SCENARIO 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker.They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars.These data are presented in the table that follows. $\begin{array}{lll} \text { Broker } & \text {Clients} & \text {Sales }\\ 1 & 27 & 52 \\ 2 & 11 & 37 \\ 3 & 42 & 64 \\ 4 & 33 & 55 \\ 5 & 15 & 29 \\ 6 & 15 & 34 \\ 7 & 25 & 58 \\ 8 & 36 & 59 \\ 9 & 28 & 44 \\ 10 & 30 & 48 \\ 11 & 17 & 31 \\ 12 & 22 & 38 \end{array}$ -Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in did not affect the amount of sales generated.The value of the test statistic is .

The answer of SCENARIO 12-4 The managers of a brokerage firm...

SCENARIO 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker.They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars.These data are presented in the table that follows. $\begin{array}{lll} \text { Broker } & \text {Clients} & \text {Sales }\\ 1 & 27 & 52 \\ 2 & 11 & 37 \\ 3 & 42 & 64 \\ 4 & 33 & 55 \\ 5 & 15 & 29 \\ 6 & 15 & 34 \\ 7 & 25 & 58 \\ 8 & 36 & 59 \\ 9 & 28 & 44 \\ 10 & 30 & 48 \\ 11 & 17 & 31 \\ 12 & 22 & 38 \end{array}$ -Referring to Scenario 12-4, suppose the managers of the brokerage firm want to construct n a99% prediction interval for the sales made by a broker who has brought into the firm 18 new clients.The t critical value they would use is .

The answer of SCENARIO 12-4 The managers of a brokerage firm...

SCENARIO 12-9 It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation.Given below is the Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students.NOTE: Only partial output is shown. $\begin{array}{lr} {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8857 \\ \text { R Square } & 0.7845 \\ \text { Adjusted R Square } & 0.7801 \\ \text { Standard Error } & 1.3704 \\ \text { Observations } & 51 \\ \hline \end{array}$ ANOVA $\begin{array}{lrrrrr} & d f & S S & M S & F & \text { Significance F } \\ \hline \text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 \\ \text { Residual } & & & 1.8782 & \\ \text { Total } & 50 & 427.0798 & & \end{array}$ $\begin{array}{lrrrrrrr} & \text { Coefficients } & \text { standered Error } & \text { tStat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -1.8940 & 0.4018 & -4.7134 & 0.0000 & -2.7015 & -1.0865 \\ \text { Hours } & 0.9795 & 0.0733 & 13.3561 & 0.0000 & 0.8321 & 1.1269 \end{array}$ Note: 2.051E - 05 = 2.051 *10-05 and 5.944 E - 18 = 5.944 *10-18 . -Referring to Scenario 12-9, the 90% confidence interval for the average change in SALARY (in thousands of dollars) as a result of spending an extra hour per day studying is

A) wider than [-2.70159, -1.08654]. B) narrower than [-2.70159, -1.08654]. C) wider than [0.8321927, 1.12697]. D) narrower than [0.8321927, 1.12697]. A) wider than [-2.70159, -1.08654]. B) narrower than [-2.70159, -1.08654]. C) wider than [0.8321927, 1.12697]. D) narrower than [0.8321927, 1.12697].

SCENARIO 12-9 It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation.Given below is the Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students.NOTE: Only partial output is shown. $\begin{array}{lr} {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8857 \\ \text { R Square } & 0.7845 \\ \text { Adjusted R Square } & 0.7801 \\ \text { Standard Error } & 1.3704 \\ \text { Observations } & 51 \\ \hline \end{array}$ ANOVA $\begin{array}{lrrrrr} & d f & S S & M S & F & \text { Significance F } \\ \hline \text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 \\ \text { Residual } & & & 1.8782 & \\ \text { Total } & 50 & 427.0798 & & \end{array}$ $\begin{array}{lrrrrrrr} & \text { Coefficients } & \text { standered Error } & \text { tStat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -1.8940 & 0.4018 & -4.7134 & 0.0000 & -2.7015 & -1.0865 \\ \text { Hours } & 0.9795 & 0.0733 & 13.3561 & 0.0000 & 0.8321 & 1.1269 \end{array}$ Note: 2.051E - 05 = 2.051 *10-05 and 5.944 E - 18 = 5.944 *10-18 . -Referring to Scenario 12-9, the p-value of the measured F-test statistic to test whether HOURSaffects SALARY is .

