SCENARIO 13-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of 6 students and generates the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.916 \\ \text { R Square } & 0.839 \\ \text { Adjusted R Square } & 0.732 \\ \text { Standard Error } & 0.24685 \\ \text { Observations } & 6 \end{array}$ ANOVA $\begin{array} { l r c c r c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & 2 & 0.95219 & 0.47610 & 7.813 & 0.0646 \\ \text { Residual } & 3 & 0.18281 & 0.06094 & & \\ \text { Total } & 5 & 1.13500 & & & \end{array}$ $\begin{array} { l c r c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\ \text { Intercept } & 4.593897 & 1.13374542 & 4.052 & 0.0271 \\ \text { Units } & - 0.247270 & 0.06268485 & - 3.945 & 0.0290 \\ \text { Total SAT } & 0.001443 & 0.00101241 & 1.425 & 0.2494 \end{array}$ -Referring to SCENARIO 13-7, the estimate of the unit change in the mean of Y per unit change in X1, holding X2 constant, is _.

The answer of SCENARIO 13-7 The department head of the accounting...

SCENARIO 13-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index).The Microsoft Excel output of this regression is partially reproduced below. $\text { SUMMARY OUTPUT }$ $\begin{array}{ll} {\text { Regression Statistics }} \\ \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$ ANOVA $\begin{array}{lccccc} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text { Residual } & 7 & 0.6277 & 0.0897 & & \\ \text { Total } & 9 & 34.0440 & & & \end{array}$ $\begin{array}{lclcc} & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\ \text { Intercept } & -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & -0.0006 & 0.0028 & -0.219 & 0.8330 \end{array}$ -Referring to SCENARIO 13-3, to test for the significance of the coefficient on aggregate price, the value of the relevant t-statistic is

A) 2.365 B) 0.143 C) - 0.219 D) - 1.960 A) 2.365 B) 0.143 C) - 0.219 D) - 1.960

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: $\begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8479 \\ \text { R Square } & 0.7189 \\ \text { Adjusted R Square } & 0.7069 \\ \text { Standard Error } & 17.5571 \\ \text { Observations } & 50 \\ \hline \end{array}$ ANOVA $\begin{array} { l r c c c c }\hline & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \hline\text { Regression } & &37043.3236 & 18521.6618 && 0.0000 \\ \text { Residual } & &14487.7627 & 308.2503 & \\ \text { Total } & 49 & 51531.0863\\\hline \end{array}$ $\begin{array}{lrrrr} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } &{\text {-value }} \\ \hline \text { Intercept } & -5.5146 & 7.2273 & -0.7630 & 0.4493 \\ \text { Income } & 0.4262 & 0.0392 & 10.8668 & 0.0000 \\ \text { Size } & 5.5437 & 1.6949 & 3.2708 & 0.0020 \end{array}$ $\text { Also } \operatorname{SSR}\left(X_{1} \mid X_{2}\right)=36400.6326 \text { and } \operatorname{SSR}\left(X_{2} \mid X_{1}\right)=3297.7917$ -Referring to SCENARIO 13-4, what annual income (in thousands of dollars) would an individual with a family size of 4 need to attain a predicted 10,000 square foot home (House = 100)?

The answer of SCENARIO 13-4 A real estate builder wishes to...

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. \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.5270 \\ \text { R Square } & 0.2778 \\ \text { Adjusted R Square } & 0.1928 \\ \text { Standard Error } & 40.9107 \\ \text { Observations } & 20 \\ \hline \end{array}\\ \text { ANOVA } \end{array}\] $\begin{array} { l r c c c c }\hline & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \hline\text { Regression } & 2 & 10943.0190 & 5471.5095 & 3.2691 & 0.0629 \\ \text { Residual } & 17 & 28452.6027 & 1673.6825 & & \\ \text { Total } & 19 & 39395.6218 & &\\\hline \end{array}$ 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 13-5 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 $\begin{array} { l l } \text { Multiple R } & 0.830 \\ \text { R Square } & 0.689 \\ \text { Adjusted R Square } & 0.662 \\ \text { Standard Error } & 17501.643 \\ \text { Observations } & 26 \end{array}$ ANOVA $\begin{array} { l r c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\ \text { Residual } & 23 & 7045072780 & 306307512 & & \\ \text { Total } & 25 & 22624849820 & & & \end{array}$ $\begin{array}{lrrrc} & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$ -Referring to SCENARIO 13-5, 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.

