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, what are the predicted sales (in millions of dollars) for a company spending $100 million on capital and $100 million on wages?

A) 15,800.00 B) 16,520.07 C) 17,277.49 D) 20,455.98 A) 15,800.00 B) 16,520.07 C) 17,277.49 D) 20,455.98

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 residual mean squares (MSE) that are missing in theANOVA table should be .

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

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 a correct statement?

A) The mean percentage of students passing the proficiency test is estimated to go up by 2.79% when mean teacher salary increases by one thousand dollars. B) The mean teacher salary is estimated to go up by 2.79% when mean percentage of students passing the proficiency test increases by 1%. C) The mean percentage of students passing the proficiency test is estimated to go up by 2.79% when mean teacher salary increases by one thousand dollars holding constant the instructional spending per pupil. D) The mean teacher salary is estimated to go up by 2.79% when mean percentage of students passing the proficiency test increases by 1% holding constant the instructional spending per pupil. A) The mean percentage of students passing the proficiency test is estimated to go up by 2.79% when mean teacher salary increases by one thousand dollars. B) The mean teacher salary is estimated to go up by 2.79% when mean percentage of students passing the proficiency test increases by 1%. C) The mean percentage of students passing the proficiency test is estimated to go up by 2.79% when mean teacher salary increases by one thousand dollars holding constant the instructional spending per pupil. D) The mean teacher salary is estimated to go up by 2.79% when mean percentage of students passing the proficiency test increases by 1% holding constant the instructional spending per pupil.

SCENARIO 13-12 As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area.Data were collected for the price ($) per hour of parking, blocks to the quadrangle, and whether the parking is on or off campus.The population regression model hypothesized is where Yi =$\alpha$ + $\beta$1 X1i + $\beta$2 X 2i + $\varepsilon$ Y is the meter price per hour X1 is the number of blocks to the quad X2 is a dummy variable that takes the value 1 if the meter is located on campus and 0 otherwise The following Excel results are obtained. \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.5536 \\ \text { R Square } & 0.3064 \\ \text { Adjusted R Square } & 0.2812 \\ \text { Standard Error } & 0.4492 \\ \text { Observations } & 58 \\ \hline \end{array}\\ \text { ANOVA }\\ \begin{array} { l r r l l r } \hline & d f & & { \text { SS } } & { \text { MS } } & \text { Significance } F \\ \hline \text { Regression } & 2 & 4.9035 & 2.4518 & 12.1501 & 0.0000 \\ \text { Residual } & 55 & 11.0984 & 0.2018 & & \\ \text { Total } & 57 & 16.0019 & & & \\ \hline \end{array}\\\\ \begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 99\% } & \text { Upper 99\% } \\ \hline \text { Intercept } & 1.6500 & 0.2028 & 8.1359 & 0.0000 & 1.1089 & 2.1912 \\ \text { Block } & - 0.2504 & 0.0529 & - 4.7355 & 0.0000 & - 0.3915 & - 0.1093 \\ \text { Campus } & 0.1552 & 0.1297 & 1.1966 & 0.2366 & - 0.1908 & 0.5011 \\ \hline \end{array} \end{array}\] -Referring to SCENARIO 13-12, predict the cost per hour if one parks off campus and 3 blocks from the quad.

The answer of SCENARIO 13-12 As a project for his business...

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 analyst wants to use a t test to test for the significance of the coefficient of X2.For a level of significance of 0.01, the critical values of the test are _.

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 reach regarding the inclusion of Income in the regression model?

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

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: \[\begin{array}{l} \begin{array} { l r } \hline \text { Multiple R } & 0.7308 \\ \text { R Square } & 0.5341 \\ \text { Adjusted R Square } & 0.4675 \\ \text { Standard Error } & 43.3275 \\ \text { Observations } & 25\\ \hline \end{array}\\ \text { ANOVA }\\ \begin{array} { l r r l l r } \hline & d f & & { \text { SS } } & { \text { MS } } & \text { Significance } F \\ \hline \text { Regression } & 3 & 45194.0661 & 15064.6887 & 8.0248 & 0.0009 \\ \text { Residual } & 21 & 39422.6542 & 1877.2692 & & \\ \text { Total } & 24 & 84616.7203 & &\\ \hline \end{array}\\\\ \begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 99\% } & \text { Upper 99\% } \\ \hline\text { Intercept } & -20.7298 & 22.3710 & -0.9266 & 0.3646 & -84.0702 & 42.6106 \\ \text { Length } & 7.2472 & 1.4992 & 4.8340 & 0.0001 & 3.0024 & 11.4919 \\ \text { Morn } & 90.1981 & 40.2336 & 2.2419 & 0.0359 & -23.7176 & 204.1138 \\ \text { Length x Morn } & -5.1024 & 3.3511 & -1.5226 & 0.1428 & -14.5905&4.3857\\ \hline \end{array} \end{array}\] -In a multiple regression model, the adjusted r 2

A) cannot be negative. B) can sometimes be negative. C) can sometimes be greater than +1. D) has to fall between 0 and +1. A) cannot be negative. B) can sometimes be negative. C) can sometimes be greater than +1. D) has to fall between 0 and +1.

