277.2586 341.7351 Total 39 22325.9 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 32.6595 23.18302 1.4088 0.1683 -14.5067 79.8257 Age 1.2915 0.3599 3.5883 0.0011 0.5592 2.0238 Edu -1.3537 1.1766 -1.1504 0.2582 -3.7476 1.0402 Job Yr 0.6171 0.5940 1.0389 0.3064 -0.5914 1.8257 Married -5.2189 7.6068 -0.6861 0.4974 -20.6950 10.2571 Head -14.2978 7.6479 -1.8695 0.0704 -29.8575 1.2618 Manager -24.8203 11.6932 -2.1226 0.0414 -48.6102 -1.0303 Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: Regression Statistics Multiple R 0.6391 R Square 0.4085 Adjusted R 0.3765 Square Standard Error 18.8929 Observations 40 $\text { ANOVA }$ df SS MS F Significance F Regression 2 9119.0897 4559.5448 12.7740 0.0000 Residual 37 13206.8103 356.9408 Total 39 22325.9 Coefficients Standard Error t Stat P -value Intercept -0.2143 11.5796 -0.0185 0.9853 Age 1.4448 0.3160 4.5717 0.0000 Manager -22.5761 11.3488 -1.9893 0.0541 -Referring to Table 14-17 Model 1, you can conclude that, holding constant the effect of the other independent variables, the number of years of education received has no impact on the mean number of weeks a worker is unemployed due to a layoff at a 5% level of significance if we use only the information of the 95% confidence interval estimate for ??.

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Question 145

TABLE 14-17 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 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. The coefficients of partial determination ( 2 Yj. (Allvariables except $j$ ) ) of each of the 6 predictors are, respectively, 0.2807, 0.0386, 0.0317, 0.0141, 0.0958, and 0.1201. Regression Statistics Multiple R 0.7035 R Square 0.4949 Adjusted R 0.4030 Square Standard 18.4861 Error 40 Observations $\text { ANOVA }$ df SS MS F significance F Regression 6 11048.6415 1841.4402 5.3885 0.00057 Residual 33 11277.2586 341.7351 Total 39 22325.9 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 32.6595 23.18302 1.4088 0.1683 -14.5067 79.8257 Age 1.2915 0.3599 3.5883 0.0011 0.5592 2.0238 Edu -1.3537 1.1766 -1.1504 0.2582 -3.7476 1.0402 Job Yr 0.6171 0.5940 1.0389 0.3064 -0.5914 1.8257 Married -5.2189 7.6068 -0.6861 0.4974 -20.6950 10.2571 Head -14.2978 7.6479 -1.8695 0.0704 -29.8575 1.2618 Manager -24.8203 11.6932 -2.1226 0.0414 -48.6102 -1.0303 Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: Regression Statistics Multiple R 0.6391 R Square 0.4085 Adjusted R 0.3765 Square Standard Error 18.8929 Observations 40 $\text { ANOVA }$ df SS MS F Significance F Regression 2 9119.0897 4559.5448 12.7740 0.0000 Residual 37 13206.8103 356.9408 Total 39 22325.9 Coefficients Standard Error t Stat P -value Intercept -0.2143 11.5796 -0.0185 0.9853 Age 1.4448 0.3160 4.5717 0.0000 Manager -22.5761 11.3488 -1.9893 0.0541 -Referring to Table 14-17 Model 1, what are the numerator and denominator degrees of freedom, respectively, for the test statistic to determine whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables?

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Question 146

TABLE 14-15 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 = % Passing as the dependent variable, X₁ = % Attendance, X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R 0.6029 Square Standard 10.4570 Error Observations 47 $\text { ANOVA }$ df SS MS Significance F Regression 3 7965.08 2655.03 24.2802 0.0000 Residual 43 4702.02 109.35 Total 46 12667.11 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 0.0000 -957.3401 -549.5050 \% Attendance 8.5014 1.0771 7.8929 0.0000 6.3292 10.6735 Salary 0.000000685 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 14-15, what is the p-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?