The answer of SCENARIO 12-9 It is believed that, the average...

SCENARIO 12-3 The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place.She takes a random sample of 4 students.For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation.These data are presented in the table below. $\begin{array} {ccc}\text { Student } & \text { Coop Jobs } & \text {Job Offer }\\ 1 & 1 & 4 \\ 2 & 2 & 6 \\ 3 & 1 & 3 \\ 4 & 0 & 1 \end{array}$ -Referring to Scenario 12-3, suppose the director of cooperative education wants to construct a95% confidence interval estimate for the mean number of job offers received by students who have had exactly one cooperative education job.The confidence interval is from to_.

The answer of SCENARIO 12-3 The director of cooperative education at...

Exam 12: Simple Linear Regression

SCENARIO 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker.They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars.These data are presented in the table that follows. Broker Clients Sales 1 27 52 2 11 37 3 42 64 4 33 55 5 15 29 6 15 34 7 25 58 8 36 59 9 28 44 10 30 48 11 17 31 12 22 38 -Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in did not affect the amount of sales generated.The value of the test statistic is .

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Question 21

SCENARIO 12-13 In this era of tough economic conditions, voters increasingly ask the question: "Is the educational achievement level of students dependent on the amount of money the state in which they reside spends on education?" The partial computer output below is the result of using spending per student ($) as the independent variable and composite score which is the sum of the math, science and reading scores as the dependent variable on 35 states that participated in a study.The table includes only partial results. Regression Statistics Multiple R 0.3122 R Square 0.0975 Adjusted R 0.0701 Square Standard 26.9122 Error Observations 35 ANOVA df SS MS F Regression 1 2581.5759 Residual 724.2674 Total 34 26482.4000 $\begin{array}{l}\begin{array} { l c c c c } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & P \text {-value } \\\hline \text { Intercept } & 595.540251 & 22.115176 & & \\\text { Spending per } & & & & \\\text { Student(\$) } & 0.007996 & 0.004235 & \\\hline\end{array}\end{array}$ -Referring to Scenario 12-13, the degrees of freedom for the F test on whether spending per student affects composite score are _.

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Question 22

The width of the prediction interval for the predicted value of Y is dependent on

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Question 23

SCENARIO 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker.They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars.These data are presented in the table that follows. Broker Clients Sales 1 27 52 2 11 37 3 42 64 4 33 55 5 15 29 6 15 34 7 25 58 8 36 59 9 28 44 10 30 48 11 17 31 12 22 38 -Referring to Scenario 12-4, suppose the managers of the brokerage firm want to construct n a99% prediction interval for the sales made by a broker who has brought into the firm 18 new clients.The t critical value they would use is .

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Question 24

SCENARIO 12-9 It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation.Given below is the Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students.NOTE: Only partial output is shown. Regression Statistics Multiple R 0.8857 R Square 0.7845 Adjusted R Square 0.7801 Standard Error 1.3704 Observations 51 ANOVA df SS MS F Significance F Regression 1 335.0472 335.0473 178.3859 Residual 1.8782 Total 50 427.0798 Coefficients standered Error tStat P-value Lower 95\% Upper 95\% Intercept -1.8940 0.4018 -4.7134 0.0000 -2.7015 -1.0865 Hours 0.9795 0.0733 13.3561 0.0000 0.8321 1.1269 Note: 2.051E - 05 = 2.051 10-05 and 5.944 E - 18 = 5.944 10-18 . -Referring to Scenario 12-9, the 90% confidence interval for the average change in SALARY (in thousands of dollars) as a result of spending an extra hour per day studying is

