Instruction 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: \[\begin{array} { | c | c | } \hline \text { Customers } & \text { Sales (Thousands of Dollars) } \\ \hline 907 & 11.20 \\ \hline 926 & 11.05 \\ \hline 713 & 8.21 \\ \hline 741 & 9.21 \\ \hline 780 & 9.42 \\ \hline 698 & 10.08 \\ \hline 510 & 6.73 \\ \hline 529 & 7.02 \\ \hline 460 & 6.12 \\ \hline 872 & 9.52 \\ \hline 650 & 7.53 \\ \hline 603 & 7.25 \\ \hline \end{array}\] -Referring to Instruction 12-10,what are the values of the estimated intercept and slope?

The answer of Instruction 12-10 The management of a chain electronic...

The sample correlation coefficient between X and Y is 0.375.It has been found out that the p-value is 0.256 when testing H0: ρ = 0 against the two-sided alternative H1: ρ ≠ 0.To test H0: ρ = 0 against the one-sided alternative H1: ρ > 0 at a significance level of 0.2,the p-value is

A) 0.256/2. B) (0.256)2. C) 1 - 0.256. D) 1 - 0.256/2. A) 0.256/2. B) (0.256)2. C) 1 - 0.256. D) 1 - 0.256/2.

Instruction 12-4 The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker.They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars.These data are presented in the table that follows. $\begin{array}{ccc} \text { Broker}&\text {Clients }&\text {Sales }\\ \hline1 & 27 & 52 \\ 2 & 11 & 37 \\ 3 & 42 & 64 \\ 4 & 33 & 55 \\ 5 & 15 & 29 \\ 6 & 15 & 34 \\ 7 & 25 & 58 \\ 8 & 36 & 59 \\ 9 & 28 & 44 \\ 10 & 30 & 48 \\ 11 & 17 & 31 \\ 12 & 22 & 38 \end{array}$ -Referring to Instruction 12-4,the managers of the brokerage firm wanted to test the hypothesis that the number of new customers brought in had a positive impact on the amount of sales generated.For a test with a level of significance of 0.01,the null hypothesis should be rejected if the value of the test statistic is ________.

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

Instruction 12-5 The managing partner of an advertising agency believes that his company's sales are related to the industry sales.He uses MicrosoftS1U1P1S1S1P0 Excel's Data Analysis tool to analyse the last four years of quarterly data with the following results: $\begin{array}{lll} {\text { Regression Statistics }} & \\ \text { Multiple R } & 0.802 & \\ \text { R Square } & 0.643 & \\ \text { Adjusted R Square } & 0.618 & \\ \text { Standard Error SYX } & 0.9224 \\ \text { Observations } & 16 \end{array}$ ANOVA $\begin{array}{lccccc} & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { Sig.F } \\ \text { Regression } & 1 & 21.497 & 21.497 & 25.27 & 0.000 \\ \text { Error } & 14 & 11.912 & 0.851 & & \\ \text { Total } & 15 & 33.409 & & &\\ \\ Predictor&Coef&StdError&t Stat&P-value\\ Intercept&3.962 & 1.440 & 2.75 & 0.016\\ Industry&0.040451 & 0.008048 & 5.03 & 0.000\\ \\ \text { Durbin-Watson Statistic } &&&1.59 \end{array}$ -Referring to Instruction 12-5,the prediction for a quarter in which X = 120 is Y = ________.

The answer of Instruction 12-5 The managing partner of an advertising...

Instruction 12-4 The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker.They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars.These data are presented in the table that follows. $\begin{array}{ccc} \text {Broker }&\text { Clients}&\text { Sales}\\ \hline1 & 27 & 52 \\ 2 & 11 & 37 \\ 3 & 42 & 64 \\ 4 & 33 & 55 \\ 5 & 15 & 29 \\ 6 & 15 & 34 \\ 7 & 25 & 58 \\ 8 & 36 & 59 \\ 9 & 28 & 44 \\ 10 & 30 & 48 \\ 11 & 17 & 31 \\ 12 & 22 & 38 \end{array}$ -Referring to Instruction 12-4,suppose the managers of the brokerage firm want to obtain a 99% prediction interval for the sales made by a broker who has brought into the firm 18 new customers.The prediction interval is from ________ to ________.

