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 is the value of the test statistic when testing whether being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff while holding constant the effect of all the other independent variables?

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

TABLE 14-6 One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X₁) the amount of insulation in inches (X₂), the number of windows in the house (X₃), and the age of the furnace in years (X₄). Given below are the Excel outputs of two regression models. Model 1 $\begin{array}{|lr} \hline{\text { Regression Statistics }} \\ \hline \text { R Square } & 0.8080 \\ \hline \text { Adjusted R Square } & 0.7568 \\ \hline \text { Observations } & 20 \\ \hline \end{array}$ $\mathrm{ANOVA}$ $\begin{array}{llrrrrrr} \hline & \text { df } &{S S} & M S & F &{\text { Significance F }} \\ \hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 0.0000 \\ \text { Residual } & 15 & 40262.3259 & 2684.155 & & & \\ \hline \text { Total } & 19 & 209765.75 & & & \\ \hline \end{array}$ $\begin{array}{lrrrrrrr} \hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 90.0\% } & \text { Upper 90.0\% } \\ \hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 0.0000 & 284.9327 & 557.9227 \\ \hline \mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 0.0000 & -5.9349 & -3.0847 \\ \mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\ \mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\ \mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702 \end{array}$ Model 2 $\begin{array}{|lr|} \hline {\text { Regression Statistics }} \\ \hline \text { R Square } & 0.7768 \\ \hline \text { Adjusted R Square } & 0.7506 \\ \hline \text { Observations } & 20 \\ \hline \end{array}$ $\text { ANOVA }$ $\begin{array}{|lrrrccc} \hline & & & & & & \text { Significance } \\ & d f & \text { SS } & \text { MS } & F & F \\ \hline \text { Regression } & 2 & 162958.2277 & 81479.11 & 29.5923 & 0.0000 \\ \text { Residual } & & 17 & 46807.5222 & 2753.384 & & \\ \hline \text { Total } & 19 & 209765.75 & & & \\ \hline \end{array}$ $\begin{array} { | l | r | r | r |r| r| r| } \hline& \text { Coefficients } & { \begin{array} { c } \text { Standard } \\ \text { Error } \end{array} } & \ { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 0.0000 & 396.5273 & 582.1180 \\ \mathrm { X } _ { 1 } \text { (Temperature) } & - 5.1103 & 0.6951 & - 7.3515 & 0.0000 & - 6.5769 & - 3.6437 \\ \hline \mathrm { X } _ { 2 } \text { (Insulation) } & - 14.7195 & 4.8864 & - 3.0123 & 0.0078 & - 25.0290 & - 4.4099\\ \hline \end{array}$ -Referring to Table 14-6, what are the degrees of freedom of the partial F test for H?: = ?? = ?? = 0 vs. H?: At least one ?? ? 0, j = 3, 4?

A) 2 numerator degrees of freedom and 15 denominator degrees of freedom B) 15 numerator degrees of freedom and 2 denominator degrees of freedom C) 2 numerator degrees of freedom and 17 denominator degrees of freedom D) 17 numerator degrees of freedom and 2 denominator degrees of freedom A) 2 numerator degrees of freedom and 15 denominator degrees of freedom B) 15 numerator degrees of freedom and 2 denominator degrees of freedom C) 2 numerator degrees of freedom and 17 denominator degrees of freedom D) 17 numerator degrees of freedom and 2 denominator degrees of freedom

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 value of the F-statistic for testing the significance of the entire regression is ________.

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

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 the correct alternative hypothesis to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

A) H?: ?? = ?? = ?? = ?? ? 0 B) H?: ?? = ?? = ?? ? 0 C) H?: At least one of ?? ? 0 for j = 0, 1, 2, 3 D) H?: At least one of ?? ? 0 for j = 1, 2, 3 A) H?: ?? = ?? = ?? = ?? ? 0 B) H?: ?? = ?? = ?? ? 0 C) H?: At least one of ?? ? 0 for j = 0, 1, 2, 3 D) H?: At least one of ?? ? 0 for j = 1, 2, 3

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, what are the predicted sales (in millions of dollars)for a company spending $100 million on capital and $100 million on wages?

A) 15,800.00 B) 16,520.07 C) 17,277.49 D) 20,455.98 A) 15,800.00 B) 16,520.07 C) 17,277.49 D) 20,455.98

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 critical value of an F test on the entire regression for a level of significance of 0.01 is ________.

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

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, which of the independent variables in the model are significant at the 5% level?

A) Income, Size, School B) Income, Size C) Size, School D) Income, School A) Income, Size, School B) Income, Size C) Size, School D) Income, School

Exam 14: Introduction to Multiple Regression

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 is the value of the test statistic when testing whether being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff while holding constant the effect of all the other independent variables?

(Short Answer)

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Question 21

The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.

(True/False)

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Question 22

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 SUV 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 SUV 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 SUV 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 SUV 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 SUV 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 SUV 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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The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression 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

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