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Question 25

SCENARIO 12-12 The manager of the purchasing department of a large saving and loan organization would like to develop a model to predict the amount of time (measured in hours) it takes to record a loan application.Data are collected from a sample of 30 days, and the number of applications recorded and completion time in hours is recorded.Below is the regression output: Regression Statistics Multiple R 0.9447 R Square 0.8924 Adjusted R 0.8886 Square Standard 0.3342 Error Observations 30 ANOVA df SS MS F Significance F Regression 1 25.9438 25.9438 232.2200 4.3946-15 Residual 28 3.1282 0.1117 Total 29 29.072 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 0.4024 0.1236 3.2559 0.0030 0.1492 0.6555 Applications 0.0126 0.0008 15.2388 0.0000 0.0109 0.0143 Recorded 12-46 Simple Linear Regression $SCENARIO 12-12 The manager of the purchasing department of a large saving and loan organization would like to develop a model to predict the amount of time (measured in hours) it takes to record a loan application.Data are collected from a sample of 30 days, and the number of applications recorded and completion time in hours is recorded.Below is the regression output: \begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.9447 \\ \text { R Square } & 0.8924 \\ \text { Adjusted R } & 0.8886 \\ \text { Square } & \\ \text { Standard } & 0.3342 \\ \text { Error } & \\ \text { Observations } & 30 \\ \hline \end{array}\\ \text { ANOVA }\\ \begin{array} { l r r r r r } \hline & { \text { df } } & { \text { SS } } & { \text { MS } } & \text { F } & \text { Significance } F \\ \hline \text { Regression } & 1 & 25.9438 & 25.9438 & 232.2200 & 4.3946 \mathrm { E } - 15 \\ \text { Residual } & 28 & 3.1282 & 0.1117 & & \\ \text { Total } & 29 & 29.072 & & & \\ \hline \end{array}\\ \begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\ \text { Applications } & 0.0126 & 0.0008 & 15.2388 & 0.0000 & 0.0109 & 0.0143 \\ \text { Recorded } & & & & & & \\ \hline \end{array} \end{array} 12-46 Simple Linear Regression Simple Linear Regression 12-47 -Referring to Scenario 12-12, the degrees of freedom for the F test on whether the number of load applications recorded affects the amount of time are$ Simple Linear Regression 12-47 -Referring to Scenario 12-12, the degrees of freedom for the F test on whether the number of load applications recorded affects the amount of time are

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Question 26

SCENARIO 12-3 The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place.She takes a random sample of 4 students.For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation.These data are presented in the table below. Student Coop Jobs Job Offer 1 1 4 2 2 6 3 1 3 4 0 1 -Referring to Scenario 12-3, suppose the director of cooperative education wants to construct both a 95% confidence interval estimate and a 95% prediction interval for X = 2.The confidence interval estimate would be the wider of the two intervals.

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Question 27

SCENARIO 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker.They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars.These data are presented in the table that follows. Broker Clients Sales 1 27 52 2 11 37 3 42 64 4 33 55 5 15 29 6 15 34 7 25 58 8 36 59 9 28 44 10 30 48 11 17 31 12 22 38 -Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the population slope was equal to 0.The value of the test statistic is _.