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, predict the percentage of students passing the proficiency test for a school which has a mean teacher salary of 40,000 dollars, and an instructional spending per pupil of 2,000 dollars.

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

SCENARIO 13-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index).The Microsoft Excel output of this regression is partially reproduced below. $\text { SUMMARY OUTPUT }$ $\begin{array}{ll} {\text { Regression Statistics }} \\ \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square } & 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \end{array}$ ANOVA $\begin{array}{lccccc} & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text { Residual } & 7 & 0.6277 & 0.0897 & & \\ \text { Total } & 9 & 34.0440 & & & \end{array}$ $\begin{array}{lclcc} & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\ \text { Intercept } & -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text { Price } & -0.0006 & 0.0028 & -0.219 & 0.8330 \end{array}$ -Referring to SCENARIO 13-3, what is the predicted consumption level for an economy withGDP equal to $4 billion and an aggregate price index of 150?

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

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. \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.5270 \\ \text { R Square } & 0.2778 \\ \text { Adjusted R Square } & 0.1928 \\ \text { Standard Error } & 40.9107 \\ \text { Observations } & 20 \\ \hline \end{array}\\ \text { ANOVA } \end{array}\] $\begin{array} { l r c c c c }\hline & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \hline\text { Regression } & 2 & 10943.0190 & 5471.5095 & 3.2691 & 0.0629 \\ \text { Residual } & 17 & 28452.6027 & 1673.6825 & & \\ \text { Total } & 19 & 39395.6218 & &\\\hline \end{array}$ 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 and allowing for a 1% probability of committing a type I error,what is the decision and conclusion for the testH : $\beta$1-2= 0 vs.H : At least one $\beta$j$\neq$ 0, j - 1, 20 1 2 1 j?

A) Do not reject H0 and conclude that the 2 independent variables taken as a group have significant linear effects on heating costs. B) Do not reject H0 and conclude that the 2 independent variables taken as a group do not have significant linear effects on heating costs. C) Reject H0 and conclude that the 2 independent variables taken as a group have significant linear effects on heating costs. D) Reject H0 and conclude that the 2 independent variables taken as a group do not have significant linear effects on heating costs. A) Do not reject H0 and conclude that the 2 independent variables taken as a group have significant linear effects on heating costs. B) Do not reject H0 and conclude that the 2 independent variables taken as a group do not have significant linear effects on heating costs. C) Reject H0 and conclude that the 2 independent variables taken as a group have significant linear effects on heating costs. D) Reject H0 and conclude that the 2 independent variables taken as a group do not have significant linear effects on heating costs.

SCENARIO 13-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 2 variables: age (X1 = Age) and experience in the field (X2 = Exper).He took a sample of 20 employees and obtained the following Microsoft Excel output: \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.8535 \\ \text { R Square } & 0.7284 \\ \text { Adjusted R Square } & 0.6964 \\ \text { Standard Error } & 10.5630 \\ \text { Observations } & 20 \\ \hline \end{array}\\ \text { ANOYA }\\ \begin{array} { l r c c c c } & d f & \text { SS } & \text { MS } & \text { F } & \text { Siqnificonce F } \\ \hline \text { Regression } & 2 & 5086.5764 & 2543.2882 & 22.7941 & 0.0000 \\ \text { Residual } & 17 & 1896.8050 & 111.5768 & & \\ \text { Total } & 19 & 6983.3814 & & & \\ \hline \end{array}\\\\ \begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 1.5740 & 9.2723 & 0.1698 & 0.8672 & - 17.9888 & 21.1368 \\ \text { Age } & 1.3045 & 0.1956 & 6.6678 & 0.0000 & 0.8917 & 1.7173 \\ \text { Exper } & - 0.1478 & 0.1944 & - 0.7604 & 0.4574 & - 0.5580 & 0.2624 \\ \hline \end{array} \end{array}\] -Referring to SCENARIO 13-8, the estimate of the unit change in the mean of Y per unit change in X1, considering the effects of the other variable, is .

The answer of SCENARIO 13-8 A financial analyst wanted to examine...

