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, when the microeconomist used a simple linear regression model with sales as the dependent variable and wages as the independent variable, she obtained an r2 value of 0.601.What additional percentage of the total variation of sales has been explained by including capital spending in the multiple regression?

A) 60.1% B) 31.1% C) 22.9% D) 8.8% A) 60.1% B) 31.1% C) 22.9% D) 8.8% D

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, what can we say about the regression model?

A) The model explains 17.12% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 27.78% of the sample variability of heating costs. B) The model explains 19.28% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 27.78% of the sample variability of heating costs. C) The model explains 27.78% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 19.28% of the sample variability of heating costs. D) The model explains 19.28% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 17.12% of the sample variability of heating costs. A) The model explains 17.12% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 27.78% of the sample variability of heating costs. B) The model explains 19.28% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 27.78% of the sample variability of heating costs. C) The model explains 27.78% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 19.28% of the sample variability of heating costs. D) The model explains 19.28% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 17.12% of the sample variability of heating costs. C

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

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

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, what is the 95% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature?

A) [256.7522, 639.8328] B) [204.7854, 497.1733] C) [-5.3721, -0.1520] D) [-37.1736, 5.2919] A) [256.7522, 639.8328] B) [204.7854, 497.1733] C) [-5.3721, -0.1520] D) [-37.1736, 5.2919]

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: \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.8546 \\ \text { R Square } & 0.7303 \\ \text { Adjusted R Square } & 0.6853 \\ \text { Standard Error } & 226.7502 \\ \text { Observations } & 15 \\ \hline \end{array}\\ \text { ANOVA }\\ \begin{array} { l r c c c c } & d f & \text { SS } & \text { MS } & \text { F } & \text { Siqnificonce F } \\ \hline \text { Regression } & 2 & & 835284.6500 & 16.2457 & 0.0004 \\ \text { Residual } & 12 & 616987.8200 & \\ \text { Total } && 2287557.1200& & & \\ \hline \end{array}\\\\ \begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 99\% } & { \text { Upper 99\% } } \\ \hline \text { Intercept } & 821.2617 & 161.9391 & 5.0714 & 0.0003 & 326.6124 & 1315.9111 \\ \text { Age } & - 1.4061 & 2.5988 & - 0.5411 & 0.5984 & - 9.3444 & 6.5321 \\ \text { Tickets } & 243.4401 & 43.2470 & 5.6291 & 0.0001 & 111.3406 & 375.5396 \\ \hline \end{array} \end{array}\] -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 13-4 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, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?

A) 0.0005 B) 0.001 C) 0.01 D) 0.05 A) 0.0005 B) 0.001 C) 0.01 D) 0.05

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 department head wants to test H0: $\beta$1 =$\beta$2 = 0 .The p-value of the test is _.

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

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: \[\begin{array}{l} \begin{array} { l r } \hline \text { Multiple R } & 0.7308 \\ \text { R Square } & 0.5341 \\ \text { Adjusted R Square } & 0.4675 \\ \text { Standard Error } & 43.3275 \\ \text { Observations } & 25\\ \hline \end{array}\\ \text { ANOVA }\\ \begin{array} { l r r l l r } \hline & d f & & { \text { SS } } & { \text { MS } } & \text { Significance } F \\ \hline \text { Regression } & 3 & 45194.0661 & 15064.6887 & 8.0248 & 0.0009 \\ \text { Residual } & 21 & 39422.6542 & 1877.2692 & & \\ \text { Total } & 24 & 84616.7203 & &\\ \hline \end{array}\\\\ \begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 99\% } & \text { Upper 99\% } \\ \hline\text { Intercept } & -20.7298 & 22.3710 & -0.9266 & 0.3646 & -84.0702 & 42.6106 \\ \text { Length } & 7.2472 & 1.4992 & 4.8340 & 0.0001 & 3.0024 & 11.4919 \\ \text { Morn } & 90.1981 & 40.2336 & 2.2419 & 0.0359 & -23.7176 & 204.1138 \\ \text { Length x Morn } & -5.1024 & 3.3511 & -1.5226 & 0.1428 & -14.5905&4.3857\\ \hline \end{array} \end{array}\] -Referring to SCENARIO 13-11, what is the experimental unit for this analysis?

A) A clinic B) A client on a weight-loss program C) A month D) A morning, afternoon, or evening session A) A clinic B) A client on a weight-loss program C) A month D) A morning, afternoon, or evening session

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 value of the test statistic when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable?

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, what are the lower and upper limits of the 95% confidence interval estimate for the difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not after taking into consideration the effect of all the other independent variables?

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

Exam 13: Multiple Regression

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 1

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0.5164

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, when the microeconomist used a simple linear regression model with sales as the dependent variable and wages as the independent variable, she obtained an r2 value of 0.601.What additional percentage of the total variation of sales has been explained by including capital spending in the multiple regression?

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D

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, what can we say about the regression model?

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C

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

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Question 4

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 should be the decision ('reject' or 'do not reject') on the null hypothesis when testing whether LawnSize makes a significant contribution to the model in the presence of Income at a 0.05 level of significance?

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Question 5

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 odds ratio for a home owner with a family income of $50,000 and a lawn size of 2,000 square feet?

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Question 6

An interaction term in a multiple regression model may be used when the relationship between X1 and Y changes for differing values of X2.

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Question 7

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, what is the 95% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature?

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Question 8

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 Siqnificonce 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 9

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 definitively that instructional spending per pupil individually has no impact on the mean percentage of students passing the proficiency test, considering the effect of mean teacher salary, at a 10% level of significance based solely on but not actually computing the 90% confidence interval estimate for $\beta$ 2 .

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Question 10

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, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?

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Question 11

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 analyst wants to use an F-test to test H0 : $\beta$ 1 = $\beta$ 2 = 0 .The appropriate alternative hypothesis is _.

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Question 12

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 department head wants to test H0: $\beta$ 1 = $\beta$ 2 = 0 .The p-value of the test is _.

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Question 13

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: Multiple R 0.7308 R Square 0.5341 Adjusted R Square 0.4675 Standard Error 43.3275 Observations 25 ANOVA df SS MS 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, the overall model for predicting weight loss(Y) is statistically significant at the 0.05 level.

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Question 14

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, we can conclude definitively that, holding constant the effect of the other independent variable, age has no impact on the mean number of weeks a worker is unemployed due to a layoff at a 1% level of significance if all we have is the information of the 95% confidence interval estimate for the effect of a one year increase in age on the mean number of weeks a worker is unemployed due to a layoff.

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Question 15

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: Multiple R 0.7308 R Square 0.5341 Adjusted R Square 0.4675 Standard Error 43.3275 Observations 25 ANOVA df SS MS 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, what is the experimental unit for this analysis?

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Question 16

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 value of the test statistic when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable?

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Question 17

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 18

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 instructional spending per pupil has an effect on percentage of students passing the proficiency test while holding constant the effect of mean teacher salary at a 5% level of significance.

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Question 19

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 are the lower and upper limits of the 95% confidence interval estimate for the difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not after taking into consideration the effect of all the other independent variables?

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Question 20

An interaction term in a multiple regression model may be used when the relationship between X1 and Y changes for differing values of X2.

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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