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Question 28

SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: $SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: \begin{array}{lr} {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\ \hline \text { R Square } & 0.7554 \\ \hline \text { Adjusted R Square } & 0.7467 \\ \hline \text { Standard Error } & 44.4765 \\ \hline \text { Observations } & 30.0000 \\ \hline \end{array} \text { ANOVA } \begin{array}{|l|r|r|r|r|r|} \hline &\text { df } & \text { SS } & \text { MS } & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\ \hline \text { Total } & 29 & 226451.3503 & & \\ \hline \end{array} Simple Linear Regression 12-41 -Referring to Scenario 12-11, which of the following assumptions appears to have been violated?$ Regression Statistics Multiple R 0.8691 R Square 0.7554 Adjusted R Square 0.7467 Standard Error 44.4765 Observations 30.0000 $\text { ANOVA }$ df SS MS F Significance F Regression 1 171062.9193 171062.9193 86.4759 0.0000 Residual 28 55388.4309 1978.1582 Total 29 226451.3503 $SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: \begin{array}{lr} {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\ \hline \text { R Square } & 0.7554 \\ \hline \text { Adjusted R Square } & 0.7467 \\ \hline \text { Standard Error } & 44.4765 \\ \hline \text { Observations } & 30.0000 \\ \hline \end{array} \text { ANOVA } \begin{array}{|l|r|r|r|r|r|} \hline &\text { df } & \text { SS } & \text { MS } & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\ \hline \text { Total } & 29 & 226451.3503 & & \\ \hline \end{array} Simple Linear Regression 12-41 -Referring to Scenario 12-11, which of the following assumptions appears to have been violated?$ $SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: \begin{array}{lr} {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\ \hline \text { R Square } & 0.7554 \\ \hline \text { Adjusted R Square } & 0.7467 \\ \hline \text { Standard Error } & 44.4765 \\ \hline \text { Observations } & 30.0000 \\ \hline \end{array} \text { ANOVA } \begin{array}{|l|r|r|r|r|r|} \hline &\text { df } & \text { SS } & \text { MS } & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\ \hline \text { Total } & 29 & 226451.3503 & & \\ \hline \end{array} Simple Linear Regression 12-41 -Referring to Scenario 12-11, which of the following assumptions appears to have been violated?$ Simple Linear Regression 12-41 $SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: \begin{array}{lr} {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\ \hline \text { R Square } & 0.7554 \\ \hline \text { Adjusted R Square } & 0.7467 \\ \hline \text { Standard Error } & 44.4765 \\ \hline \text { Observations } & 30.0000 \\ \hline \end{array} \text { ANOVA } \begin{array}{|l|r|r|r|r|r|} \hline &\text { df } & \text { SS } & \text { MS } & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\ \hline \text { Total } & 29 & 226451.3503 & & \\ \hline \end{array} Simple Linear Regression 12-41 -Referring to Scenario 12-11, which of the following assumptions appears to have been violated?$ -Referring to Scenario 12-11, which of the following assumptions appears to have been violated?

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Question 29

SCENARIO 12-3 The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place.She takes a random sample of 4 students.For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation.These data are presented in the table below. Student Coop Jobs Job Offer 1 1 4 2 2 6 3 1 3 4 0 1 -Referring to Scenario 12-3, the coefficient of correlation is .

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Question 30

14.Referring to Scenario 12-2, what is the standard error of the regression slope estimate, S ? $b$ 1 a) 0.784 b) 0.885 c) 12.650 d) 16.299 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: standard error, slope -Referring to Scenario 12-2, what is $14.Referring to Scenario 12-2, what is the standard error of the regression slope estimate, S ? b 1 a) 0.784 b) 0.885 c) 12.650 d) 16.299 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: standard error, slope -Referring to Scenario 12-2, what is \star ( X - \bar { X } ) ^ { 2 } for these data?$ $\star ( X - \bar { X } ) ^ { 2 }$ for these data?

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Question 31

SCENARIO 12-3 The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place.She takes a random sample of 4 students.For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation.These data are presented in the table below. Student Coop Jobs Job Offer 1 1 4 2 2 6 3 1 3 4 0 1 -Referring to Scenario 12-3, set up a scatter plot.