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

Instruction 12-8 It is believed that average grade (based on a four -point scale)should have a positive linear relationship with university entrance exam scores.Given below is the MicrosoftS1U1P1S1S1P0 Excel output from regressing average grade on university entrance exam scores using a data set of eight randomly chosen students from a large university. Regressing average grade on university entrance exam score }\\ Regression Statistics $\begin{array}{|lr} \hline \text { Multiple R } & 0.7598 \\ \text { R Square } & 0.5774 \\ \hline \text { Adjusted R Square } & 0.5069 \\ \hline \text { Standard Error } & 0.2691 \\ \hline \text { Observations } & 8 \\ \hline \end{array}$ ANOVA $\begin{array}{|lllll|r|r|} \hline & d f & {\text { SS }} & \text { MS } & F & \text { Significance F } \\ \hline \text { Regression } & 1 & 0.5940 & 0.5940 & 8.1986 & 0.0286 \\ \hline \text { Residual } & 6 & 0.4347 & 0.0724 & & \\ \hline \text { Total } & 7 & 1.0287 & & & \\ \hline \end{array}$ $\begin{array}{|l|r|r|r|r|r|r} \hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 0.5681 & 0.9284 & 0.6119 & 0.5630 & -1.7036 & 2.8398 \\ \hline \text { University entrance } & & & & & & 0.1895 \\ \text { exam score } & 0.1021 & 0.0356 & 2.8633 & 0.0286 & 0.0148 & 0.1895 \\ \hline \end{array}$ -Referring to Instruction 12-8,what is the predicted average value of average grade when university entrance exam score = 20?

A) 2.80 B) 2.61 C) 2.66 D) 3.12 A) 2.80 B) 2.61 C) 2.66 D) 3.12

Instruction 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 MicrosoftS1U1P1S1S1P0 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. $\begin{array}{|l|r|} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8857 \\ \hline \text { R Square } & 0.7845 \\ \hline \text { Adjusted R Square } & 0.7801 \\ \hline \text { Standard Error } & 1.3704 \\ \hline \text { Observations } & 51 \\ \hline \end{array}$ ANOVA $\begin{array}{|l|r|r|r|r|r} & d f & \text { SS } & {M S} & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 & \\ \hline \text { Residual } & & & 1.8782 & & \\ \hline \text { Total } & 50 & 427.0798 & & & \end{array}$ $\begin{array}{l|r|r|r|r|r|r} & \text { Coefficients } & \begin{array}{c} \text { Standard } \\ \text { Error } \end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -1.8940 & 0.4018 & -4.7134 & 2.051 \mathrm{E}-05 & -2.7015 & -1.0865 \\ \hline \text { Hours } & 0.9795 & 0.0733 & 13.3561 & 5.944 \mathrm{E}-18 & 0.8321 & 1.1269 \end{array}$ Note: 2.051E-05 = 2.051 * 10S1U1P1-0.5S1S1P0 and 5.944E-18 = 5.944 * 10S1U1P1-18S1S1P0. -Referring to Instruction 12-9,the value of the measured t test statistic to test whether average SALARY depends linearly on HOURS is

A) 13.3561. B) -4.7134. C) 0.9795. D) -1.8940. A) 13.3561. B) -4.7134. C) 0.9795. D) -1.8940.

Exam 12: Simple Linear Regression

Instruction 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 9.42 698 10.08 510 6.73 529 7.02 460 6.12 872 9.52 650 7.53 603 7.25 -Referring to Instruction 12-10,construct a 95% confidence interval for the average weekly sales when the number of customers who make purchases is 600.

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Question 141

Instruction 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 9.42 698 10.08 510 6.73 529 7.02 460 6.12 872 9.52 650 7.53 603 7.25 -Referring to Instruction 12-10,what are the values of the estimated intercept and slope?

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Question 142

Instruction 12-1 A large national bank charges local companies for using their services.A bank official reported the results of a regression analysis designed to predict the bank's charges (Y)- measured in dollars per month - for services rendered to local companies.One independent variable used to predict service charge to a company is the company's sales revenue (X)- measured in millions of dollars.Data for 21 companies who use the bank's services were used to fit the model: Y₁ = β₀ + β₁X₁+ ε_i The results of the simple linear regression are provided below. $\hat { Y }$ = -2,700 + 20 X,S_YX = 65,two-tailed p value = 0.034 (for testing β₁) -Referring to Instruction 12-1,a 95% confidence interval for ?₁is (15,30).Interpret the interval.

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Question 143

The sample correlation coefficient between X and Y is 0.375.It has been found out that the p-value is 0.256 when testing H₀: ρ = 0 against the two-sided alternative H₁: ρ ≠ 0.To test H₀: ρ = 0 against the one-sided alternative H₁: ρ > 0 at a significance level of 0.2,the p-value is

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Question 144

Instruction 12-4 The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker.They sample 12 brokers and determine the number of new customers 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 Instruction 12-4,the managers of the brokerage firm wanted to test the hypothesis that the number of new customers brought in had a positive impact on the amount of sales generated.For a test with a level of significance of 0.01,the null hypothesis should be rejected if the value of the test statistic is ________.

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Question 145

Instruction 12-5 The managing partner of an advertising agency believes that his company's sales are related to the industry sales.He uses Microsoft Excel's Data Analysis tool to analyse the last four years of quarterly data with the following results: Regression Statistics Multiple R 0.802 R Square 0.643 Adjusted R Square 0.618 Standard Error SYX 0.9224 Observations 16 ANOVA df SS MS F Sig.F Regression 1 21.497 21.497 25.27 0.000 Error 14 11.912 0.851 Total 15 33.409 Predictor Coef StdError tStat P-value Intercept 3.962 1.440 2.75 0.016 Industry 0.040451 0.008048 5.03 0.000 Durbin-Watson Statistic 1.59 -Referring to Instruction 12-5,the prediction for a quarter in which X = 120 is Y = ________.

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Question 146

Instruction 12-3 The director of cooperative education at a university wants to examine the effect of cooperative education job experience on marketability in the workplace.She takes a random sample of four students.For these four,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 CoopJobs JobOffer 1 1 4 2 2 6 3 1 3 4 0 1 -Referring to Instruction 12-3,suppose the director of cooperative education wants to obtain a 95% prediction interval estimate for the number of job offers received by students who have had exactly one cooperative education job.The prediction interval is from to .

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Question 147

Instruction 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 9.42 698 10.08 510 6.73 529 7.02 460 6.12 872 9.52 650 7.53 603 7.25 -Referring to Instruction 12-10,the value of the F test statistic equals the square of the t test statistic when testing whether the number of customers who make purchases is a good predictor for weekly sales.

(True/False)

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Question 148

Instruction 12-4 The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker.They sample 12 brokers and determine the number of new customers 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 Instruction 12-4,the managers of the brokerage firm wanted to test the hypothesis that the true slope was equal to 0.The p-value of the test is ________.

