Concept explainers
Exercise 13.18 described a
- a. Test the hypothesis H0: β = 0 versus Ha: β ≠ 0 using a significance level of 0.05. What does the conclusion say about the nature of the relationship between x and y?
- b. Consider the hypothesis H0: β = 40 versus Ha: β > 40. The null hypothesis states that the average change in sales revenue associated with a 1-unit increase in advertising expenditure is (at most) $40,000. Carry out a test using significance level 0.01.
13.18 A simple linear regression model was used to describe the relationship between sales revenue y (in thousands of dollars) and advertising expenditure x (also in thousands of dollars) for fast-food outlets during a 3-month period. A random sample of 15 outlets resulted in the accompanying summary quantities.
- a. What proportion of observed variation in sales revenue can be attributed to the linear relationship between revenue and advertising expenditure?
- b. Calculate se and sb.
- c. Calculate a 90% confidence interval for β, the average change in revenue associated with a $1000 (that is, 1 unit) increase in advertising expenditure.
Trending nowThis is a popular solution!
Chapter 13 Solutions
INTRODUCTION TO STATISTICS & DATA ANALYS
- The Wall Street Journal asked Concur Technologies, Inc., an expense management company, to examine data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city. The following table shows the average daily hotel room rate (X) and the average amount spent on entertainment (Y) for a random sample of 9 of the 25 most-visited U.S. cities. These data lead to the estimated regression equation y = 17.49 + 1.0334x. For these data SSE = 1541.4. Use Table 1 of Appendix B. a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals). b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals). c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).arrow_forwardThe Wall Street Journal asked Concur Technologies, Inc., an expense management company, to examine data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city. The following table shows the average daily hotel room rate (X) and the average amount spent on entertainment (Y) for a random sample of 9 of the 25 most-visited U.S. cities. These data lead to the estimated regression equation y = 17.49 + 1.0334x. For these data SSE = 1541.4. Use Table 1 of Appendix B. (NEED ANSWER FOR A) a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals).arrow_forwardon the basis of the value of linear correlation coefficient, would you conclude, at the /r/>0.9 level, that the data can be reasonably modeled linear equation?arrow_forward
- Mr. James, president of Daniel-James Financial Services, believes that there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, he gathered the following information from a sample of clients for the last month. Let X represent the number of times that the client was contacted and Y represent the valye of sales ($1000) for each client sampled. Number of Contacts (X) Sales ($1000) 14 24 12 14 20 28 16 30 23 30 a) Compute the regression equation for client contacts and sales. Interpret the slope and intercept parameters.arrow_forwardWhich of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2arrow_forwardA regression between foot length(response variable in cm) and height (eexplanatory variable in inches) for 33 students resulted in the following regression equation: y^=10,9+0,23X one student in the sample was 73 inches tall with a foot length of 29cm.What is the predicted foot length for A)33cm B)17,57cm C)27,69cm D)29cmarrow_forward
- In exercise 4, the following estimated regression equation relating sales to inventory investment and advertising expenditures was given.The data used to develop the model came from a survey of 10 stores; for these dataSST = 16,000 and SSR =12,000. yˆ = 25 + 10x1 + 8x2 a. Compute SSE, MSE, and MSR.b. Use an F test and a .05 level of significance to determine whether there is a relationship among the variables.arrow_forwardThe data from exercise 3 follow. xi 2 6 9 13 20 yi 7 18 9 26 23 The estimated regression equation is = 7.6 + .9x. What is the value of the standard error of the estimate (to 4 decimals)? What is the value of the t test statistic (to 2 decimals)? What is the p-value? Use Table 1 of Appendix B.Selectless than .01between .01 and .02between .02 and .05between .05 and .10between .10 and .20between .20 and .40greater than .40Item 3 What is your conclusion ( = .05)?SelectConclude a significant relationship exists between x and yCannot conclude a significant relationship exists between x and yItem 4 Use the F test to test for a significant relationship. Use = .05.Compute the value of the F test statistic (to 2 decimals). What is the p-value?Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6 What is your conclusion?SelectConclude a significant relationship exists between x and yCannot conclude a significant relationship exists…arrow_forwardDr. Spring is a consultant for the National Youth Organization of long jumpers. His goal is to predict how farany given individual will jump (4 attempts) based only on his/her height. Fortunately he had access to height and length of jumps from last year’s competition. Initial analyses of the data were as follows: contestant height (inches) (X) Length of jumps (inches) (Y) mean: 53.100 mean: 123.650 SD: 4.667 SD: 10.535 correlation coefficient= .485, p= .030 (a) Conduct a linear regressionanalysis to predict the length of jumps for the following contestants. (do not round) Contestant number one 52inches tall, length of jumps = Contestant number two 70inches tall, length of jumps = Contestant number three 77inches tall, length of jumps =arrow_forward
- A newspaper used an estimated regression equation to describe the relationship between y = error percentage for subjects reading a four-digit liquid crystal display and the independent variables x1 = level of backlight, x2 = character subtense, x3 = viewing angle, and x4 = level of ambient light. From a table given in the article, SSRegr = 21.6, SSResid = 22, and n = 30. What is the value of the test statistic F What is the P-value What is r2 What is Searrow_forwardIn exercise 1, the following estimated regression equation based on 10 observations was presented. y^=29.1270+.5906x1+.4980x2Develop a point estimate of the mean value of y when x1=180 and x2=310. Predict an individual value of y when x1=180 and x2=310.arrow_forwardWould someone familiar with SPSS be able to help me complete the table and the questions? (a) Explain which of the variables have statistically significant effects at the α = 0.05 level. (b) Are the conclusions different to the results obtained by univariate regression? Explain why and which approach is likely to be preferable?arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman