TABLE 14-11 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in pounds). Two variables thought to affect weight-loss are client's length of time on the weight-loss program and time of session. These variables are described below: Y = Weight-loss (in pounds) X₁ = Length of time in weight-loss program (in months) X₂ = 1 if morning session, 0 if not X₃ = 1 if afternoon session, 0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₁X₂ + β₅X₁X₂ + ε Partial output from Microsoft Excel follows: Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.73514 \\ \text { R Square } & 0.540438 \\ \text { Adjusted R Square } & 0.157469 \\ \text { Standard Error } & 12.4147 \\ \text { Observations } & 12 \end{array}$ ANOVA $F = 5.41118 \quad$ Significance $F = 0.040201$ $\begin{array}{crrrr} & \text { Coeff } & \text { StdError } & {t \text { Stat }} & p \text {-value } \\ \text { Intercept } & 0.089744 & 14.127 & 0.0060 & 0.9951 \\ \text { Length }\left(X_{1}\right) & 6.22538 & 2.43473 & 2.54956 & 0.0479 \\ \text { Morn Ses }\left(X_{2}\right) & 2.217272 & 22.1416 & 0.100141 & 0.9235 \\ \text { Aft Ses }\left(X_{3}\right) & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\ \text { Length*Morn Ses } & 0.77058 & 3.562 & 0.216334 & 0.8359 \\ \text { Length }{ }^{*} \text { Aft Ses } & -0.54147 & 3.35988 & -0.161158 & 0.8773 \end{array}$ -Referring to Table 14-11, which of the following statements is supported by the analysis shown?

A) There is sufficient evidence (at ? = 0.05) of curvature in the relationship between weight-loss (Y) and months in program(X?). B) There is sufficient evidence (at ? = 0.05) to indicate that the relationship between weight-loss (Y) and months in program (X?) depends on session time. C) There is sufficient evidence (at ? = 0.10) to indicate that the session time (morning, afternoon, evening) affects weight-loss (Y). D) There is insufficient evidence (at ? = 0.10) to indicate that the relationship between weight-loss (Y) and months in program(X?) depends on session time. A) There is sufficient evidence (at ? = 0.05) of curvature in the relationship between weight-loss (Y) and months in program(X?). B) There is sufficient evidence (at ? = 0.05) to indicate that the relationship between weight-loss (Y) and months in program (X?) depends on session time. C) There is sufficient evidence (at ? = 0.10) to indicate that the session time (morning, afternoon, evening) affects weight-loss (Y). D) There is insufficient evidence (at ? = 0.10) to indicate that the relationship between weight-loss (Y) and months in program(X?) depends on session time.

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 age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of all the other independent variables?

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, the estimated value of the partial regression parameter ?? in Model 1 means that

A) holding the effect of the other independent variables constant, an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature by 4.51 degrees. B) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $4.51. C) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $4.51. D) holding the effect of the other independent variables constant, a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 4.51%. A) holding the effect of the other independent variables constant, an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature by 4.51 degrees. B) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $4.51. C) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $4.51. D) holding the effect of the other independent variables constant, a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 4.51%.

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, at the 0.01 level of significance, what conclusion should the microeconomist reach regarding the inclusion of Capital in the regression model?

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

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 reach regarding the inclusion of Income in the regression model?

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

TABLE 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Atitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below: Logistic Regression Table $\begin{array}{lrrrrrrr} & & & & & \text { Odds } & {95 \% \text { CI }} \\ \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { Z } & \text { P } & \text { Ratio } & \text { Lower } & \text { Upper } \\ \text { Constant } & -70.49 & 47.22 & -1.49 & 0.135 & & & \\ \text { Income } & 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\ \text { LawnSiz } & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\ \text { Attitude } & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\ \text { Teenager } & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\ \text { Age } & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45 \end{array}$ Log-Likelihood $= - 4.890$ Test that all slopes are zero: $\mathrm { G } = 31.808 , \mathrm { DF } = 5 , p$-value $= 0.000$ Goodness-of-Fit Tests $\begin{array} { l c r c } \text { Method } & \text { Chi-Square } & \text { DF } & \mathrm { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000 \end{array}$ -Referring to Table 14-19, which of the following is the correct interpretation for the Attitude slope coefficient?