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: $\begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8479 \\ \text { R Square } & 0.7189 \\ \text { Adjusted R Square } & 0.7069 \\ \text { Standard Error } & 17.5571 \\ \text { Observations } & 50 \\ \hline \end{array}$ ANOVA $\begin{array} { l r c c c c }\hline & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \hline\text { Regression } & &37043.3236 & 18521.6618 && 0.0000 \\ \text { Residual } & &14487.7627 & 308.2503 & \\ \text { Total } & 49 & 51531.0863\\\hline \end{array}$ $\begin{array}{lrrrr} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } &{\text {-value }} \\ \hline \text { Intercept } & -5.5146 & 7.2273 & -0.7630 & 0.4493 \\ \text { Income } & 0.4262 & 0.0392 & 10.8668 & 0.0000 \\ \text { Size } & 5.5437 & 1.6949 & 3.2708 & 0.0020 \end{array}$ $\text { Also } \operatorname{SSR}\left(X_{1} \mid X_{2}\right)=36400.6326 \text { and } \operatorname{SSR}\left(X_{2} \mid X_{1}\right)=3297.7917$ -Referring to SCENARIO 13-4, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of Size in the regression model?

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

SCENARIO 13-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 2 variables: age (X1 = Age) and experience in the field (X2 = Exper).He took a sample of 20 employees and obtained the following Microsoft Excel output: \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.8535 \\ \text { R Square } & 0.7284 \\ \text { Adjusted R Square } & 0.6964 \\ \text { Standard Error } & 10.5630 \\ \text { Observations } & 20 \\ \hline \end{array}\\ \text { ANOYA }\\ \begin{array} { l r c c c c } & d f & \text { SS } & \text { MS } & \text { F } & \text { Siqnificonce F } \\ \hline \text { Regression } & 2 & 5086.5764 & 2543.2882 & 22.7941 & 0.0000 \\ \text { Residual } & 17 & 1896.8050 & 111.5768 & & \\ \text { Total } & 19 & 6983.3814 & & & \\ \hline \end{array}\\\\ \begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 1.5740 & 9.2723 & 0.1698 & 0.8672 & - 17.9888 & 21.1368 \\ \text { Age } & 1.3045 & 0.1956 & 6.6678 & 0.0000 & 0.8917 & 1.7173 \\ \text { Exper } & - 0.1478 & 0.1944 & - 0.7604 & 0.4574 & - 0.5580 & 0.2624 \\ \hline \end{array} \end{array}\] -Referring to SCENARIO 13-8, _% of the variation in salary can be explained by the variation in age while holding experience constant.

The answer of SCENARIO 13-8 A financial analyst wanted to examine...

Exam 13: Multiple Regression

SCENARIO 13-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of 6 students and generates the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics Multiple R 0.916 R Square 0.839 Adjusted R Square 0.732 Standard Error 0.24685 Observations 6 ANOVA df SS MS F Signif F Regression 2 0.95219 0.47610 7.813 0.0646 Residual 3 0.18281 0.06094 Total 5 1.13500 Coeff StdError t Stat P -value Intercept 4.593897 1.13374542 4.052 0.0271 Units -0.247270 0.06268485 -3.945 0.0290 Total SAT 0.001443 0.00101241 1.425 0.2494 -Referring to SCENARIO 13-7, the estimate of the unit change in the mean of Y per unit change in X1, holding X2 constant, is _.

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Question 181

SCENARIO 13-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index).The Microsoft Excel output of this regression is partially reproduced below. $\text { SUMMARY OUTPUT }$ Regression Statistics Multiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 ANOVA df SS MS F Signif F Regression 2 33.4163 16.7082 186.325 0.0001 Residual 7 0.6277 0.0897 Total 9 34.0440 Coeff StdError t Stat P -value Intercept -0.0861 0.5674 -0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price -0.0006 0.0028 -0.219 0.8330 -Referring to SCENARIO 13-3, to test for the significance of the coefficient on aggregate price, the value of the relevant t-statistic is

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Question 182

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 null hypothesis should be rejected at a 10% level of significance when testing whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables.

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Question 183

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 a) $h _ { i } < 2 ( k + 1 ) / n$ b) $h _ { i } > 2 ( k + 1 ) / n$ c) $h _ { i } < n ( k + 1 ) / 2$ d) $h _ { i } > n ( k + 1 ) / 2$

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Question 184

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 ANOVA df SS MS F Signif F Regression 37043.3236 18521.6618 0.0000 Residual 14487.7627 308.2503 Total 49 51531.0863 Coefficients Standard Error t Stat -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, what annual income (in thousands of dollars) would an individual with a family size of 4 need to attain a predicted 10,000 square foot home (House = 100)?

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Question 185

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 186

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 are the lower and upper limits of the 95% confidence interval estimate for the effect of a one thousand dollars increase in instructional spending per pupil on the mean percentage of students passing the proficiency test?

