Exam 12: Simple Linear Regression

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 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.

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 average weekly sales will increase by an estimated $0.01 for each additional purchasing customer.

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,what is the estimated slope parameter for the chocolate bar price and sales data?

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,the null hypothesis that there is no linear relationship between revenue and number of downloads should be rejected 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,the director of cooperative education wanted to test the hypothesis that the true slope was equal to 0.The p-value of the test is between ________ and ________.

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 average weekly sales will increase by an estimated $10 for each additional purchasing customer.

If the plot of the residuals is fan shaped,which assumption is violated?

A simple regression has a b₀ value of 1.3 and a b₁ value of 2.6.What is the predicted Y for an X value of 0?

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,________% of the total variation in sales generated can be explained by the number of new customers brought in.

The least squares method minimises which of the following?

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 is the p-value of the t test statistic when testing whether the number of customers who make purchases affects weekly sales?

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 value of the test statistic 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,suppose the managers of the brokerage firm want to obtain both a 99% confidence interval estimate and a 99% prediction interval for X = 24.The confidence interval estimate would be the ________ (wider or narrower)of the two intervals.

Instruction 12-7 An investment specialist claims that if one holds a portfolio that moves in opposite direction to the market index like the All Ordinaries Index,then it is possible to reduce the variability of the portfolio's return.In other words,one can create a portfolio with positive returns but less exposure to risk.A sample of 26 years of the All Ordinaries index and a portfolio consisting of stocks of private prisons,which are believed to be negatively related to the All Ordinaries index,is collected.A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y)on the returns of All Ordinaries index (X)to prove that the prison stocks portfolio is negatively related to the All Ordinaries index at a 5% level of significance.The results are given in the following Microsoft Excel output. Coefficients Standard Error T Stat P-value Intercept 4.866004258 0.35743609 13.61363441 8.7932-13 \& -0.502513506 0.071597152 -7.01862425 2.94942-07 -Referring to Instruction 12-7,to test whether the prison stocks portfolio is negatively related to the All Ordinaries index,the measured value of the test statistic is

The slope (b₁)represents

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% confidence interval estimate for the mean sales made by brokers who have brought into the firm 24 new customers.The t critical value they would use is ________.

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,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,what is the value of the coefficient of correlation?

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 exam score 0.1021 0.0356 2.8633 0.0286 0.0148 0.1895 -Referring to Instruction 12-8,what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between average grade and university entrance exam scores?