TABLE 14-18 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on mean total Scholastic Aptitude Test score (SAT) at the university or college, the room and board expense measured in thousands of dollars (Room/Brd), and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise). The Minitab output is given below: Logistic Regression Table $\begin{array}{lrrrcrrrr} & & & & &{\text { Odds }} &{95 \% \mathrm{CI}} \\ \text { Predictor } & \text { Coef } & \text { SE Coef } & \mathrm{Z} & \mathrm{P} & \text { Ratio } & \text { Lower } & \text { Upper } \\ \text { Constant } & -27.118 & 6.696 & -4.05 & 0.000 & & & \\ \text { SAT } & 0.015 & 0.004666 & 3.17 & 0.002 & 1.01 & 1.01 & 1.02 \\ \text { Toefl550 } & -0.390 & 0.9538 & -0.41 & 0.682 & 0.68 & 0.10 & 4.39 \\ \text { Room/Brd } & 2.078 & 0.5076 & 4.09 & 0.000 & 7.99 & 2.95 & 21.60 \end{array}$ Log-Likelihood $= - 21.883$ Test that all slopes are zero: $\mathrm { G } = 62.083 , \mathrm { DF } = 3 , p$-value $= 0.000$ Goodness-of-Fit Tests $\begin{array} { l r r c } \text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 143.551 & 76 & 0.000 \\ \text { Deviance } & 43.767 & 76 & 0.999 \\ \text { Hosmer-Lemeshow } & 15.731 & 8 & 0.046 \end{array}$ -Referring to Table 14-18, 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 14-18 A logistic regression model was estimated...

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, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of School in the regression model?

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

TABLE 14-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. SUMMARY OUTPUT Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$ ANOVA $\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text { Residual } & 7 & 0.6277 & 0.0897 & & \\ \text { Total } & 9 & 34.0440 & & & \end{array}$ $\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$ -Referring to Table 14-3, one economy in the sample had an aggregate consumption level of $3 billion, a GDP of $3.5 billion, and an aggregate price level of 125. What is the residual for this data point?

A) $2.52 billion B) $0.48 billion C) -$1.33 billion D) -$2.52 billion A) $2.52 billion B) $0.48 billion C) -$1.33 billion D) -$2.52 billion

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, which of the following is the correct null hypothesis 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?

A) H?: ?? = ?? = ?? = ?? = ?? = ?? = ?? = 0 B) H?: ?? = ?? = ?? = ?? = ?? = ?? = 0 C) H?: ?? = ?? = ?? = ?? = ?? = ?? = ?? D) H?: ?? = ?? = ?? = ?? = ?? = ?? A) H?: ?? = ?? = ?? = ?? = ?? = ?? = ?? = 0 B) H?: ?? = ?? = ?? = ?? = ?? = ?? = 0 C) H?: ?? = ?? = ?? = ?? = ?? = ?? = ?? D) H?: ?? = ?? = ?? = ?? = ?? = ??

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 $\begin{array}{l} \text { Regression Statistics }\\ \begin{array}{ll} \text { Multiple R } & 0.916 \\ \text { R Square } & 0.839 \\ \text { Adjusted R Square } & 0.732 \\ \text { Standard Error } & 0.24685 \\ \text { Observations } & 6 \end{array} \end{array}$ ANOVA $\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & 2 & 0.95219 & 0.47610 & 7.813 & 0.0646 \\ \text { Residual } & 3 & 0.18281 & 0.06094 & & \\ \text { Total } & 5 & 1.13500 & & & \end{array}$ $\begin{array} { l r c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & 4.593897 & 1.13374542 & 4.052 & 0.0271 \\ \text { Units } & - 0.247270 & 0.06268485 & - 3.945 & 0.0290 \\ \text { SAT Total } & 0.001443 & 0.00101241 & 1.425 & 0.2494 \end{array}$ -Referring to Table 14-7, the net regression coefficient of X₂ is ________.

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

TABLE 14-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. SUMMARY OUTPUT Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$ ANOVA $\begin{array}{llrrrr} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text { Residual } & 7 & 0.6277 & 0.0897 & & \\ \text { Total } & 9 & 34.0440 & & & \end{array}$ $\begin{array} { l c l r l } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 0.0861 & 0.5674 & - 0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 \end{array}$ -Referring to Table 14-3, what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?