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 analyst wants to use a t test to test for the significance of the coefficient of X2.The value of the test statistic is .

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

SCENARIO 13-12 As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area.Data were collected for the price ($) per hour of parking, blocks to the quadrangle, and whether the parking is on or off campus.The population regression model hypothesized is where Yi =$\alpha$ + $\beta$1 X1i + $\beta$2 X 2i + $\varepsilon$ Y is the meter price per hour X1 is the number of blocks to the quad X2 is a dummy variable that takes the value 1 if the meter is located on campus and 0 otherwise The following Excel results are obtained. \[\begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.5536 \\ \text { R Square } & 0.3064 \\ \text { Adjusted R Square } & 0.2812 \\ \text { Standard Error } & 0.4492 \\ \text { Observations } & 58 \\ \hline \end{array}\\ \text { ANOVA }\\ \begin{array} { l r r l l r } \hline & d f & & { \text { SS } } & { \text { MS } } & \text { Significance } F \\ \hline \text { Regression } & 2 & 4.9035 & 2.4518 & 12.1501 & 0.0000 \\ \text { Residual } & 55 & 11.0984 & 0.2018 & & \\ \text { Total } & 57 & 16.0019 & & & \\ \hline \end{array}\\\\ \begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 99\% } & \text { Upper 99\% } \\ \hline \text { Intercept } & 1.6500 & 0.2028 & 8.1359 & 0.0000 & 1.1089 & 2.1912 \\ \text { Block } & - 0.2504 & 0.0529 & - 4.7355 & 0.0000 & - 0.3915 & - 0.1093 \\ \text { Campus } & 0.1552 & 0.1297 & 1.1966 & 0.2366 & - 0.1908 & 0.5011 \\ \hline \end{array} \end{array}\] -Referring to SCENARIO 13-12, what is the correct interpretation for the estimated coefficient for X2?

A) Holding the effect of the distance from the quad constant, the estimated mean costs for parking on campus is $0.16 per hour more than parking off campus. B) Holding the effect of the distance from the quad constant, the estimated mean costs for parking off campus is $0.16 per hour more than parking on campus. C) Holding the effect of the distance from the quad constant, the estimated mean costs for parking on campus is $0.16 per hour more than parking off campus for each additional block away from the quad. D) Holding the effect of the distance from the quad constant, the estimated mean costs for parking off campus is $0.16 per hour more than parking on campus for each additional block away from the quad. A) Holding the effect of the distance from the quad constant, the estimated mean costs for parking on campus is $0.16 per hour more than parking off campus. B) Holding the effect of the distance from the quad constant, the estimated mean costs for parking off campus is $0.16 per hour more than parking on campus. C) Holding the effect of the distance from the quad constant, the estimated mean costs for parking on campus is $0.16 per hour more than parking off campus for each additional block away from the quad. D) Holding the effect of the distance from the quad constant, the estimated mean costs for parking off campus is $0.16 per hour more than parking on campus for each additional block away from the quad.

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, a worker who is a year older is estimated to stay jobless shorter by approximately 0.2143 weeks while holding constant the effects of the manager dummy variable. B) On average, a worker who is a year older is estimated to stay jobless longer by approximately 0.2143 weeks while holding constant the effects of the manager dummy variable. C) On average, a worker who is a year older is estimated to stay jobless shorter by approximately 1.4448 weeks while holding constant the effects of the manager dummy variable. D) On average, a worker who is a year older is estimated to stay jobless longer by approximately 1.4448 weeks while holding constant the effects of the manager dummy variable. A) On average, a worker who is a year older is estimated to stay jobless shorter by approximately 0.2143 weeks while holding constant the effects of the manager dummy variable. B) On average, a worker who is a year older is estimated to stay jobless longer by approximately 0.2143 weeks while holding constant the effects of the manager dummy variable. C) On average, a worker who is a year older is estimated to stay jobless shorter by approximately 1.4448 weeks while holding constant the effects of the manager dummy variable. D) On average, a worker who is a year older is estimated to stay jobless longer by approximately 1.4448 weeks while holding constant the effects of the manager dummy variable.

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, the null hypothesis should be rejected at a 5% level of significance when testing whether mean teacher salary has any effect on percentage of students passing the proficiency test, considering the effect of instructional spending per pupil.

(True/False)

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Question 221

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, what are the predicted sales (in millions of dollars) for a company spending $100 million on capital and $100 million on wages?

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Question 222

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 residual mean squares (MSE) that are missing in theANOVA table should be .

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Question 223

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 H0 : $\beta$ 1 = $\beta$ 2 = 0 implies that the number of weeks a worker is unemployed due to a layoff is not related to any of the explanatory variables.

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Question 224

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 $100,000 and a lawn size of 2,000 square feet?

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Question 225

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 a correct statement?

