SCENARIO 13-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size).House size is measured in hundreds of square feet and income is measured in thousands of dollars.The builder randomly selected 50 families and ran the multiple regression.Partial Microsoft Excel output is provided below: $\begin{array}{lr} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8479 \\ \text { R Square } & 0.7189 \\ \text { Adjusted R Square } & 0.7069 \\ \text { Standard Error } & 17.5571 \\ \text { Observations } & 50\\ \hline \end{array}$ $\text { ANOVA }$ $\begin{array}{lrrrrr} & d f & \text { SS } & {M S} & F & \text { Significance } F \\ \hline \text { Regression } & & & 37043.3236 & 18521.6618 & 0.0000 \\ \text { Residual } & & 14487.7627 & 308.2503 & \\ \text { Total } & & 49 & 51531.0863 & & \end{array}$ $\begin{array}{lrrrr} \hline & \text { Coefficients } & \text { Standard Error } &{t \text { Stat }} & \text { P-value } \\ \hline \text { Intercept } & -5.5146 & 7.2273 & -0.7630 & 0.4493 \\ \text { Income } & 0.4262 & 0.0392 & 10.8668 & 0.0000 \\ \text { Size } & 5.5437 & 1.6949 & 3.2708 & 0.0020\\ \hline \end{array}$ $\text { Also } \operatorname{SSR}\left(X_{1} \mid X_{2}\right)=36400.6326 \text { and } \operatorname{SSR}\left(X_{2} \mid X_{1}\right)=3297.7917$ -Referring to SCENARIO 13-4, which of the independent variables in the model are significant at the 5% level?

A) Income only B) Size only C) Income and Size D) None A) Income only B) Size only C) Income and Size D) None

SCENARIO 13-1 A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2).A random sample of 8 employees provides the following: \[\begin{array} { c r r r } \text { Emplovee } & { Y } & { X _ { 1 } } & X _ { 2 } \\ \hline 1 & 100 & 10 & 7 \\ 2 & 90 & 3 & 10 \\ 3 & 80 & 8 & 9 \\ 4 & 70 & 5 & 4 \\ 5 & 60 & 5 & 8 \\ 6 & 50 & 7 & 5 \\ 7 & 40 & 1 & 4 \\ 8 & 30 & 1 & 1 \end{array}\] -Referring to SCENARIO 13-1, for these data, what is the estimated coefficient for the variable representing years an employee has been with the company, b1?

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

SCENARIO 13-10 You worked as an intern at We Always Win Car Insurance Company last summer.You notice that individual car insurance premiums depend very much on the age of the individual and the number of traffic tickets received by the individual.You performed a regression analysis in EXCEL and obtained the following partial information: \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.8546 \\ \text { R Square } & 0.7303 \\ \text { Adjusted R Square } & 0.6853 \\ \text { Standard Error } & 226.7502 \\ \text { Observations } & 15 \\ \hline \end{array}\\\\ \text { ANOVA }\\ \begin{array}{lrrrrrr} & d f & & \text { SS } & \text { MS } & \text { F } & \text { Significance } F \\ \hline \text { Regression } & & 2 & & \text { 835284.6500 } & 16.2457 & 0.0004 \\ \text { Residual } & & 12 & 616987.8200 & & & \\ \text { Total } & & & 2287557.1200 & & & \\ \hline \end{array}\\\\ \begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 99\% } & { \text { Upper 99\% } } \\ \hline \text { Intercept } & 821.2617 & 161.9391 & 5.0714 & 0.0003 & 326.6124 & 1315.9111 \\ \text { Age } & - 1.4061 & 2.5988 & - 0.5411 & 0.5984 & - 9.3444 & 6.5321 \\ \text { Tickets } & 243.4401 & 43.2470 & 5.6291 & 0.0001 & 111.3406 & 375.5396 \\ \hline \end{array} \end{array}\] -Referring to SCENARIO 13-10, to test the significance of the multiple regression model, what is the form of the null hypothesis?