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Question 149

Instruction 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: Regression Statistics Multiple R 0.8691 R Square 0.7554 Adjusted R Square 0.7467 Standard Error 44.4765 Observations 30.0000 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 Coefficients Standard Emor t Stat P-value Lower 95\% Upper 95\% Intercept -95.0614 26.9183 -3.5315 0.0015 -150.2009 -39.9218 Download 3.7297 0.4011 9.2992 0.0000 2.9082 4.5513 $Instruction 12-11 A computer software developer would like to use the number of downloads (in thousands)for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars)he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\ \hline \text { R Square } & 0.7554 \\ \hline \text { Adjusted R Square } & 0.7467 \\ \text { Standard Error } & 44.4765 \\ \text { Observations } & 30.0000 \\ \hline \end{array} ANOVA \begin{array}{lr|r|r|r|r} \hline & d f & {\text { SS }} &{\text { MS }} & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\ \hline \text { Total } & 29 & 226451.3503 & & & \\ \hline \end{array} \begin{array}{lrrrrrrr} \hline & \text { Coefficients } & \text { Standard Emor } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\ \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\ \hline \end{array} -Referring to Instruction 12-11,which of the following is the correct interpretation for the coefficient of determination?$ $Instruction 12-11 A computer software developer would like to use the number of downloads (in thousands)for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars)he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\ \hline \text { R Square } & 0.7554 \\ \hline \text { Adjusted R Square } & 0.7467 \\ \text { Standard Error } & 44.4765 \\ \text { Observations } & 30.0000 \\ \hline \end{array} ANOVA \begin{array}{lr|r|r|r|r} \hline & d f & {\text { SS }} &{\text { MS }} & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\ \hline \text { Total } & 29 & 226451.3503 & & & \\ \hline \end{array} \begin{array}{lrrrrrrr} \hline & \text { Coefficients } & \text { Standard Emor } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\ \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\ \hline \end{array} -Referring to Instruction 12-11,which of the following is the correct interpretation for the coefficient of determination?$ -Referring to Instruction 12-11,which of the following is the correct interpretation for the coefficient of determination?

(Multiple Choice)

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Question 150

Instruction 12-4 The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker.They sample 12 brokers and determine the number of new customers 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 Instruction 12-4,suppose the managers of the brokerage firm want to obtain a 99% prediction interval for the sales made by a broker who has brought into the firm 18 new customers.The prediction interval is from to .

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Question 151

Instruction 12-8 It is believed that average grade (based on a four -point scale)should have a positive linear relationship with university entrance exam scores.Given below is the Microsoft Excel output from regressing average grade on university entrance exam scores using a data set of eight randomly chosen students from a large university. Regressing average grade on university entrance exam score }\\ Regression Statistics Multiple R 0.7598 R Square 0.5774 Adjusted R Square 0.5069 Standard Error 0.2691 Observations 8 ANOVA df SS MS F Significance F Regression 1 0.5940 0.5940 8.1986 0.0286 Residual 6 0.4347 0.0724 Total 7 1.0287 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 0.5681 0.9284 0.6119 0.5630 -1.7036 2.8398 University entrance 0.1895 exam score 0.1021 0.0356 2.8633 0.0286 0.0148 0.1895 -Referring to Instruction 12-8,what is the predicted average value of average grade when university entrance exam score = 20?

(Multiple Choice)