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Question 226

SCENARIO 13-12 As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area.Data were collected for the price ($) per hour of parking, blocks to the quadrangle, and whether the parking is on or off campus.The population regression model hypothesized is where Yi = $\alpha$ + $\beta$ 1 X1i + $\beta$ 2 X 2i + $\varepsilon$ Y is the meter price per hour X1 is the number of blocks to the quad X2 is a dummy variable that takes the value 1 if the meter is located on campus and 0 otherwise The following Excel results are obtained. Regression Statistics Multiple R 0.5536 R Square 0.3064 Adjusted R Square 0.2812 Standard Error 0.4492 Observations 58 ANOVA df SS MS Significance F Regression 2 4.9035 2.4518 12.1501 0.0000 Residual 55 11.0984 0.2018 Total 57 16.0019 Coefficients Standard Error t Stat P-value Lower 99\% Upper 99\% Intercept 1.6500 0.2028 8.1359 0.0000 1.1089 2.1912 Block -0.2504 0.0529 -4.7355 0.0000 -0.3915 -0.1093 Campus 0.1552 0.1297 1.1966 0.2366 -0.1908 0.5011 -Referring to SCENARIO 13-12, predict the cost per hour if one parks off campus and 3 blocks from the quad.

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Question 227

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 a t test to test for the significance of the coefficient of X2.For a level of significance of 0.01, the critical values of the test are _.

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Question 228

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 related to one of the explanatory variables.

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Question 229

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 an impact on the mean number of weeks a worker is unemployed due to a layoff at a 10% 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 230

In calculating the standard error of the estimate, SYX = MSE , there are n - k - 1 degrees of freedom, where n is the sample size and k represents the number of independent variables in the model.

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Question 231

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 reach regarding the inclusion of Income in the regression model?

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Question 232

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 -In a multiple regression model, the adjusted r 2

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Question 233

Multiple regression is the process of using several independent variables to predict a number of dependent variables.

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Question 234

SCENARIO 13-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age) and a dummy variable for management position (Manager: 1 = yes, 0 = no). The results of the regression analysis are given below: Regression Statistics Multiple R 0.6391 R Square 0.4085 Adjusted R Square 0.3765 Standard Error 18.8929 Observations 40 ANOVA df SS MS F Significance F Regression 2 9119.0897 4559.5448 12.7740 0.0000 Residual 37 13206.8103 356.9408 Total 39 22325.9 Coefficients Standard Error t Stat P -value Intercept -0.2143 11.5796 -0.0185 0.9853 Age 1.4448 0.3160 4.5717 0.0000 Manager -22.5761 11.3488 -1.9893 0.0541 -Referring to SCENARIO 13-17, the alternative hypothesis H 1 :At least one of $\beta$ j $\neq$ 0 for j =1, 2 implies that the number of weeks a worker is unemployed due to a layoff is related to all of the explanatory variables.

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Question 235

The coefficient of multiple determination is calculated by taking the ratio of the regression sum of squares over the total sum of squares (SSR/SST) and subtracting that value from1.

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Question 236

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 a t test to test for the significance of the coefficient of X2.The value of the test statistic is .

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Question 237

SCENARIO 13-12 As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area.Data were collected for the price ($) per hour of parking, blocks to the quadrangle, and whether the parking is on or off campus.The population regression model hypothesized is where Yi = $\alpha$ + $\beta$ 1 X1i + $\beta$ 2 X 2i + $\varepsilon$ Y is the meter price per hour X1 is the number of blocks to the quad X2 is a dummy variable that takes the value 1 if the meter is located on campus and 0 otherwise The following Excel results are obtained. Regression Statistics Multiple R 0.5536 R Square 0.3064 Adjusted R Square 0.2812 Standard Error 0.4492 Observations 58 ANOVA df SS MS Significance F Regression 2 4.9035 2.4518 12.1501 0.0000 Residual 55 11.0984 0.2018 Total 57 16.0019 Coefficients Standard Error t Stat P-value Lower 99\% Upper 99\% Intercept 1.6500 0.2028 8.1359 0.0000 1.1089 2.1912 Block -0.2504 0.0529 -4.7355 0.0000 -0.3915 -0.1093 Campus 0.1552 0.1297 1.1966 0.2366 -0.1908 0.5011 -Referring to SCENARIO 13-12, what is the correct interpretation for the estimated coefficient for X2?

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Question 238

If a categorical independent variable contains 4 categories, then dummy variable(s)will be needed to uniquely represent these categories.

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Question 239

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?

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Question 240

In calculating the standard error of the estimate, SYX = MSE , there are n - k - 1 degrees of freedom, where n is the sample size and k represents the number of independent variables in the model.

Multiple regression is the process of using several independent variables to predict a number of dependent variables.

The coefficient of multiple determination is calculated by taking the ratio of the regression sum of squares over the total sum of squares (SSR/SST) and subtracting that value from1.

If a categorical independent variable contains 4 categories, then dummy variable(s)will be needed to uniquely represent these categories.

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

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