A) $H _ { 0 } : \beta _ { 1 } = 0$ B) $H _ { 0 } : \beta _ { 2 } = 0$ C) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = 0$ D) $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = 0$ A) $H _ { 0 } : \beta _ { 1 } = 0$ B) $H _ { 0 } : \beta _ { 2 } = 0$ C) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = 0$ D) $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = 0$

SCENARIO 13-1 A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2).A random sample of 8 employees provides the following: \[\begin{array} { c r r r } \text { Emplovee } & { Y } & { X _ { 1 } } & X _ { 2 } \\ \hline 1 & 100 & 10 & 7 \\ 2 & 90 & 3 & 10 \\ 3 & 80 & 8 & 9 \\ 4 & 70 & 5 & 4 \\ 5 & 60 & 5 & 8 \\ 6 & 50 & 7 & 5 \\ 7 & 40 & 1 & 4 \\ 8 & 30 & 1 & 1 \end{array}\] -Referring to SCENARIO 13-1, for these data, what is the estimated coefficient for the variable representing scores on the aptitude test, b2?

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

SCENARIO 13-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size).House size is measured in hundreds of square feet and income is measured in thousands of dollars.The builder randomly selected 50 families and ran the multiple regression.Partial Microsoft Excel output is provided below: $\begin{array}{lr} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8479 \\ \text { R Square } & 0.7189 \\ \text { Adjusted R Square } & 0.7069 \\ \text { Standard Error } & 17.5571 \\ \text { Observations } & 50\\ \hline \end{array}$ $\text { ANOVA }$ $\begin{array}{lrrrrr} & d f & \text { SS } & {M S} & F & \text { Significance } F \\ \hline \text { Regression } & & & 37043.3236 & 18521.6618 & 0.0000 \\ \text { Residual } & & 14487.7627 & 308.2503 & \\ \text { Total } & & 49 & 51531.0863 & & \end{array}$ $\begin{array}{lrrrr} \hline & \text { Coefficients } & \text { Standard Error } &{t \text { Stat }} & \text { P-value } \\ \hline \text { Intercept } & -5.5146 & 7.2273 & -0.7630 & 0.4493 \\ \text { Income } & 0.4262 & 0.0392 & 10.8668 & 0.0000 \\ \text { Size } & 5.5437 & 1.6949 & 3.2708 & 0.0020\\ \hline \end{array}$ $\text { Also } \operatorname{SSR}\left(X_{1} \mid X_{2}\right)=36400.6326 \text { and } \operatorname{SSR}\left(X_{2} \mid X_{1}\right)=3297.7917$ -Referring to SCENARIO 13-4, which of the following values for the level of significance is the smallest for which at least one explanatory variable is significant individually?

A) 0.005 B) 0.010 C) 0.025 D) 0.050 A) 0.005 B) 0.010 C) 0.025 D) 0.050

SCENARIO 13-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size).House size is measured in hundreds of square feet and income is measured in thousands of dollars.The builder randomly selected 50 families and ran the multiple regression.Partial Microsoft Excel output is provided below: $\begin{array}{lr} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8479 \\ \text { R Square } & 0.7189 \\ \text { Adjusted R Square } & 0.7069 \\ \text { Standard Error } & 17.5571 \\ \text { Observations } & 50\\ \hline \end{array}$ $\text { ANOVA }$ $\begin{array}{lrrrrr} & d f & \text { SS } & {M S} & F & \text { Significance } F \\ \hline \text { Regression } & & & 37043.3236 & 18521.6618 & 0.0000 \\ \text { Residual } & & 14487.7627 & 308.2503 & \\ \text { Total } & & 49 & 51531.0863 & & \end{array}$ $\begin{array}{lrrrr} \hline & \text { Coefficients } & \text { Standard Error } &{t \text { Stat }} & \text { P-value } \\ \hline \text { Intercept } & -5.5146 & 7.2273 & -0.7630 & 0.4493 \\ \text { Income } & 0.4262 & 0.0392 & 10.8668 & 0.0000 \\ \text { Size } & 5.5437 & 1.6949 & 3.2708 & 0.0020\\ \hline \end{array}$ $\text { Also } \operatorname{SSR}\left(X_{1} \mid X_{2}\right)=36400.6326 \text { and } \operatorname{SSR}\left(X_{2} \mid X_{1}\right)=3297.7917$ -Referring to SCENARIO 13-4, when the builder used a simple linear regression model with house size (House) as the dependent variable and family size (Size) as the independent variable, he obtained an r2 value of 1.25%.What additional percentage of the total variation in house size has been explained by including income in the multiple regression?