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Question 147

TABLE 14-15 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 = % Passing as the dependent variable, X₁ = % Attendance, X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R 0.6029 Square Standard 10.4570 Error Observations 47 $\text { ANOVA }$ df SS MS Significance F Regression 3 7965.08 2655.03 24.2802 0.0000 Residual 43 4702.02 109.35 Total 46 12667.11 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 0.0000 -957.3401 -549.5050 \% Attendance 8.5014 1.0771 7.8929 0.0000 6.3292 10.6735 Salary 0.000000685 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 14-15, what is the value of the test statistic to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

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Question 148

TABLE 14-15 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 = % Passing as the dependent variable, X₁ = % Attendance, X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R 0.6029 Square Standard 10.4570 Error Observations 47 $\text { ANOVA }$ df SS MS Significance F Regression 3 7965.08 2655.03 24.2802 0.0000 Residual 43 4702.02 109.35 Total 46 12667.11 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 0.0000 -957.3401 -549.5050 \% Attendance 8.5014 1.0771 7.8929 0.0000 6.3292 10.6735 Salary 0.000000685 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 14-15, which of the following is a correct statement?

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Question 149

A multiple regression is called "multiple" because it has several explanatory variables.

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Question 150

Consider a regression in which b₂ = -1.5 and the standard error of this coefficient equals 0.3. To determine whether X₂ is a significant explanatory variable, you would compute an observed t-value of -5.0.

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Question 151

TABLE 14-14 An automotive engineer would like to be able to predict automobile mileages. She believes that the two most important characteristics that affect mileage are horsepower and the number of cylinders (4 or 6) of a car. She believes that the appropriate model is Y = 40 - 0.05X₁ + 20X₂ - 0.1X₁X₂ where X₁ = horsepower X₂ = 1 if 4 cylinders, 0 if 6 cylinders Y = mileage. -Referring to Table 14-14, the predicted mileage for a 300 horsepower, 6-cylinder car is ________.