A) Holding constant the effect of the other variables, the estimated number of lawn service purchased is 12.74 lower for a home owner who has a favorable attitude toward outdoor recreational activities than one that has an unfavorable attitude. B) Holding constant the effect of the other variables, the estimated odds ratio of purchasing a lawn service is 12.74 lower for a home owner who has a favorable attitude toward outdoor recreational activities than one that has an unfavorable attitude. C) Holding constant the effect of the other variables, the estimated natural logarithm of the odds ratio of purchasing a lawn service is 12.74 lower for a home owner who has a favorable attitude toward outdoor recreational activities than one that has an unfavorable attitude. D) Holding constant the effect of the other variables, the estimated probability of purchasing a lawn service is 12.74 lower for a home owner who has a favorable attitude toward outdoor recreational activities than one that has an unfavorable attitude. A) Holding constant the effect of the other variables, the estimated number of lawn service purchased is 12.74 lower for a home owner who has a favorable attitude toward outdoor recreational activities than one that has an unfavorable attitude. B) Holding constant the effect of the other variables, the estimated odds ratio of purchasing a lawn service is 12.74 lower for a home owner who has a favorable attitude toward outdoor recreational activities than one that has an unfavorable attitude. C) Holding constant the effect of the other variables, the estimated natural logarithm of the odds ratio of purchasing a lawn service is 12.74 lower for a home owner who has a favorable attitude toward outdoor recreational activities than one that has an unfavorable attitude. D) Holding constant the effect of the other variables, the estimated probability of purchasing a lawn service is 12.74 lower for a home owner who has a favorable attitude toward outdoor recreational activities than one that has an unfavorable attitude.

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, when the builder used a simple linear regression model with house size (House)as the dependent variable and education (School)as the independent variable, he obtained an r² value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

A) 2.8% B) 51.8% C) 72.6% D) 74.8% A) 2.8% B) 51.8% C) 72.6% D) 74.8%

TABLE 14-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array}$ ANOVA $\begin{array} { l c r r r r } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \\ \text { Residual } & & 1214.2264 & 26.3962 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$ $\begin{array} { l c c r c } & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text {-value } \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$ -Referring to Table 14-4, what is the predicted house size (in hundreds of square feet)for an individual earning an annual income of $40,000, having a family size of 4, and going to school a total of 13 years?

A) 11.43 B) 15.15 C) 24.88 D) 53.87 A) 11.43 B) 15.15 C) 24.88 D) 53.87

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, ________ of the variation in the number of weeks a worker is unemployed due to a layoff can be explained by whether the worker is head of household while controlling for the other independent variables.

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

TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. 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, the observed value of the F-statistic is given on the printout as 25.432. What are the degrees of freedom for this F-statistic?

A) 25 for the numerator, 2 for the denominator B) 2 for the numerator, 23 for the denominator C) 23 for the numerator, 25 for the denominator D) 2 for the numerator, 25 for the denominator A) 25 for the numerator, 2 for the denominator B) 2 for the numerator, 23 for the denominator C) 23 for the numerator, 25 for the denominator D) 2 for the numerator, 25 for the denominator

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 is the estimated odds ratio for a school with an mean SAT score of 1100, a TOEFL criterion that is not at least 550, and the room and board expense of 7 thousand dollars?

The answer of TABLE 14-18 A logistic regression model was estimated...

TABLE 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Atitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below: Logistic Regression Table $\begin{array}{lrrrrrrr} & & & & & \text { Odds } & {95 \% \text { CI }} \\ \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { Z } & \text { P } & \text { Ratio } & \text { Lower } & \text { Upper } \\ \text { Constant } & -70.49 & 47.22 & -1.49 & 0.135 & & & \\ \text { Income } & 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\ \text { LawnSiz } & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\ \text { Attitude } & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\ \text { Teenager } & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\ \text { Age } & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45 \end{array}$ Log-Likelihood $= - 4.890$ Test that all slopes are zero: $\mathrm { G } = 31.808 , \mathrm { DF } = 5 , p$-value $= 0.000$ Goodness-of-Fit Tests $\begin{array} { l c r c } \text { Method } & \text { Chi-Square } & \text { DF } & \mathrm { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000 \end{array}$ -Referring to Table 14-19, what should be the decision ('reject' or 'do not reject')on the null hypothesis when testing whether Teenager makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance?

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

TABLE 14-4 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, one individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. This individual owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet)for this data point?

A) 7.40 B) 2.52 C) -2.52 D) -5.40 A) 7.40 B) 2.52 C) -2.52 D) -5.40

Exam 14: Introduction to Multiple Regression

TABLE 14-11 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in pounds). Two variables thought to affect weight-loss are client's length of time on the weight-loss program and time of session. These variables are described below: Y = Weight-loss (in pounds) X₁ = Length of time in weight-loss program (in months) X₂ = 1 if morning session, 0 if not X₃ = 1 if afternoon session, 0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₁X₂ + β₅X₁X₂ + ε Partial output from Microsoft Excel follows: Regression Statistics Multiple R 0.73514 R Square 0.540438 Adjusted R Square 0.157469 Standard Error 12.4147 Observations 12 ANOVA $F = 5.41118 \quad$ Significance $F = 0.040201$ Coeff StdError t Stat p -value Intercept 0.089744 14.127 0.0060 0.9951 Length 6.22538 2.43473 2.54956 0.0479 Morn Ses 2.217272 22.1416 0.100141 0.9235 Aft Ses 11.8233 3.1545 3.558901 0.0165 Length*Morn Ses 0.77058 3.562 0.216334 0.8359 Length Aft Ses -0.54147 3.35988 -0.161158 0.8773 -Referring to Table 14-11, which of the following statements is supported by the analysis shown?