A) 15.00% B) 70.64% C) 71.50% D) 73.62% A) 15.00% B) 70.64% C) 71.50% D) 73.62%

SCENARIO 13-6 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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X1 ) and the amount of insulation in inches ( X 2 ).Given below is EXCEL output of the regression model. \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.5270 \\ \text { R Square } & 0.2778 \\ \text { Adjusted R Square } & 0.1928 \\ \text { Standard Error } & 40.9107 \\ \text { Observations } & 20 \\ \hline \end{array}\\ \end{array}\] $\begin{array}{lrrrrr} \text { ANOVA }\\ \hline&\text { df } & \text { SS } & \text { MS } & F & \text { Significance F }\\ \hline\text { Regression } & 2 & 10943.0190 & 5471.5095 & 3.2691 & 0.0629 \\ \text { Residual } & 17 & 28452.6027 & 1673.6825 & & \\ \text { Total } & 19 & 39395.6218 & & & \end{array}$ 13-22 Multiple Regression \[\begin{array}{l} \begin{array} { l r r r r r r } \hline & \text { Coefficients } &{ \text { Standard Error } } & { \text { t Stat } } & \text { P-volue } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 448.2925 & 90.7853 & 4.9379 & 0.0001 & 256.7522 & 639.8328 \\ \text { Temperature } & - 2.7621 & 1.2371 & - 2.2327 & 0.0393 & - 5.3721 & - 0.1520 \\ \text { Insulation } & - 15.9408 & 10.0638 & - 1.5840 & 0.1316 & - 37.1736 & 5.2919 \\ \hline \end{array}\\ \text { Also } \operatorname { SSR } \left( X _ { 1 } \mid X _ { 2 } \right) = 8343.3572 \text { and } \operatorname { SSR } \left( X _ { 2 } \mid X _ { 1 } \right) = 4199.2672 \end{array}\] -Referring to SCENARIO 13-6, the estimated value of the regression parameter $\beta$1 in means that

A) holding the effect of the amount of insulation constant, an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature By 2.76 degrees. B) holding the effect of the amount of insulation constant, a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $2.76. C) holding the effect of the amount of insulation constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $2.76. D) holding the effect of the amount of insulation constant, a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 2.76%. A) holding the effect of the amount of insulation constant, an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature By 2.76 degrees. B) holding the effect of the amount of insulation constant, a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $2.76. C) holding the effect of the amount of insulation constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $2.76. D) holding the effect of the amount of insulation constant, a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 2.76%.

SCENARIO 13-15 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), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X1 = Salaries and X 2 = Spending: \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.4276 \\ \text { R Square } & 0.1828 \\ \text { Adjusted R Square } & 0.1457 \\ \text { Standard Error } & 5.7351 \\ \text { Observations } & 47 \\ \hline \end{array}\\\\ \text { ANOVA }\\ \begin{array} { l r r r r r } \hline & d f & { \text { SS } } & { \text { MS } } & \text { F } & { \text { Significance } F } \\ \hline \text { Regression } & 2 & 323.8284 & 161.9142 & 4.9227 & 0.0118 \\ \text { Residual } & 44 & 1447.2094 & 32.8911 & & \\ \text { Total } & 46 & 1771.0378 & & & \\ \hline \end{array}\\\\ \begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & - 72.9916 & 45.9106 & - 1.5899 & 0.1190 & - 165.5184 & 19.5352 \\ \text { Salary } & 2.7939 & 0.8974 & 3.1133 & 0.0032 & 0.9853 & 4.6025 \\ \text { Spending } & 0.3742 & 0.9782 & 0.3825 & 0.7039 & - 1.5972 & 2.3455 \\ \hline \end{array} \end{array}\] -Referring to SCENARIO 13-15, what is the p-value of the test statistic when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, considering the effect of mean teacher salary?

The answer of SCENARIO 13-15 The superintendent of a school district...