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Question 32

SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: $SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: \begin{array}{lr} {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\ \hline \text { R Square } & 0.7554 \\ \hline \text { Adjusted R Square } & 0.7467 \\ \hline \text { Standard Error } & 44.4765 \\ \hline \text { Observations } & 30.0000 \\ \hline \end{array} \text { ANOVA } \begin{array}{|l|r|r|r|r|r|} \hline &\text { df } & \text { SS } & \text { MS } & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\ \hline \text { Total } & 29 & 226451.3503 & & \\ \hline \end{array} Simple Linear Regression 12-41 -Referring to Scenario 12-11, the normality of error assumption appears to have been violated.$ Regression Statistics Multiple R 0.8691 R Square 0.7554 Adjusted R Square 0.7467 Standard Error 44.4765 Observations 30.0000 $\text { ANOVA }$ df SS MS F Significance F Regression 1 171062.9193 171062.9193 86.4759 0.0000 Residual 28 55388.4309 1978.1582 Total 29 226451.3503 $SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: \begin{array}{lr} {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\ \hline \text { R Square } & 0.7554 \\ \hline \text { Adjusted R Square } & 0.7467 \\ \hline \text { Standard Error } & 44.4765 \\ \hline \text { Observations } & 30.0000 \\ \hline \end{array} \text { ANOVA } \begin{array}{|l|r|r|r|r|r|} \hline &\text { df } & \text { SS } & \text { MS } & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\ \hline \text { Total } & 29 & 226451.3503 & & \\ \hline \end{array} Simple Linear Regression 12-41 -Referring to Scenario 12-11, the normality of error assumption appears to have been violated.$ $SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: \begin{array}{lr} {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\ \hline \text { R Square } & 0.7554 \\ \hline \text { Adjusted R Square } & 0.7467 \\ \hline \text { Standard Error } & 44.4765 \\ \hline \text { Observations } & 30.0000 \\ \hline \end{array} \text { ANOVA } \begin{array}{|l|r|r|r|r|r|} \hline &\text { df } & \text { SS } & \text { MS } & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\ \hline \text { Total } & 29 & 226451.3503 & & \\ \hline \end{array} Simple Linear Regression 12-41 -Referring to Scenario 12-11, the normality of error assumption appears to have been violated.$ Simple Linear Regression 12-41 $SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: \begin{array}{lr} {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\ \hline \text { R Square } & 0.7554 \\ \hline \text { Adjusted R Square } & 0.7467 \\ \hline \text { Standard Error } & 44.4765 \\ \hline \text { Observations } & 30.0000 \\ \hline \end{array} \text { ANOVA } \begin{array}{|l|r|r|r|r|r|} \hline &\text { df } & \text { SS } & \text { MS } & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\ \hline \text { Total } & 29 & 226451.3503 & & \\ \hline \end{array} Simple Linear Regression 12-41 -Referring to Scenario 12-11, the normality of error assumption appears to have been violated.$ -Referring to Scenario 12-11, the normality of error assumption appears to have been violated.

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Question 33

SCENARIO 12-3 The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place.She takes a random sample of 4 students.For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation.These data are presented in the table below. Student Coop Jobs Job Offer 1 1 4 2 2 6 3 1 3 4 0 1 -Referring to Scenario 12-3, the prediction for the number of job offers for a person with 2 coop jobs is _.

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Question 34

Based on the residual plot below, you will conclude that there might be a violation of which of the following assumptions.