(Multiple Choice)

4.8/5

(26)

Question 161

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 error appears to be right-skewed.$ $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 error appears to be right-skewed.$ $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 error appears to be right-skewed.$ $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 error appears to be right-skewed.$ $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 error appears to be right-skewed.$ 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 error appears to be right-skewed.

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Question 162

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 age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of all the other independent variables?

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Question 163

TABLE 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Atitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below: Logistic Regression Table Odds 95\% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -70.49 47.22 -1.49 0.135 Income 0.2868 0.1523 1.88 0.060 1.33 0.99 1.80 LawnSiz 1.0647 0.7472 1.42 0.154 2.90 0.67 12.54 Attitude -12.744 9.455 -1.35 0.178 0.00 0.00 326.06 Teenager -0.200 1.061 -0.19 0.850 0.82 0.10 6.56 Age 1.0792 0.8783 1.23 0.219 2.94 0.53 16.45 Log-Likelihood $= - 4.890$ Test that all slopes are zero: $\mathrm { G } = 31.808 , \mathrm { DF } = 5 , p$ -value $= 0.000$ Goodness-of-Fit Tests Method Chi-Square DF Pearson 9.313 24 0.997 Deviance 9.780 24 0.995 Hosmer-Lemeshow 0.571 8 1.000 -Referring to Table 14-19, there is not enough evidence to conclude that Attitude makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance.

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Question 164

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 Regression Statistics R Square 0.8080 Adjusted R Square 0.7568 Observations 20 $\mathrm{ANOVA}$ df SS MS F Significance F Regression 4 169503.4241 42375.86 15.7874 0.0000 Residual 15 40262.3259 2684.155 Total 19 209765.75 Coefficients Standard Error t Stat P-value Lower 90.0\% Upper 90.0\% Intercept 421.4277 77.8614 5.4125 0.0000 284.9327 557.9227 (Temperature) -4.5098 0.8129 -5.5476 0.0000 -5.9349 -3.0847 (Insulation) -14.9029 5.0508 -2.9505 0.0099 -23.7573 -6.0485 (Windows) 0.2151 4.8675 0.0442 0.9653 -8.3181 8.7484 (Furnace Age) 6.3780 4.1026 1.5546 0.1408 -0.8140 13.5702 Model 2 Regression Statistics R Square 0.7768 Adjusted R Square 0.7506 Observations 20 $\text { ANOVA }$ Significance df SS MS F F Regression 2 162958.2277 81479.11 29.5923 0.0000 Residual 17 46807.5222 2753.384 Total 19 209765.75 Coefficients Standard Error \ t Stat P-value Lower 95\% Upper 95\% Intercept 489.3227 43.9826 11.1253 0.0000 396.5273 582.1180 (Temperature) -5.1103 0.6951 -7.3515 0.0000 -6.5769 -3.6437 (Insulation) -14.7195 4.8864 -3.0123 0.0078 -25.0290 -4.4099 -Referring to Table 14-6, the estimated value of the partial regression parameter ?? in Model 1 means that

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Question 165

When an additional explanatory variable is introduced into a multiple regression model, the adjusted r² can never decrease.

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Question 166

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 null hypothesis H?: ?? = ?? = ?? = ?? = ?? = ?? = 0 implies that the number of weeks a worker is unemployed due to a layoff is not affected by some of the explanatory variables.

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Question 167

TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT Regression Statistics Multiple R 0.830 R Square 0.689 Adjusted R Square 0.662 Standard Error 17501.643 Observations 26 ANOVA df SS MS F Signif F Regression 2 15579777040 7789888520 25.432 0.0001 Residual 23 7045072780 306307512 Total 25 22624849820 Coeff StdError t Stat p -value Intercept 15800.0000 6038.2999 2.617 0.0154 Capital 0.1245 0.2045 0.609 0.5485 Wages 7.0762 1.4729 4.804 0.0001 -Referring to Table 14-5, at the 0.01 level of significance, what conclusion should the microeconomist reach regarding the inclusion of Capital in the regression model?

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Question 168

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 reach regarding the inclusion of Income in the regression model?