Exam 13: Multiple Regression

SCENARIO 13-15 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), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X1 = Salaries and X 2 = Spending: Regression Statistics Multiple R 0.4276 R Square 0.1828 Adjusted R Square 0.1457 Standard Error 5.7351 Observations 47 ANOVA df SS MS F Significance F Regression 2 323.8284 161.9142 4.9227 0.0118 Residual 44 1447.2094 32.8911 Total 46 1771.0378 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -72.9916 45.9106 -1.5899 0.1190 -165.5184 19.5352 Salary 2.7939 0.8974 3.1133 0.0032 0.9853 4.6025 Spending 0.3742 0.9782 0.3825 0.7039 -1.5972 2.3455 -Referring to SCENARIO 13-15, you can conclude that instructional spending per pupil has no impact on the mean percentage of students passing the proficiency test, considering the effect of mean teacher salary, at a 5% level of significance using the confidence interval estimate for $\beta$ 2 .

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Question 121

SCENARIO 13-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size).House size is measured in hundreds of square feet and income is measured in thousands of dollars.The builder randomly selected 50 families and ran the multiple regression.Partial Microsoft Excel output is provided below: Regression Statistics Multiple R 0.8479 R Square 0.7189 Adjusted R Square 0.7069 Standard Error 17.5571 Observations 50 $\text { ANOVA }$ df SS MS F Significance F Regression 37043.3236 18521.6618 0.0000 Residual 14487.7627 308.2503 Total 49 51531.0863 Coefficients Standard Error t Stat P-value Intercept -5.5146 7.2273 -0.7630 0.4493 Income 0.4262 0.0392 10.8668 0.0000 Size 5.5437 1.6949 3.2708 0.0020 $\text { Also } \operatorname{SSR}\left(X_{1} \mid X_{2}\right)=36400.6326 \text { and } \operatorname{SSR}\left(X_{2} \mid X_{1}\right)=3297.7917$ -Referring to SCENARIO 13-4, which of the independent variables in the model are significant at the 5% level?

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Question 122

SCENARIO 13-1 A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2).A random sample of 8 employees provides the following: Emplovee Y 1 100 10 7 2 90 3 10 3 80 8 9 4 70 5 4 5 60 5 8 6 50 7 5 7 40 1 4 8 30 1 1 -Referring to SCENARIO 13-1, for these data, what is the estimated coefficient for the variable representing years an employee has been with the company, b1?

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Question 123

SCENARIO 13-10 You worked as an intern at We Always Win Car Insurance Company last summer.You notice that individual car insurance premiums depend very much on the age of the individual and the number of traffic tickets received by the individual.You performed a regression analysis in EXCEL and obtained the following partial information: Regression Statistics Multiple R 0.8546 R Square 0.7303 Adjusted R Square 0.6853 Standard Error 226.7502 Observations 15 ANOVA df SS MS F Significance F Regression 2 835284.6500 16.2457 0.0004 Residual 12 616987.8200 Total 2287557.1200 Coefficients Standard Error t Stat P-value Lower 99\% Upper 99\% Intercept 821.2617 161.9391 5.0714 0.0003 326.6124 1315.9111 Age -1.4061 2.5988 -0.5411 0.5984 -9.3444 6.5321 Tickets 243.4401 43.2470 5.6291 0.0001 111.3406 375.5396 -Referring to SCENARIO 13-10, to test the significance of the multiple regression model, what is the form of the null hypothesis?

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Question 124

Using the hat matrix elements hi to determine influential points in a multiple regression model with k independent variable and n observations, Xi is an influential point if

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Question 125

SCENARIO 13-9 You decide to predict gasoline prices in different cities and towns in the United States for your term project.Your dependent variable is price of gasoline per gallon and your explanatory variables are per capita income and the number of firms that manufacture automobile parts in and around the city.You collected data of 32 cities and obtained a regression sum of squares SSR= 122.8821.Your computed value of standard error of the estimate is 1.9549. -Referring to SCENARIO 13-9, if the variable that measures the number of firms that manufacture automobile parts in and around the city is removed from the multiple regression model, which of the following would be true?

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Question 126

SCENARIO 13-1 A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2).A random sample of 8 employees provides the following: Emplovee Y 1 100 10 7 2 90 3 10 3 80 8 9 4 70 5 4 5 60 5 8 6 50 7 5 7 40 1 4 8 30 1 1 -Referring to SCENARIO 13-1, for these data, what is the estimated coefficient for the variable representing scores on the aptitude test, b2?