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Question 152

TABLE 14-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. Regression Statistics Multiple R 0.8013 R Square 0.6421 Adjusted R Square 0.6313 Standard Error 1.0507 Observations 171 $\text { ANOVA }$ df SS MS F Significance F Regression 5 326.8700 65.3740 59.2168 0.0000 Residual 165 182.1564 1.1040 Total 170 509.0263 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 12.8627 1.0927 11.7713 0.0000 10.7052 15.0202 Cargo Vol 0.0259 0.0102 2.5518 0.0116 0.0059 0.0460 HP -0.0200 0.0018 -11.3307 0.0000 -0.0235 -0.0165 MPG -0.0620 0.0303 -2.0464 0.0423 -0.1218 -0.0022 SUV 0.7679 0.4314 1.7802 0.0769 -0.0838 1.6196 Sedan 0.6427 0.2790 2.3034 0.0225 0.0918 1.1935 The various residual plots are as shown below. $TABLE 14-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. \begin{array}{|lr|} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8013 \\ \hline \text { R Square } & 0.6421 \\ \hline \text { Adjusted R Square } & 0.6313 \\ \hline \text { Standard Error } & 1.0507 \\ \hline \text { Observations } & 171 \\ \hline \end{array} \text { ANOVA } \begin{array}{|lrrrrrr} \hline & d f & \text { SS } & \text { MS } &{\text { F }} &{\text { Significance F }} \\ \hline \text { Regression } & 5 & 326.8700 & 65.3740 & 59.2168 & 0.0000 \\ \hline \text { Residual } & 165 & 182.1564 & 1.1040 & & \\ \hline \text { Total } & 170 & 509.0263 & & & \\ \hline \end{array} \begin{array}{|lr|rrr|r|r|} \hline & \text { Coefficients } & \text { Standard Error } &{\text { t Stat }} & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 12.8627 & 1.0927 & 11.7713 & 0.0000 & 10.7052 & 15.0202 \\ \hline \text { Cargo Vol } & 0.0259 & 0.0102 & 2.5518 & 0.0116 & 0.0059 & 0.0460 \\ \hline \text { HP } & -0.0200 & 0.0018 & -11.3307 & 0.0000 & -0.0235 & -0.0165 \\ \hline \text { MPG } & -0.0620 & 0.0303 & -2.0464 & 0.0423 & -0.1218 & -0.0022 \\ \hline \text { SUV } & 0.7679 & 0.4314 & 1.7802 & 0.0769 & -0.0838 & 1.6196 \\ \hline \text { Sedan } & 0.6427 & 0.2790 & 2.3034 & 0.0225 & 0.0918 & 1.1935 \\ \hline \end{array} The various residual plots are as shown below. The coefficients of partial determination \left( R ^ { 2 }_{Y j} \right. . (All variables except \left. j \right) of each of the 5 predictors are, respectively, 0.0380,0.4376,0.0248,0.0188 , and 0.0312 . The coefficient of multiple determination for the regression model using each of the 5 variables X _ { j } as the dependent variable and all other X variables as independent variables \left( R _ { j } ^ { 2 } \right) are, respectively, 0.7461,0.5676,0.6764,0.8582,0.6632 . -Referring to 14-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.7679 seconds higher than that of an SUV.$ $TABLE 14-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. \begin{array}{|lr|} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8013 \\ \hline \text { R Square } & 0.6421 \\ \hline \text { Adjusted R Square } & 0.6313 \\ \hline \text { Standard Error } & 1.0507 \\ \hline \text { Observations } & 171 \\ \hline \end{array} \text { ANOVA } \begin{array}{|lrrrrrr} \hline & d f & \text { SS } & \text { MS } &{\text { F }} &{\text { Significance F }} \\ \hline \text { Regression } & 5 & 326.8700 & 65.3740 & 59.2168 & 0.0000 \\ \hline \text { Residual } & 165 & 182.1564 & 1.1040 & & \\ \hline \text { Total } & 170 & 509.0263 & & & \\ \hline \end{array} \begin{array}{|lr|rrr|r|r|} \hline & \text { Coefficients } & \text { Standard Error } &{\text { t Stat }} & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 12.8627 & 1.0927 & 11.7713 & 0.0000 & 10.7052 & 15.0202 \\ \hline \text { Cargo Vol } & 0.0259 & 0.0102 & 2.5518 & 0.0116 & 0.0059 & 0.0460 \\ \hline \text { HP } & -0.0200 & 0.0018 & -11.3307 & 0.0000 & -0.0235 & -0.0165 \\ \hline \text { MPG } & -0.0620 & 0.0303 & -2.0464 & 0.0423 & -0.1218 & -0.0022 \\ \hline \text { SUV } & 0.7679 & 0.4314 & 1.7802 & 0.0769 & -0.0838 & 1.6196 \\ \hline \text { Sedan } & 0.6427 & 0.2790 & 2.3034 & 0.0225 & 0.0918 & 1.1935 \\ \hline \end{array} The various residual plots are as shown below. The coefficients of partial determination \left( R ^ { 2 }_{Y j} \right. . (All variables except \left. j \right) of each of the 5 predictors are, respectively, 0.0380,0.4376,0.0248,0.0188 , and 0.0312 . The coefficient of multiple determination for the regression model using each of the 5 variables X _ { j } as the dependent variable and all other X variables as independent variables \left( R _ { j } ^ { 2 } \right) are, respectively, 0.7461,0.5676,0.6764,0.8582,0.6632 . -Referring to 14-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.7679 seconds higher than that of an SUV.$ $TABLE 14-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. \begin{array}{|lr|} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8013 \\ \hline \text { R Square } & 0.6421 \\ \hline \text { Adjusted R Square } & 0.6313 \\ \hline \text { Standard Error } & 1.0507 \\ \hline \text { Observations } & 171 \\ \hline \end{array} \text { ANOVA } \begin{array}{|lrrrrrr} \hline & d f & \text { SS } & \text { MS } &{\text { F }} &{\text { Significance F }} \\ \hline \text { Regression } & 5 & 326.8700 & 65.3740 & 59.2168 & 0.0000 \\ \hline \text { Residual } & 165 & 182.1564 & 1.1040 & & \\ \hline \text { Total } & 170 & 509.0263 & & & \\ \hline \end{array} \begin{array}{|lr|rrr|r|r|} \hline & \text { Coefficients } & \text { Standard Error } &{\text { t Stat }} & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 12.8627 & 1.0927 & 11.7713 & 0.0000 & 10.7052 & 15.0202 \\ \hline \text { Cargo Vol } & 0.0259 & 0.0102 & 2.5518 & 0.0116 & 0.0059 & 0.0460 \\ \hline \text { HP } & -0.0200 & 0.0018 & -11.3307 & 0.0000 & -0.0235 & -0.0165 \\ \hline \text { MPG } & -0.0620 & 0.0303 & -2.0464 & 0.0423 & -0.1218 & -0.0022 \\ \hline \text { SUV } & 0.7679 & 0.4314 & 1.7802 & 0.0769 & -0.0838 & 1.6196 \\ \hline \text { Sedan } & 0.6427 & 0.2790 & 2.3034 & 0.0225 & 0.0918 & 1.1935 \\ \hline \end{array} The various residual plots are as shown below. The coefficients of partial determination \left( R ^ { 2 }_{Y j} \right. . (All variables except \left. j \right) of each of the 5 predictors are, respectively, 0.0380,0.4376,0.0248,0.0188 , and 0.0312 . The coefficient of multiple determination for the regression model using each of the 5 variables X _ { j } as the dependent variable and all other X variables as independent variables \left( R _ { j } ^ { 2 } \right) are, respectively, 0.7461,0.5676,0.6764,0.8582,0.6632 . -Referring to 14-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.7679 seconds higher than that of an SUV.$ $TABLE 14-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. \begin{array}{|lr|} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8013 \\ \hline \text { R Square } & 0.6421 \\ \hline \text { Adjusted R Square } & 0.6313 \\ \hline \text { Standard Error } & 1.0507 \\ \hline \text { Observations } & 171 \\ \hline \end{array} \text { ANOVA } \begin{array}{|lrrrrrr} \hline & d f & \text { SS } & \text { MS } &{\text { F }} &{\text { Significance F }} \\ \hline \text { Regression } & 5 & 326.8700 & 65.3740 & 59.2168 & 0.0000 \\ \hline \text { Residual } & 165 & 182.1564 & 1.1040 & & \\ \hline \text { Total } & 170 & 509.0263 & & & \\ \hline \end{array} \begin{array}{|lr|rrr|r|r|} \hline & \text { Coefficients } & \text { Standard Error } &{\text { t Stat }} & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 12.8627 & 1.0927 & 11.7713 & 0.0000 & 10.7052 & 15.0202 \\ \hline \text { Cargo Vol } & 0.0259 & 0.0102 & 2.5518 & 0.0116 & 0.0059 & 0.0460 \\ \hline \text { HP } & -0.0200 & 0.0018 & -11.3307 & 0.0000 & -0.0235 & -0.0165 \\ \hline \text { MPG } & -0.0620 & 0.0303 & -2.0464 & 0.0423 & -0.1218 & -0.0022 \\ \hline \text { SUV } & 0.7679 & 0.4314 & 1.7802 & 0.0769 & -0.0838 & 1.6196 \\ \hline \text { Sedan } & 0.6427 & 0.2790 & 2.3034 & 0.0225 & 0.0918 & 1.1935 \\ \hline \end{array} The various residual plots are as shown below. The coefficients of partial determination \left( R ^ { 2 }_{Y j} \right. . (All variables except \left. j \right) of each of the 5 predictors are, respectively, 0.0380,0.4376,0.0248,0.0188 , and 0.0312 . The coefficient of multiple determination for the regression model using each of the 5 variables X _ { j } as the dependent variable and all other X variables as independent variables \left( R _ { j } ^ { 2 } \right) are, respectively, 0.7461,0.5676,0.6764,0.8582,0.6632 . -Referring to 14-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.7679 seconds higher than that of an SUV.$ $TABLE 14-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. \begin{array}{|lr|} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8013 \\ \hline \text { R Square } & 0.6421 \\ \hline \text { Adjusted R Square } & 0.6313 \\ \hline \text { Standard Error } & 1.0507 \\ \hline \text { Observations } & 171 \\ \hline \end{array} \text { ANOVA } \begin{array}{|lrrrrrr} \hline & d f & \text { SS } & \text { MS } &{\text { F }} &{\text { Significance F }} \\ \hline \text { Regression } & 5 & 326.8700 & 65.3740 & 59.2168 & 0.0000 \\ \hline \text { Residual } & 165 & 182.1564 & 1.1040 & & \\ \hline \text { Total } & 170 & 509.0263 & & & \\ \hline \end{array} \begin{array}{|lr|rrr|r|r|} \hline & \text { Coefficients } & \text { Standard Error } &{\text { t Stat }} & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 12.8627 & 1.0927 & 11.7713 & 0.0000 & 10.7052 & 15.0202 \\ \hline \text { Cargo Vol } & 0.0259 & 0.0102 & 2.5518 & 0.0116 & 0.0059 & 0.0460 \\ \hline \text { HP } & -0.0200 & 0.0018 & -11.3307 & 0.0000 & -0.0235 & -0.0165 \\ \hline \text { MPG } & -0.0620 & 0.0303 & -2.0464 & 0.0423 & -0.1218 & -0.0022 \\ \hline \text { SUV } & 0.7679 & 0.4314 & 1.7802 & 0.0769 & -0.0838 & 1.6196 \\ \hline \text { Sedan } & 0.6427 & 0.2790 & 2.3034 & 0.0225 & 0.0918 & 1.1935 \\ \hline \end{array} The various residual plots are as shown below. The coefficients of partial determination \left( R ^ { 2 }_{Y j} \right. . (All variables except \left. j \right) of each of the 5 predictors are, respectively, 0.0380,0.4376,0.0248,0.0188 , and 0.0312 . The coefficient of multiple determination for the regression model using each of the 5 variables X _ { j } as the dependent variable and all other X variables as independent variables \left( R _ { j } ^ { 2 } \right) are, respectively, 0.7461,0.5676,0.6764,0.8582,0.6632 . -Referring to 14-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.7679 seconds higher than that of an SUV.$ The coefficients of partial determination $\left( R ^ { 2 }_{Y j} \right.$ . (All variables except $\left. j \right)$ of each of the 5 predictors are, respectively, $0.0380,0.4376,0.0248,0.0188$ , and $0.0312$ . The coefficient of multiple determination for the regression model using each of the 5 variables $X _ { j }$ as the dependent variable and all other $X$ variables as independent variables $\left( R _ { j } ^ { 2 } \right)$ are, respectively, $0.7461,0.5676,0.6764,0.8582,0.6632$ . -Referring to 14-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.7679 seconds higher than that of an SUV.

