Exam 12: Simple Linear Regression

SCENARIO 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 to analyze the last 4 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 $\text { Durbin-Watson Statistic } \quad 1.59$ -Referring to Scenario 12-5, the partner wants to test for autocorrelation using the Durbin-Watson statistic.Using a level of significance of 0.05, the decision he should make is:

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 t critical value she would use is _.

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 Simple Linear Regression 12-47 -Referring to Scenario 12-12, there is a 95% probability that the mean amount of time needed to record one additional loan application is somewhere between 0.0109 and 0.0143 hours.

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 had a positive impact on the amount of sales generated.Fora test with a level of significance of 0.01, the null hypothesis should be rejected if the value of the test statistic is _.