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

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

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 $\begin{array} { l r c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\ \text { Residual } & 23 & 7045072780 & 306307512 & & \\ \text { Total } & 25 & 22624849820 & & & \end{array}$ $\begin{array}{lrrrr} & \text { Coeff } & \text { StdError } & t \text { Stat } & \text { P-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$ -Referring to SCENARIO 13-5, which of the independent variables in the model are significant at the 5% level?

A) Capital, Wages B) Capital C) Wages D) None of the above A) Capital, Wages B) Capital C) Wages D) None of the above

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 value of the partial F test statistic is forH0: Variable X2 does not significantly improve the model after variable X1 has been includedH1: Variable X2 significantly improves the model after variable X1 has been included

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: $\begin{array}{lr} \hline{\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8479 \\ \text { R Square } & 0.7189 \\ \text { Adjusted R Square } & 0.7069 \\ \text { Standard Error } & 17.5571 \\ \text { Observations } & 50\\ \hline \end{array}$ $\text { ANOVA }$ $\begin{array}{lrrrrr} & d f & \text { SS } & {M S} & F & \text { Significance } F \\ \hline \text { Regression } & & & 37043.3236 & 18521.6618 & 0.0000 \\ \text { Residual } & & 14487.7627 & 308.2503 & \\ \text { Total } & & 49 & 51531.0863 & & \end{array}$ $\begin{array}{lrrrr} \hline & \text { Coefficients } & \text { Standard Error } &{t \text { Stat }} & \text { P-value } \\ \hline \text { Intercept } & -5.5146 & 7.2273 & -0.7630 & 0.4493 \\ \text { Income } & 0.4262 & 0.0392 & 10.8668 & 0.0000 \\ \text { Size } & 5.5437 & 1.6949 & 3.2708 & 0.0020\\ \hline \end{array}$ $\text { Also } \operatorname{SSR}\left(X_{1} \mid X_{2}\right)=36400.6326 \text { and } \operatorname{SSR}\left(X_{2} \mid X_{1}\right)=3297.7917$ -Referring to SCENARIO 13-4, what is the value of the calculated F test statistic that is missing from the output for testing whether the whole regression model is significant?

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

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 $\begin{array} { l r c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \\ \text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\ \text { Residual } & 23 & 7045072780 & 306307512 & & \\ \text { Total } & 25 & 22624849820 & & & \end{array}$ $\begin{array}{lrrrr} & \text { Coeff } & \text { StdError } & t \text { Stat } & \text { P-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$ -Referring to SCENARIO 13-5, the observed value of the F-statistic is given on the printout as25.432.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

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 13-10 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, the 99% confidence interval for the change in mean insurance premiums of a person who has become 1 year older (i.e., the slope coefficient for AGE) -1.4061 $\pm$.

The answer of SCENARIO 13-10 You worked as an intern at...

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: \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.6391 \\ \text { R Square } & 0.4085 \\ \text { Adjusted R Square } & 0.3765 \\ \text { Standard Error } & 18.8929 \\ \text { Observations } & 40 \\ \hline \end{array}\\\\ \text { ANOVA }\\ \begin{array} { l r r r r r } \hline &{ \text { df } } & { \text { SS } } & { \text { MS } } &{ \text { F } } & { \text { Significance } F } \\ \hline \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\ \text { Residual } & 37 & 13206.8103 & 356.9408 & \\ \text { Total } & 39 & 22325.9 & & \\ \hline \end{array}\\\\ \begin{array} { l r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & { P \text {-value } } \\ \hline \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 \\ \text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 \\ \text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 \\ \hline \end{array} \end{array}\] -Referring to SCENARIO 13-17, which of the following is a correct statement?

A) On average, those who are in a management position are estimated to stay jobless shorter by approximately 1.4448 weeks while holding constant the effects of age. B) On average, those who are in a management position are estimated to stay jobless longer by approximately 1.4448 weeks while holding constant the effects of age. C) On average, those who are in a management position are estimated to stay jobless shorter by approximately 22.5761 weeks while holding constant the effects of age. D) On average, those who are in a management position are estimated to stay jobless longer by approximately 22.5761 weeks while holding constant the effects of age. A) On average, those who are in a management position are estimated to stay jobless shorter by approximately 1.4448 weeks while holding constant the effects of age. B) On average, those who are in a management position are estimated to stay jobless longer by approximately 1.4448 weeks while holding constant the effects of age. C) On average, those who are in a management position are estimated to stay jobless shorter by approximately 22.5761 weeks while holding constant the effects of age. D) On average, those who are in a management position are estimated to stay jobless longer by approximately 22.5761 weeks while holding constant the effects of age.

