Exam 12: Simple Linear Regression

The value of r is always positive.

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 -Referring to Instruction 12-11,what are the lower and upper limits of the 95% confidence interval estimate for the mean change in revenue as a result of a 1 thousand increase in the 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: 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 Error 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 -Referring to Instruction 12-11,the normality of error assumption appears to have been violated.

In a simple linear regression problem,r and b₁

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 two 95% confidence interval estimates.One is for the mean number of job offers received by people who have had exactly one cooperative education job and one for people who have had two.The confidence interval for people who have had one cooperative education job would be the wider of the two intervals.

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,to test whether a change in price will have any impact on average sales,what would be the critical values? Use ? = 0.05.

If the correlation coefficient (r)= 1.00,then

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,set up a scatter diagram.

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.The p-value of the test is between ________ and ________.

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 30 Observations 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 RECORD 0.0126 0.0008 15.2388 4.3946-15 0.0109 0.0143 Note: 4.3946E-15 is 4.3946 x 10^-15. -Referring to Instruction 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.

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 for the number of job offers received by a student who has had exactly two cooperative education jobs.The t critical value she would use is ________.

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 estimates of the Y-intercept and slope are ________ and ________,respectively.

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 regression sum of squares (SSR)is ________.

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 30 Observations 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 Applications Recorded 0.4024 0.1236 3.2559 0.0030 0.1492 0.6555 Note: 4.3946E-15 is 4.3946 x 10^-15. -Referring to Instruction 12-12,the error sum of squares (SSE)of the above regression is

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.The p-value of the test is ________.

The Chancellor of a university has commissioned a team to collect data on students' GPAs and the amount of time they spend bar hopping every week (measured in minutes).He wants to know if imposing much tougher regulations on all campus bars to make it more difficult for students to spend time in any campus bar will have a significant impact on general students' GPAs.His team should use a t test on the slope of the population regression.

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.The value of the test statistic is ________.

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 -Referring to Instruction 12-11,what is the standard deviation around the regression line?

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 standard error of estimate is ________.

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 null hypothesis for testing whether the number of customers who make purchase effects weekly sales cannot be rejected if 1% probability of committing a Type I error is desired.