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Question 127

SCENARIO 13-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size).House size is measured in hundreds of square feet and income is measured in thousands of dollars.The builder randomly selected 50 families and ran the multiple regression.Partial Microsoft Excel output is provided below: Regression Statistics Multiple R 0.8479 R Square 0.7189 Adjusted R Square 0.7069 Standard Error 17.5571 Observations 50 $\text { ANOVA }$ df SS MS F Significance F Regression 37043.3236 18521.6618 0.0000 Residual 14487.7627 308.2503 Total 49 51531.0863 Coefficients Standard Error t Stat P-value Intercept -5.5146 7.2273 -0.7630 0.4493 Income 0.4262 0.0392 10.8668 0.0000 Size 5.5437 1.6949 3.2708 0.0020 $\text { Also } \operatorname{SSR}\left(X_{1} \mid X_{2}\right)=36400.6326 \text { and } \operatorname{SSR}\left(X_{2} \mid X_{1}\right)=3297.7917$ -Referring to SCENARIO 13-4, which of the following values for the level of significance is the smallest for which at least one explanatory variable is significant individually?

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Question 128

SCENARIO 13-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size).House size is measured in hundreds of square feet and income is measured in thousands of dollars.The builder randomly selected 50 families and ran the multiple regression.Partial Microsoft Excel output is provided below: Regression Statistics Multiple R 0.8479 R Square 0.7189 Adjusted R Square 0.7069 Standard Error 17.5571 Observations 50 $\text { ANOVA }$ df SS MS F Significance F Regression 37043.3236 18521.6618 0.0000 Residual 14487.7627 308.2503 Total 49 51531.0863 Coefficients Standard Error t Stat P-value Intercept -5.5146 7.2273 -0.7630 0.4493 Income 0.4262 0.0392 10.8668 0.0000 Size 5.5437 1.6949 3.2708 0.0020 $\text { Also } \operatorname{SSR}\left(X_{1} \mid X_{2}\right)=36400.6326 \text { and } \operatorname{SSR}\left(X_{2} \mid X_{1}\right)=3297.7917$ -Referring to SCENARIO 13-4, when the builder used a simple linear regression model with house size (House) as the dependent variable and family size (Size) as the independent variable, he obtained an r2 value of 1.25%.What additional percentage of the total variation in house size has been explained by including income in the multiple regression?

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Question 129

SCENARIO 13-6 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 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X1 ) and the amount of insulation in inches ( X 2 ).Given below is EXCEL output of the regression model. Regression Statistics Multiple R 0.5270 R Square 0.2778 Adjusted R Square 0.1928 Standard Error 40.9107 Observations 20 ANOVA df SS MS F Significance F Regression 2 10943.0190 5471.5095 3.2691 0.0629 Residual 17 28452.6027 1673.6825 Total 19 39395.6218 13-22 Multiple Regression Coefficients Standard Error t Stat P-volue Lower 95\% Upper 95\% Intercept 448.2925 90.7853 4.9379 0.0001 256.7522 639.8328 Temperature -2.7621 1.2371 -2.2327 0.0393 -5.3721 -0.1520 Insulation -15.9408 10.0638 -1.5840 0.1316 -37.1736 5.2919 Also SSR \mid =8343.3572 and SSR \mid =4199.2672 -Referring to SCENARIO 13-6, the estimated value of the regression parameter $\beta$ 1 in means that

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Question 130

If a categorical independent variable contains 2 categories, then dummy variable(s)will be needed to uniquely represent these categories.

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Question 131

SCENARIO 13-18 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 and whether the TOEFL criterion is at least 90 (Toefl90 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise).There are 80 universities in the sample. The PHStat output is given below: Binary Logistic Regression Predictor Coefficients SE Coef Z p -Value Intercept -3.9594 1.6741 -2.3650 0.0180 SAT 0.0028 0.0011 2.5459 0.0109 Toefl90:1 0.1928 0.5827 0.3309 0.7407 Deviance 101.9826 -Referring to SCENARIO 13-18, what are the degrees of freedom for the chi-square distribution when testing whether the model is a good-fitting model?