SCENARIO 13-11 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 Data for 25 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: \[Y = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \beta _ { 3 } X _ { 1 } X _ { 2 } + \varepsilon\] Output from Microsoft Excel follows: $\begin{array}{lr} {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.7308 \\ \text { R Square } & 0.5341 \\ \text { Adjusted R Square } & 0.4675 \\ \text { Standard Error } & 43.3275 \\ \text { Observations } & 25\\ \hline \end{array}$ $\text { ANOVA }$ $\begin{array}{lrrrrr} \hline&\text { df } & \text { SS }&M S &F & \text { Significance } F\\ \hline\text { Regression } & 3 & 45194.0661 & 15064.6887 & 8.0248 & 0.0009 \\ \text { Residual } & 21 & 39422.6542 & 1877.2692 & & \\ \text { Total } & 24 & 84616.7203 & &\\ \hline \end{array}$ $\begin{array}{lrrrrrr} \hline & \text { Coefficients } & \text { Standard Error } &{\text { t Stat }} & \text { P-value } & \text { Lower 99\% } & \text { Upper 99\% } \\ \hline \text { Intercept } & -20.7298 & 22.3710 & -0.9266 & 0.3646 & -84.0702 & 42.6106 \\ \text { Length } & 7.2472 & 1.4992 & 4.8340 & 0.0001 & 3.0024 & 11.4919 \\ \text { Morn } & 90.1981 & 40.2336 & 2.2419 & 0.0359 & -23.7176 & 204.1138 \\ \text { Length x Morn } & -5.1024 & 3.3511 & -1.5226 & 0.1428 & -14.5905 & 4.3857 \\ \hline \end{array}$ -Referring to SCENARIO 13-11, in terms of the $\beta$ s in the model, give the mean change in weight loss (Y) for every 1 month increase in time on the program (X1) when not attending the morning session.

A) $\beta$1 B) $\beta$1 +$\beta$2 C) $\beta$1 + $\beta$3 D) $\beta$2 + $\beta$3 A) $\beta$1 B) $\beta$1 +$\beta$2 C) $\beta$1 + $\beta$3 D) $\beta$2 + $\beta$3

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: \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.6391 \\ \text { R Square } & 0.4085 \\ \text { Adjusted R Square } & 0.3765 \\ \text { Standard Error } & 18.8929 \\ \text { Observations } & 40 \\ \hline \end{array}\\\\ \text { ANOVA }\\ \begin{array} { l r r r r r } \hline &{ \text { df } } & { \text { SS } } & { \text { MS } } &{ \text { F } } & { \text { Significance } F } \\ \hline \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\ \text { Residual } & 37 & 13206.8103 & 356.9408 & \\ \text { Total } & 39 & 22325.9 & & \\ \hline \end{array}\\\\ \begin{array} { l r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & { P \text {-value } } \\ \hline \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 \\ \text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 \\ \text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 \\ \hline \end{array} \end{array}\] -Referring to SCENARIO 13-17, what is the standard error of estimate?

The answer of SCENARIO 13-17 Given below are results from the...

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: \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.6391 \\ \text { R Square } & 0.4085 \\ \text { Adjusted R Square } & 0.3765 \\ \text { Standard Error } & 18.8929 \\ \text { Observations } & 40 \\ \hline \end{array}\\\\ \text { ANOVA }\\ \begin{array} { l r r r r r } \hline &{ \text { df } } & { \text { SS } } & { \text { MS } } &{ \text { F } } & { \text { Significance } F } \\ \hline \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\ \text { Residual } & 37 & 13206.8103 & 356.9408 & \\ \text { Total } & 39 & 22325.9 & & \\ \hline \end{array}\\\\ \begin{array} { l r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & { P \text {-value } } \\ \hline \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 \\ \text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 \\ \text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 \\ \hline \end{array} \end{array}\] -Referring to SCENARIO 13-17, which of the following is a correct statement?

A) 37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager. B) 37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager after adjusting for the number of predictors and sample size. C) 37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager after adjusting for the level of significance D) 37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager holding constant the effect of all the independent variables. A) 37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager. B) 37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager after adjusting for the number of predictors and sample size. C) 37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager after adjusting for the level of significance D) 37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager holding constant the effect of all the independent variables.

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 estimated change in the mean salary (in $1,000) when an employee is a year older holding experience constant is _.