A) $1.39 billion B) $2.89 billion C) $4.75 billion D) $9.45 billion A) $1.39 billion B) $2.89 billion C) $4.75 billion D) $9.45 billion

TABLE 14-10 You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in Excel and obtained the following information: \[\text { Regression Analysis }\] $\begin{array}{lr} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.63 \\ \hline \text { R Square } & 0.40 \\ \hline \text { Adjusted R Square } & 0.23 \\ \hline \text { Standard Error } & 50.00 \\ \hline \text { Observations } & 15.00 \\ \hline \end{array}$ $\text { ANOVA }$ $\begin{array} { | r | r | c | c | r| r| } \hline & d f & S S & M S & F & \text { Significance F } \\ \hline \text { Regression } & 3 & & 5994.24 & 2.40 & 0.12 \\ \hline \text { Residual } & 11 & 27496.82 & & & \\ \hline \text { Total } & & 45479.54 & & & \\ \hline \end{array}$ $\begin{array}{|lr|r|r|r|r|r} \hline & \text { Coefficients } & \begin{array}{c} \text { Standard } \\ \text { Error } \end{array} &{t \text { Stat }} & \text { P-value } & \text { Lower 99.0\% } & \text { Upper 99.0\% } \\ \hline \text { Intercept } & 123.80 & 48.71 & 2.54 & 0.03 & -27.47 & 275.07 \\ \hline \text { AGE } & -0.82 & 0.87 & -0.95 & 0.36 & -3.51 & 1.87 \\ \hline \text { TICKETS } & 21.25 & 10.66 & 1.99 & 0.07 & -11.86 & 54.37 \\ \hline \text { DENSITY } & -3.14 & 6.46 & -0.49 & 0.64 & -23.19 & 16.91 \\ \hline \end{array}$ -Referring to Table 14-10, the proportion of the total variability in insurance premiums that can be explained by AGE, TICKETS, and DENSITY is ________.

The answer of TABLE 14-10 You worked as an intern at...

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, predict the number of weeks being unemployed due to a layoff for a worker who is a thirty-year old, has 10 years of education, has 15 years of experience at the previous job, is married, is the head of household and is a manager.

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

Exam 14: Introduction to Multiple Regression

TABLE 14-18 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on mean total Scholastic Aptitude Test score (SAT) at the university or college, the room and board expense measured in thousands of dollars (Room/Brd), and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise). The Minitab output is given below: Logistic Regression Table Odds 95\% Predictor Coef SE Coef Ratio Lower Upper Constant -27.118 6.696 -4.05 0.000 SAT 0.015 0.004666 3.17 0.002 1.01 1.01 1.02 Toefl550 -0.390 0.9538 -0.41 0.682 0.68 0.10 4.39 Room/Brd 2.078 0.5076 4.09 0.000 7.99 2.95 21.60 Log-Likelihood $= - 21.883$ Test that all slopes are zero: $\mathrm { G } = 62.083 , \mathrm { DF } = 3 , p$ -value $= 0.000$ Goodness-of-Fit Tests Method Chi-Square DF P Pearson 143.551 76 0.000 Deviance 43.767 76 0.999 Hosmer-Lemeshow 15.731 8 0.046 -Referring to Table 14-18, 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 301

A multiple regression is called "multiple" because it has several data points.

(True/False)

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Question 302

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, there is sufficient evidence that instructional spending per pupil has an effect on percentage of students passing the proficiency test while holding constant the effect of all the other independent variables at a 5% level of significance.

(True/False)

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Question 303

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 coupe is predicted to be 0.7679 seconds lower 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 coupe is predicted to be 0.7679 seconds lower 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 coupe is predicted to be 0.7679 seconds lower 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 coupe is predicted to be 0.7679 seconds lower 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 coupe is predicted to be 0.7679 seconds lower 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 coupe is predicted to be 0.7679 seconds lower than that of an SUV.

(True/False)

4.7/5

(38)

Question 304

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, what is the value of the test statistic to determine whether HP makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?$ $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, what is the value of the test statistic to determine whether HP makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?$ $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, what is the value of the test statistic to determine whether HP makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?$ $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, what is the value of the test statistic to determine whether HP makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?$ $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, what is the value of the test statistic to determine whether HP makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?$ 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, what is the value of the test statistic to determine whether HP makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

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Question 305

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, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of School in the regression model?