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Question 187

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

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Question 188

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 189

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 Signif 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 190

Using the Studentized residuals ti to determine influential points in a multiple regression model with k independent variable and n observations and letting tn-k-2 denote the upper critical value of a two-tail t test with a 0.10 level of significance, Xi is an influential point if a) $| t | < t _ { n - k - 1 }$ b) $| t | > t _ { n - k - 1 }$ c) $\left| t _ { i } \right| < t _ { n - k - 2 }$ d) $\left| t _ { i } \right| > t _ { n - k - 2 }$

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Question 191

SCENARIO 13-13 An econometrician is interested in evaluating the relationship of demand for building materials to mortgage rates in Los Angeles and San Francisco.He believes that the appropriate model is $Y = 10 + 5 X _ { 1 } + 8 X _ { 2 }$ where = mortgage rate in \% =1 if SF, 0 if LA Y= demand in \ 100 per capita -Referring to SCENARIO 13-13, the predicted demand in San Francisco when the mortgage rate is 10% is _.

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Question 192

SCENARIO 13-5 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 SCENARIO 13-5, 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 193

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, there is sufficient evidence that the percentage of students passing the proficiency test depends on at least one of the explanatory variables at a5% level of significance.

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Question 194

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, predict the percentage of students passing the proficiency test for a school which has a mean teacher salary of 40,000 dollars, and an instructional spending per pupil of 2,000 dollars.

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Question 195

SCENARIO 13-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index).The Microsoft Excel output of this regression is partially reproduced below. $\text { SUMMARY OUTPUT }$ Regression Statistics Multiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 ANOVA df SS MS F Signif F Regression 2 33.4163 16.7082 186.325 0.0001 Residual 7 0.6277 0.0897 Total 9 34.0440 Coeff StdError t Stat P -value Intercept -0.0861 0.5674 -0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price -0.0006 0.0028 -0.219 0.8330 -Referring to SCENARIO 13-3, what is the predicted consumption level for an economy withGDP equal to $4 billion and an aggregate price index of 150?

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Question 196

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 Signif 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 and allowing for a 1% probability of committing a type I error,what is the decision and conclusion for the testH : $\beta$ 1-2= 0 vs.H : At least one $\beta$ j $\neq$ 0, j - 1, 20 1 2 1 j?

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Question 197

SCENARIO 13-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 2 variables: age (X1 = Age) and experience in the field (X2 = Exper).He took a sample of 20 employees and obtained the following Microsoft Excel output: Regression Statistics Multiple R 0.8535 R Square 0.7284 Adjusted R Square 0.6964 Standard Error 10.5630 Observations 20 ANOYA df SS MS F Siqnificonce F Regression 2 5086.5764 2543.2882 22.7941 0.0000 Residual 17 1896.8050 111.5768 Total 19 6983.3814 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 1.5740 9.2723 0.1698 0.8672 -17.9888 21.1368 Age 1.3045 0.1956 6.6678 0.0000 0.8917 1.7173 Exper -0.1478 0.1944 -0.7604 0.4574 -0.5580 0.2624 -Referring to SCENARIO 13-8, the estimate of the unit change in the mean of Y per unit change in X1, considering the effects of the other variable, is .

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Question 198

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 ANOVA df SS MS F Signif F Regression 37043.3236 18521.6618 0.0000 Residual 14487.7627 308.2503 Total 49 51531.0863 Coefficients Standard Error t Stat -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, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of Size in the regression model?

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Question 199

SCENARIO 13-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 2 variables: age (X1 = Age) and experience in the field (X2 = Exper).He took a sample of 20 employees and obtained the following Microsoft Excel output: Regression Statistics Multiple R 0.8535 R Square 0.7284 Adjusted R Square 0.6964 Standard Error 10.5630 Observations 20 ANOYA df SS MS F Siqnificonce F Regression 2 5086.5764 2543.2882 22.7941 0.0000 Residual 17 1896.8050 111.5768 Total 19 6983.3814 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 1.5740 9.2723 0.1698 0.8672 -17.9888 21.1368 Age 1.3045 0.1956 6.6678 0.0000 0.8917 1.7173 Exper -0.1478 0.1944 -0.7604 0.4574 -0.5580 0.2624 -Referring to SCENARIO 13-8, _% of the variation in salary can be explained by the variation in age while holding experience constant.

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Question 200

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.

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

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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