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Question 132

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

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Question 133

SCENARIO 13-15 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), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X1 = Salaries and X 2 = Spending: Regression Statistics Multiple R 0.4276 R Square 0.1828 Adjusted R Square 0.1457 Standard Error 5.7351 Observations 47 ANOVA df SS MS F Significance F Regression 2 323.8284 161.9142 4.9227 0.0118 Residual 44 1447.2094 32.8911 Total 46 1771.0378 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -72.9916 45.9106 -1.5899 0.1190 -165.5184 19.5352 Salary 2.7939 0.8974 3.1133 0.0032 0.9853 4.6025 Spending 0.3742 0.9782 0.3825 0.7039 -1.5972 2.3455 -Referring to SCENARIO 13-15, the null hypothesis H0 : $\beta$ 1 = $\beta$ 2 = 0 implies that percentageof students passing the proficiency test is not related to either of the explanatory variables.

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Question 134

SCENARIO 13-17 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) and a dummy variable for management position (Manager: 1 = yes, 0 = no). The results of the regression analysis are given below: Regression Statistics Multiple R 0.6391 R Square 0.4085 Adjusted R Square 0.3765 Standard Error 18.8929 Observations 40 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 SCENARIO 13-17, the alternative hypothesis H 1: At least one of $\beta$ j $\neq$ 0 for j =1, 2 implies that the number of weeks a worker is unemployed due to a layoff is related to at least one of the explanatory variables.

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Question 135

SCENARIO 13-15 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), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X1 = Salaries and X 2 = Spending: Regression Statistics Multiple R 0.4276 R Square 0.1828 Adjusted R Square 0.1457 Standard Error 5.7351 Observations 47 ANOVA df SS MS F Significance F Regression 2 323.8284 161.9142 4.9227 0.0118 Residual 44 1447.2094 32.8911 Total 46 1771.0378 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -72.9916 45.9106 -1.5899 0.1190 -165.5184 19.5352 Salary 2.7939 0.8974 3.1133 0.0032 0.9853 4.6025 Spending 0.3742 0.9782 0.3825 0.7039 -1.5972 2.3455 -Referring to SCENARIO 13-15, what is the p-value of the test statistic when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, considering the effect of mean teacher salary?

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Question 136

SCENARIO 13-2 A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2).The professor randomly selects 6 workers and collects the following information: Employee Y(\ ) 1 10 3 0 2 12 1 5 3 15 8 1 4 17 5 8 5 20 7 12 6 25 10 9 -Referring to SCENARIO 13-2, for these data, what is the estimated coefficient for the number of economics courses taken, b2?

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Question 137

SCENARIO 13-18 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 and whether the TOEFL criterion is at least 90 (Toefl90 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise).There are 80 universities in the sample. The PHStat output is given below: Binary Logistic Regression Predictor Coefficients SE Coef Z p -Value Intercept -3.9594 1.6741 -2.3650 0.0180 SAT 0.0028 0.0011 2.5459 0.0109 Toefl90:1 0.1928 0.5827 0.3309 0.7407 Deviance 101.9826 -Referring to SCENARIO 13-18, which of the following is the correct expression for the estimated model?

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Question 138

SCENARIO 13-18 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 and whether the TOEFL criterion is at least 90 (Toefl90 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise).There are 80 universities in the sample. The PHStat output is given below: Binary Logistic Regression Predictor Coefficients SE Coef Z p -Value Intercept -3.9594 1.6741 -2.3650 0.0180 SAT 0.0028 0.0011 2.5459 0.0109 Toefl90:1 0.1928 0.5827 0.3309 0.7407 Deviance 101.9826 -Referring to SCENARIO 13-18, which of the following is the correct interpretation for theToefl90 slope coefficient?

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Question 139

The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by

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Question 140

Using the hat matrix elements hi to determine influential points in a multiple regression model with k independent variable and n observations, Xi is an influential point if

If a categorical independent variable contains 2 categories, then dummy variable(s)will be needed to uniquely represent these categories.

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

The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by

Defining and Collecting Data

Organizing and Visualizing Variables

Numerical Descriptive Measures

Basic Probability

Discrete Probability Distributions

The Normal Distribution

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Two-Sample Tests

Chi-Square Tests

Simple Linear Regression

Business Analytics

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