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Question 306

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, there is sufficient evidence that daily mean of the percentage of students attending class has an effect on percentage of students passing the proficiency test while holding constant the effect of all the other independent variables at a 5% level of significance.

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Question 307

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, there is sufficient evidence that the number of weeks a worker is unemployed due to a layoff depends on all of the explanatory variables at a 10% level of significance.

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Question 308

TABLE 14-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. SUMMARY OUTPUT Regression Statistics Multiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 ANOVA df SS MS F Signif F Regression 2 33.4163 16.7082 186.325 0.0001 Residual 7 0.6277 0.0897 Total 9 34.0440 Coeff StdError t Stat p -value Intercept -0.0861 0.5674 -0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price -0.0006 0.0028 -0.219 0.8330 -Referring to Table 14-3, one economy in the sample had an aggregate consumption level of $3 billion, a GDP of $3.5 billion, and an aggregate price level of 125. What is the residual for this data point?

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Question 309

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, which of the following is the correct null hypothesis 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 310

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 net regression coefficient of X₂ is ________.

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Question 311

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, the alternative hypothesis H?: At least one of ?? ? 0 for j = 1, 2, 3 implies that percentage of students passing the proficiency test is affected by at least one of the explanatory variables.

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Question 312

TABLE 14-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. SUMMARY OUTPUT Regression Statistics Multiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 ANOVA df SS MS F Signif F Regression 2 33.4163 16.7082 186.325 0.0001 Residual 7 0.6277 0.0897 Total 9 34.0440 Coeff StdError t Stat p -value Intercept -0.0861 0.5674 -0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price -0.0006 0.0028 -0.219 0.8330 -Referring to Table 14-3, what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?

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Question 313

TABLE 14-10 You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in Excel and obtained the following information: $\text { Regression Analysis }$ Regression Statistics Multiple R 0.63 R Square 0.40 Adjusted R Square 0.23 Standard Error 50.00 Observations 15.00 $\text { ANOVA }$ df SS MS F Significance F Regression 3 5994.24 2.40 0.12 Residual 11 27496.82 Total 45479.54 Coefficients Standard Error t Stat P-value Lower 99.0\% Upper 99.0\% Intercept 123.80 48.71 2.54 0.03 -27.47 275.07 AGE -0.82 0.87 -0.95 0.36 -3.51 1.87 TICKETS 21.25 10.66 1.99 0.07 -11.86 54.37 DENSITY -3.14 6.46 -0.49 0.64 -23.19 16.91 -Referring to Table 14-10, the proportion of the total variability in insurance premiums that can be explained by AGE, TICKETS, and DENSITY is ________.

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Question 314

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, if variables that measure the number of new business starts in the last year and population density of the city were removed from the multiple regression model, which of the following would be true?

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Question 315

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, predict the number of weeks being unemployed due to a layoff for a worker who is a thirty-year old, has 10 years of education, has 15 years of experience at the previous job, is married, is the head of household and is a manager.

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Question 316

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, what is the p-value of the test statistic to determine whether MPG makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?$ $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, what is the p-value of the test statistic to determine whether MPG makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?$ $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, what is the p-value of the test statistic to determine whether MPG makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?$ $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, what is the p-value of the test statistic to determine whether MPG makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?$ $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, what is the p-value of the test statistic to determine whether MPG makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?$ 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, what is the p-value of the test statistic to determine whether MPG makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

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Question 317

TABLE 14-2 A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X₁) and the number of economics courses the employee successfully completed in college (X₂). The professor randomly selects 6 workers and collects the following information: $\begin{array}{cccccc}\underline { \text { Employee } } &\underline { Y (\$)} & \underline { X } _ { 1 } & \underline { X _ { 2 } }\\1 & 10 & 3 & 0 \\2 & 12 & 1 & 5 \\3 & 15 & 8 & 1 \\4 & 17 & 5 & 8 \\5 & 20 & 7 & 12 \\6 & 25 & 10 & 9\end{array}$ -The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by

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Question 318

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 319

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, the alternative hypothesis H?: At least one of ?? ? 0 for j = 1, 2, 3, 4, 5, 6 implies that the number of weeks a worker is unemployed due to a layoff is related to at least one of the explanatory variables.

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Question 320

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A multiple regression is called "multiple" because it has several data points.

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

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