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Question 153

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. SUMMARY OUTPUT Regression Statistics Multiple R 0.830 R Square 0.689 Adjusted R Square 0.662 Standard Error 17501.643 Observations 26 ANOVA df SS MS F Signif F Regression 2 15579777040 7789888520 25.432 0.0001 Residual 23 7045072780 306307512 Total 25 22624849820 Coeff StdError t Stat p -value Intercept 15800.0000 6038.2999 2.617 0.0154 Capital 0.1245 0.2045 0.609 0.5485 Wages 7.0762 1.4729 4.804 0.0001 -Referring to Table 14-5, one company in the sample had sales of $20 billion (Sales = 20,000). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars)for this data point?

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Question 154

The coefficient of multiple determination is calculated by taking the ratio of the regression sum of squares over the total sum of squares (SSR/SST)and subtracting that value from 1.

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Question 155

TABLE 14-13 An econometrician is interested in evaluating the relationship of demand for building materials to mortgage rates in Los Angeles and San Francisco. He believes that the appropriate model is Y = 10 + 5X₁ + 8X₂ where X₁ = mortgage rate in % X₂ = 1 if SF, 0 if LA Y = demand in $100 per capita -Referring to Table 14-13, the effect of living in San Francisco rather than Los Angeles is to increase the mean demand by an estimated ________.

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Question 156

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: SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA df SS MS F Signif F Regression 3605.7736 1201.9245 0.0000 Residual 1214.2264 26.3962 Total 49 4820.0000 Coeff StdError 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, 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)?

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Question 157

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: SUMMARY OUTPUT SUMMARY OUTPUT Regression Statistics Multiple R 0.916 R Square 0.839 Adjusted R Square 0.732 Standard Error 0.24685 Observations 6 ANOVA df SS MS F Signif F Regression 2 0.95219 0.47610 7.813 0.0646 Residual 3 0.18281 0.06094 Total 5 1.13500 Coeff StdError 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 X?. At a level of significance of 0.05, the department head would decide that = ?? ? = 0.

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Question 158

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: SUMMARY OUTPUT Regression Statistics Multiple R 0.992 R Square 0.984 Adjusted R Square 0.979 Standard Error 2.26743 Observations 20 ANOVA df SS MS F Signif F Regression 4 4609.83164 1152.45791 224.160 0.0001 Residual 15 77.11836 5.14122 Total 19 4686.95000 Coeff StdError 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 estimate of the unit change in the mean of Y per unit change in X₄, taking into account the effects of the other 3 variables, is ________.

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Question 159

In calculating the standard error of the estimate, SYX = $\sqrt { \mathrm { MSE } }$ , there are n - k - 1 degrees of freedom, where n is the sample size and k represents the number of independent variables in the model.

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Question 160

Showing 141 - 160 of 355

A multiple regression is called "multiple" because it has several explanatory variables.

Consider a regression in which b₂ = -1.5 and the standard error of this coefficient equals 0.3. To determine whether X₂ is a significant explanatory variable, you would compute an observed t-value of -5.0.

The coefficient of multiple determination is calculated by taking the ratio of the regression sum of squares over the total sum of squares (SSR/SST)and subtracting that value from 1.

In calculating the standard error of the estimate, SYX = $\sqrt { \mathrm { MSE } }$ , there are n - k - 1 degrees of freedom, where n is the sample size and k represents the number of independent variables in the model.

Introduction

Organizing and Visualizing Data

Numerical Descriptive Measures

Basic Probability

Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling and Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Two-Sample Tests

Analysis of Variance

Chi-Square Tests and Nonparametric Tests

Simple Linear Regression

Multiple Regression Model Building

Time-Series Forecasting

Statistical Applications in Quality Management

A Roadmap for Analyzing Data

Filters

Exam 14: Introduction to Multiple Regression

A multiple regression is called "multiple" because it has several explanatory variables.

Consider a regression in which b₂ = -1.5 and the standard error of this coefficient equals 0.3. To determine whether X₂ is a significant explanatory variable, you would compute an observed t-value of -5.0.

The coefficient of multiple determination is calculated by taking the ratio of the regression sum of squares over the total sum of squares (SSR/SST)and subtracting that value from 1.

In calculating the standard error of the estimate, SYX = MSE\sqrt { \mathrm { MSE } }MSE​ , there are n - k - 1 degrees of freedom, where n is the sample size and k represents the number of independent variables in the model.

Introduction

Organizing and Visualizing Data

Numerical Descriptive Measures

Basic Probability

Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling and Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Two-Sample Tests

Analysis of Variance

Chi-Square Tests and Nonparametric Tests

Simple Linear Regression

Multiple Regression Model Building

Time-Series Forecasting

Statistical Applications in Quality Management

A Roadmap for Analyzing Data

Filters

In calculating the standard error of the estimate, SYX = $\sqrt { \mathrm { MSE } }$ , there are n - k - 1 degrees of freedom, where n is the sample size and k represents the number of independent variables in the model.