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

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

(Multiple Choice)

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Question 201

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

(Multiple Choice)

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Question 202

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 value of the partial F test statistic is forH0: Variable X2 does not significantly improve the model after variable X1 has been includedH1: Variable X2 significantly improves the model after variable X1 has been included

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Question 203

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, what is the value of the calculated F test statistic that is missing from the output for testing whether the whole regression model is significant?

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Question 204

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, the observed value of the F-statistic is given on the printout as25.432.What are the degrees of freedom for this F-statistic?

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Question 205

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 206

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 alternative hypothesis H 1: At least one of $\beta$ j $\neq$ 0 for j =1, 2 implies that percentage of students passing the proficiency test is related to at least one of the explanatory variables.

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Question 207

SCENARIO 13-19 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; 11 did not have a lawn service (code 0) and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars) and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: Binary Logistic Regression Predictor Coefficients SE Coef Z p -Value Intercept -7.8562 3.8224 -2.0553 0.0398 Income 0.0304 0.0133 2.2897 0.0220 Lawn Size 1.2804 0.6971 1.8368 0.0662 Deviance 25.3089 -Referring to SCENARIO 13-19, what is the estimated probability that a home owner with a family income of $50,000 and a lawn size of 5,000 square feet will purchase a lawn service?

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Question 208

SCENARIO 13-19 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; 11 did not have a lawn service (code 0) and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars) and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: Binary Logistic Regression Predictor Coefficients SE Coef Z p -Value Intercept -7.8562 3.8224 -2.0553 0.0398 Income 0.0304 0.0133 2.2897 0.0220 Lawn Size 1.2804 0.6971 1.8368 0.0662 Deviance 25.3089 -Referring to SCENARIO 13-19, there is not enough evidence to conclude that Income makes a significant contribution to the model in the presence of LawnSize at a 0.05 level of significance.

(True/False)

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Question 209

A regression had the following results: SST = 82.55, SSE = 29.85.It can be said that 63.84% of the variation in the dependent variable is explained by the independent variables in the regression.

(True/False)

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Question 210

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, the 99% confidence interval for the change in mean insurance premiums of a person who has become 1 year older (i.e., the slope coefficient for AGE) -1.4061 $\pm$ .

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Question 211

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 effect of living in San Francisco rather than Los Angeles is to increase the mean demand by an estimated .

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Question 212

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, which of the following is a correct statement?

(Multiple Choice)

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Question 213

SCENARIO 13-19 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; 11 did not have a lawn service (code 0) and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars) and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: Binary Logistic Regression Predictor Coefficients SE Coef Z p -Value Intercept -7.8562 3.8224 -2.0553 0.0398 Income 0.0304 0.0133 2.2897 0.0220 Lawn Size 1.2804 0.6971 1.8368 0.0662 Deviance 25.3089 -Referring to SCENARIO 13-19, what is the p-value of the test statistic when testing whether the model is a good-fitting model?

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Question 214

SCENARIO 13-11 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 Data for 25 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: $Y = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \beta _ { 3 } X _ { 1 } X _ { 2 } + \varepsilon$ Output from Microsoft Excel follows: Regression Statistics Multiple R 0.7308 R Square 0.5341 Adjusted R Square 0.4675 Standard Error 43.3275 Observations 25 $\text { ANOVA }$ df SS MS F Significance F Regression 3 45194.0661 15064.6887 8.0248 0.0009 Residual 21 39422.6542 1877.2692 Total 24 84616.7203 Coefficients Standard Error t Stat P-value Lower 99\% Upper 99\% Intercept -20.7298 22.3710 -0.9266 0.3646 -84.0702 42.6106 Length 7.2472 1.4992 4.8340 0.0001 3.0024 11.4919 Morn 90.1981 40.2336 2.2419 0.0359 -23.7176 204.1138 Length x Morn -5.1024 3.3511 -1.5226 0.1428 -14.5905 4.3857 -Referring to SCENARIO 13-11, in terms of the $\beta$ s in the model, give the mean change in weight loss (Y) for every 1 month increase in time on the program (X1) when not attending the morning session.

(Multiple Choice)

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Question 215

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 percentage of students passing the proficiency test is not affected by one of the explanatory variables.

(True/False)

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Question 216

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, what is the standard error of estimate?

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Question 217

A multiple regression is called "multiple" because it has several explanatory variables.

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Question 218

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, which of the following is a correct statement?

(Multiple Choice)

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Question 219

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 estimated change in the mean salary (in $1,000) when an employee is a year older holding experience constant is _.

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Question 220

A regression had the following results: SST = 82.55, SSE = 29.85.It can be said that 63.84% of the variation in the dependent variable is explained by the independent variables in the regression.

A multiple regression is called "multiple" because it has several explanatory variables.

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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