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Question 35

SCENARIO 12-12 The manager of the purchasing department of a large saving and loan organization would like to develop a model to predict the amount of time (measured in hours) it takes to record a loan application.Data are collected from a sample of 30 days, and the number of applications recorded and completion time in hours is recorded.Below is the regression output: Regression Statistics Multiple R 0.9447 R Square 0.8924 Adjusted R 0.8886 Square Standard 0.3342 Error Observations 30 ANOVA df SS MS F Significance F Regression 1 25.9438 25.9438 232.2200 4.3946-15 Residual 28 3.1282 0.1117 Total 29 29.072 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 0.4024 0.1236 3.2559 0.0030 0.1492 0.6555 Applications 0.0126 0.0008 15.2388 0.0000 0.0109 0.0143 Recorded 12-46 Simple Linear Regression $SCENARIO 12-12 The manager of the purchasing department of a large saving and loan organization would like to develop a model to predict the amount of time (measured in hours) it takes to record a loan application.Data are collected from a sample of 30 days, and the number of applications recorded and completion time in hours is recorded.Below is the regression output: \begin{array}{l} \begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.9447 \\ \text { R Square } & 0.8924 \\ \text { Adjusted R } & 0.8886 \\ \text { Square } & \\ \text { Standard } & 0.3342 \\ \text { Error } & \\ \text { Observations } & 30 \\ \hline \end{array}\\ \text { ANOVA }\\ \begin{array} { l r r r r r } \hline & { \text { df } } & { \text { SS } } & { \text { MS } } & \text { F } & \text { Significance } F \\ \hline \text { Regression } & 1 & 25.9438 & 25.9438 & 232.2200 & 4.3946 \mathrm { E } - 15 \\ \text { Residual } & 28 & 3.1282 & 0.1117 & & \\ \text { Total } & 29 & 29.072 & & & \\ \hline \end{array}\\ \begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\ \text { Applications } & 0.0126 & 0.0008 & 15.2388 & 0.0000 & 0.0109 & 0.0143 \\ \text { Recorded } & & & & & & \\ \hline \end{array} \end{array} 12-46 Simple Linear Regression Simple Linear Regression 12-47 -Referring to Scenario 12-12, there is sufficient evidence that the amount of time needed linearly depends on the number of loan applications at a 5% level of significance.$ Simple Linear Regression 12-47 -Referring to Scenario 12-12, there is sufficient evidence that the amount of time needed linearly depends on the number of loan applications at a 5% level of significance.

(True/False)

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Question 36

SCENARIO 12-9 It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation.Given below is the Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students.NOTE: Only partial output is shown. Regression Statistics Multiple R 0.8857 R Square 0.7845 Adjusted R Square 0.7801 Standard Error 1.3704 Observations 51 ANOVA df SS MS F Significance F Regression 1 335.0472 335.0473 178.3859 Residual 1.8782 Total 50 427.0798 Coefficients standered Error tStat P-value Lower 95\% Upper 95\% Intercept -1.8940 0.4018 -4.7134 0.0000 -2.7015 -1.0865 Hours 0.9795 0.0733 13.3561 0.0000 0.8321 1.1269 Note: 2.051E - 05 = 2.051 10-05 and 5.944 E - 18 = 5.944 10-18 . -Referring to Scenario 12-9, the p-value of the measured F-test statistic to test whether HOURSaffects SALARY is .

(Short Answer)

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Question 37

The residuals represent

(Multiple Choice)

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Question 38

SCENARIO 12-3 The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place.She takes a random sample of 4 students.For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation.These data are presented in the table below. Student Coop Jobs Job Offer 1 1 4 2 2 6 3 1 3 4 0 1 -Referring to Scenario 12-3, suppose the director of cooperative education wants to construct a95% confidence interval estimate for the mean number of job offers received by students who have had exactly one cooperative education job.The confidence interval is from to_.

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Question 39

SCENARIO 12-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousands of dollars) for individual stores based on the number of customers who made purchases.A random sample of 12 stores yields the following results: Customers Sales (Thousands of Dollars) 907 11.20 926 11.05 713 8.21 741 9.21 780 9.42 898 10.08 510 6.73 529 7.02 460 6.12 872 9.52 650 7.53 603 7.25 -Referring to Scenario 12-10, construct a 95% confidence interval for the mean weekly sales when the number of customers who make purchases is 600.

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Question 40

Showing 21 - 40 of 209

The width of the prediction interval for the predicted value of Y is dependent on

Based on the residual plot below, you will conclude that there might be a violation of which of the following assumptions.

The residuals represent

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

Multiple Regression

Business Analytics

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