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Question 169

TABLE 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Atitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below: Logistic Regression Table Odds 95\% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -70.49 47.22 -1.49 0.135 Income 0.2868 0.1523 1.88 0.060 1.33 0.99 1.80 LawnSiz 1.0647 0.7472 1.42 0.154 2.90 0.67 12.54 Attitude -12.744 9.455 -1.35 0.178 0.00 0.00 326.06 Teenager -0.200 1.061 -0.19 0.850 0.82 0.10 6.56 Age 1.0792 0.8783 1.23 0.219 2.94 0.53 16.45 Log-Likelihood $= - 4.890$ Test that all slopes are zero: $\mathrm { G } = 31.808 , \mathrm { DF } = 5 , p$ -value $= 0.000$ Goodness-of-Fit Tests Method Chi-Square DF Pearson 9.313 24 0.997 Deviance 9.780 24 0.995 Hosmer-Lemeshow 0.571 8 1.000 -Referring to Table 14-19, which of the following is the correct interpretation for the Attitude slope coefficient?

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Question 170

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 and using both Model 1 and Model 2, what are the degrees of freedom of the test statistic for testing whether the independent variables that are not significant individually are also not significant as a group in explaining the variation in the dependent variable at a 5% level of significance?

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Question 171

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 at least one of the explanatory variables is related to the number of weeks a worker is unemployed due to a layoff at a 10% level of significance.

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Question 172

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, when the builder used a simple linear regression model with house size (House)as the dependent variable and education (School)as the independent variable, he obtained an r² value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

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Question 173

TABLE 14-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA df SS MS F Signif F Regression 3605.7736 1201.9245 0.0000 Residual 1214.2264 26.3962 Total 49 4820.0000 Coeff StdError t Stat p -value Intercept -1.6335 5.8078 -0.281 0.7798 Income 0.4485 0.1137 3.9545 0.0003 Size 4.2615 0.8062 5.286 0.0001 School -0.6517 0.4319 -1.509 0.1383 -Referring to Table 14-4, what is the predicted house size (in hundreds of square feet)for an individual earning an annual income of $40,000, having a family size of 4, and going to school a total of 13 years?

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Question 174

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, ________ of the variation in the number of weeks a worker is unemployed due to a layoff can be explained by whether the worker is head of household while controlling for the other independent variables.

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Question 175

TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. SUMMARY OUTPUT Regression Statistics Multiple R 0.830 R Square 0.689 Adjusted R Square 0.662 Standard Error 17501.643 Observations 26 ANOVA df SS MS F Signif F Regression 2 15579777040 7789888520 25.432 0.0001 Residual 23 7045072780 306307512 Total 25 22624849820 Coeff StdError t Stat p -value Intercept 15800.0000 6038.2999 2.617 0.0154 Capital 0.1245 0.2045 0.609 0.5485 Wages 7.0762 1.4729 4.804 0.0001 -Referring to Table 14-5, the observed value of the F-statistic is given on the printout as 25.432. What are the degrees of freedom for this F-statistic?

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Question 176

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 is the estimated odds ratio for a school with an mean SAT score of 1100, a TOEFL criterion that is not at least 550, and the room and board expense of 7 thousand dollars?

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Question 177

The coefficient of multiple determination measures the proportion of the total variation in the dependent variable that is explained by the set of independent variables.

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Question 178

TABLE 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Atitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below: Logistic Regression Table Odds 95\% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -70.49 47.22 -1.49 0.135 Income 0.2868 0.1523 1.88 0.060 1.33 0.99 1.80 LawnSiz 1.0647 0.7472 1.42 0.154 2.90 0.67 12.54 Attitude -12.744 9.455 -1.35 0.178 0.00 0.00 326.06 Teenager -0.200 1.061 -0.19 0.850 0.82 0.10 6.56 Age 1.0792 0.8783 1.23 0.219 2.94 0.53 16.45 Log-Likelihood $= - 4.890$ Test that all slopes are zero: $\mathrm { G } = 31.808 , \mathrm { DF } = 5 , p$ -value $= 0.000$ Goodness-of-Fit Tests Method Chi-Square DF Pearson 9.313 24 0.997 Deviance 9.780 24 0.995 Hosmer-Lemeshow 0.571 8 1.000 -Referring to Table 14-19, what should be the decision ('reject' or 'do not reject')on the null hypothesis when testing whether Teenager makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance?

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Question 179

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, one individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. This individual owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet)for this data point?

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Question 180

Showing 161 - 180 of 355

When an additional explanatory variable is introduced into a multiple regression model, the adjusted r² can never decrease.

The coefficient of multiple determination measures the proportion of the total variation in the dependent variable that is explained by the set of independent variables.

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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