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Question 152

Instruction 12-12 The manager of the purchasing department of a large savings 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 4.3946-15 0.0109 0.0143 Recorded Note: 4.3946E-15 is 4.3946 x 10^-15. $Instruction 12-12 The manager of the purchasing department of a large savings and loan organization would like to develop a model to predict the amount of time (measured in hours)it takes to record a loan application.Data are collected from a sample of 30 days,and the number of applications recorded and completion time in hours is recorded.Below is the regression output: \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.9447 \\ \text { R Square } & 0.8924 \\ \text { Adjusted R } & 0.8886 \\ \text { Square } & \\ \text { Standard } & 0.3342 \\ \text { Error } & \\ \text { Observations } & 30 \\ \hline \end{array} ANOVA \begin{array}{lrrrrr} \hline & d f & { S S } & { M S } & F & \text { Significance } F \\ \text { Regression } & 1 & 25.9438 & 25.9438 & 232.2200 & 4.3946 \mathrm{E}-15 \\ \text { Residual } & 28 & 3.1282 & 0.1117 & & \\ \text { Total } & 29 & 29.072 & & & \end{array} \begin{array}{l} \begin{array}{lrrrrrr} & \text { Coefficients } & \begin{array}{c} \text { Standard } \\ \text { Error } \end{array} & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\ \text { Applications } & 0.0126 & 0.0008 & 15.2388 & 4.3946 \mathrm{E}-15 & 0.0109 & 0.0143 \end{array}\\ \text { Recorded } \end{array} Note: 4.3946E-15 is 4.3946 x 10<sup>-15</sup>. -Referring to Instruction 12-12,the model appears to be adequate based on the residual analyses.$ $Instruction 12-12 The manager of the purchasing department of a large savings and loan organization would like to develop a model to predict the amount of time (measured in hours)it takes to record a loan application.Data are collected from a sample of 30 days,and the number of applications recorded and completion time in hours is recorded.Below is the regression output: \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.9447 \\ \text { R Square } & 0.8924 \\ \text { Adjusted R } & 0.8886 \\ \text { Square } & \\ \text { Standard } & 0.3342 \\ \text { Error } & \\ \text { Observations } & 30 \\ \hline \end{array} ANOVA \begin{array}{lrrrrr} \hline & d f & { S S } & { M S } & F & \text { Significance } F \\ \text { Regression } & 1 & 25.9438 & 25.9438 & 232.2200 & 4.3946 \mathrm{E}-15 \\ \text { Residual } & 28 & 3.1282 & 0.1117 & & \\ \text { Total } & 29 & 29.072 & & & \end{array} \begin{array}{l} \begin{array}{lrrrrrr} & \text { Coefficients } & \begin{array}{c} \text { Standard } \\ \text { Error } \end{array} & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\ \text { Applications } & 0.0126 & 0.0008 & 15.2388 & 4.3946 \mathrm{E}-15 & 0.0109 & 0.0143 \end{array}\\ \text { Recorded } \end{array} Note: 4.3946E-15 is 4.3946 x 10<sup>-15</sup>. -Referring to Instruction 12-12,the model appears to be adequate based on the residual analyses.$ -Referring to Instruction 12-12,the model appears to be adequate based on the residual analyses.

(True/False)

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Question 153

Instruction 12-1 A large national bank charges local companies for using their services.A bank official reported the results of a regression analysis designed to predict the bank's charges (Y)- measured in dollars per month - for services rendered to local companies.One independent variable used to predict service charge to a company is the company's sales revenue (X)- measured in millions of dollars.Data for 21 companies who use the bank's services were used to fit the model: Y₁ = β₀ + β₁X₁+ ε_i The results of the simple linear regression are provided below. $\hat { Y }$ = -2,700 + 20 X,S_YX = 65,two-tailed p value = 0.034 (for testing β₁) -Referring to Instruction 12-1,interpret the estimate of ?₀,the Y-intercept of the line.

(Multiple Choice)

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Question 154

Instruction 12-3 The director of cooperative education at a university wants to examine the effect of cooperative education job experience on marketability in the workplace.She takes a random sample of four students.For these four,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 CoopJobs JobOffer 1 1 4 2 2 6 3 1 3 4 0 1 -Referring to Instruction 12-3,the director of cooperative education wanted to test the hypothesis that the true slope was equal to 3.0.For a test with a level of significance of 0.05,the null hypothesis should be rejected if the value of the test statistic is ________.

(Short Answer)

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Question 155

Instruction 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: Regression Statistics Multiple R 0.8691 R Square 0.7554 Adjusted R Square 0.7467 Standard Error 44.4765 Observations 30.0000 ANOVA df SS MS F Significance F Regression 1 171062.9193 171062.9193 86.4759 0.0000 Residuall 28 55388.4309 1978.1582 Total 29 226451.3503 Coefficients Standard Eror t Stat P-value Lower 95\% Upper 95\% Intercept -95.0614 26.9183 -3.5315 0.0015 -150.2009 -39.9218 Download 3.7297 0.4011 9.2992 0.0000 2.9082 4.5513 $Instruction 12-11 A computer software developer would like to use the number of downloads (in thousands)for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars)he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\ \hline \text { R Square } & 0.7554 \\ \hline \text { Adjusted R Square } & 0.7467 \\ \hline \text { Standard Error } & 44.4765 \\ \hline \text { Observations } & 30.0000 \\ \hline \end{array} ANOVA \begin{array}{|l|r|r|r|r|r|} & d f & \text { SS } & {M S} & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \hline \text { Residuall } & 28 & 55388.4309 & 1978.1582 & \\ \hline \text { Total } & 29 & 226451.3503 & & \end{array} \begin{array}{lrrrrrrr} \hline & \text { Coefficients } & \text { Standard Eror } &{t \text { Stat }} & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\ \hline \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \end{array} -Referring to Instruction 12-11,which of the following is the correct null hypothesis for testing whether there is a linear relationship between revenue and number of downloads?$ $Instruction 12-11 A computer software developer would like to use the number of downloads (in thousands)for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars)he can make on the full version of the new shareware.Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\ \hline \text { R Square } & 0.7554 \\ \hline \text { Adjusted R Square } & 0.7467 \\ \hline \text { Standard Error } & 44.4765 \\ \hline \text { Observations } & 30.0000 \\ \hline \end{array} ANOVA \begin{array}{|l|r|r|r|r|r|} & d f & \text { SS } & {M S} & F & \text { Significance } F \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \hline \text { Residuall } & 28 & 55388.4309 & 1978.1582 & \\ \hline \text { Total } & 29 & 226451.3503 & & \end{array} \begin{array}{lrrrrrrr} \hline & \text { Coefficients } & \text { Standard Eror } &{t \text { Stat }} & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\ \hline \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \end{array} -Referring to Instruction 12-11,which of the following is the correct null hypothesis for testing whether there is a linear relationship between revenue and number of downloads?$ -Referring to Instruction 12-11,which of the following is the correct null hypothesis for testing whether there is a linear relationship between revenue and number of downloads?

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Question 156

Data that exhibit an autocorrelation effect violate the regression assumption of independence.

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Question 157

Instruction 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 Microsoft 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 Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -1.8940 0.4018 -4.7134 2.051-05 -2.7015 -1.0865 Hours 0.9795 0.0733 13.3561 5.944-18 0.8321 1.1269 Note: 2.051E-05 = 2.051 * 10^-0.5 and 5.944E-18 = 5.944 * 10^-18. -Referring to Instruction 12-9,the value of the measured t test statistic to test whether average SALARY depends linearly on HOURS is

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Question 158

Which of the following assumptions concerning the probability distribution of the random error term is stated incorrectly?

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Question 159

Instruction 12-2 A chocolate bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product.To do this,the company randomly chooses six country towns and cities and offers the chocolate bar at different prices.Using chocolate bar sales as the dependent variable,the company will conduct a simple linear regression on the data below: City Price (\ ) Sales Toowoomba 1.30 100 Broken Hill 1.60 90 Bendigo 1.80 90 Kalgoorlie 2.00 40 Launceston 2.40 38 Port Augusta 2.90 32 -Referring to Instruction 12-2,if the price of the chocolate bar is set at $2,the predicted sales will be

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Question 160

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The sample correlation coefficient between X and Y is 0.375.It has been found out that the p-value is 0.256 when testing H₀: ρ = 0 against the two-sided alternative H₁: ρ ≠ 0.To test H₀: ρ = 0 against the one-sided alternative H₁: ρ > 0 at a significance level of 0.2,the p-value is

Data that exhibit an autocorrelation effect violate the regression assumption of independence.

Which of the following assumptions concerning the probability distribution of the random error term is stated incorrectly?

Introduction and Data Collection

Presenting Data in Tables and Charts

Numerical Descriptive Measures

Basic Probability

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Hypothesis Testing: Two Sample Tests

Analysis of Variance

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Multiple Regression Model Building

Decision Making

Statistical Applications in Quality and Productivity Management

Further Non-Parametric Tests

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