Solutions
Stat 351 Homework #3 Due date: Tuesday, July 06, 2020 at 11.59 p.m. CDT. Submit your homework via one of the following methods. 1. Type your answers in a word document and submit as a word document file or pdf file. 2. Write down your answers in separate sheets of paper and submit the scan copy of the answer. 3. Write down your answers in separate sheets of paper and submit snapshot of the answer. Make sure to show your work for full credit. 1. A sales manager collected data on weekly gross revenue (?, $1000?), television advertising (?1, $1000?), and newspaper advertising (?2, $1000?) for Showtime Movie Theaters. Please use the following Minitab output to help you answer the questions. Regression Analysis: Weekly Gross Revenue versus Televison Advertising, Newspaper Advertising Regression Equation Weekly Gross Revenue = 83.23 + 2.290 Televison Advertising + 1.301 Newspaper Advertising Coefficients Term Coef SE Coef T- Value P- Value VIF Constant 83.23 1.57 52.88 0.000 Televison Advertising 2.290 0.304 7.53 0.001 1.45 Newspaper Advertising 1.301 0.321 4.06 0.010 1.45 Model Summary S R-sq R-sq(adj) R-sq(pred) 0.642587 91.90% 88.66% 68.19% Analysis of Variance Source DF Adj SS Adj MS F- Value P- Value Regression 2 23.435 11.7177 28.38 0.002 Televison Advertising 1 23.425 23.4247 56.73 0.001 Newspaper Advertising 1 6.795 6.7953 16.46 0.010 Error 5 2.065 0.4129 Total 7 25.500 SRES TRES HI COOK -1.62463035 -2.1148304 0.63293866 1.51708824 -1.07750463 -1.09986911 0.64517604 0.70369154 1.22455448 1.3090166 0.30141025 0.21566058 -0.36807947 -0.33377339 0.22646981 0.01322193 1.09775575 1.12702538 0.26175005 0.14242084 -0.39943251 -0.36310345 0.14012225 0.00866635 -1.1206967 -1.15837163 0.6603374 0.81390384 1.08039791 1.1037203 0.13179554 0.05906428 Here SRES - Standardized residual, TRES – Studentized deleted residuals, HI – leverage values, COOK – Cook’s distance. a) Develop an estimated regression equation to predict Weekly Gross Revenue (y) using Television Advertising (?1) and Newspaper Advertising (?2) as the independent variables. b) Interpret the coefficients of the Television Advertising (?1) c) Interpret the coefficients of the Newspaper Advertising (?2) d) Are there any outliers? Please use each of the two methods of standardized residuals, standardized deleted residuals SEPERATELY to detect outliers. Explain them clearly. e) Are there any influential observations? Please use each of the two methods of leverages, and Cook’s Distances SEPERATELY to detect influential observations. Explain them clearly. 2. Johnson Filtration, Inc., provides maintenance service for water-filtration systems throughout southern Florida. Customers contact Johnson with requests for maintenance service on their water-filtration systems. To estimate the service time and the service cost, Johnson’s managers want to predict the repair time necessary for each maintenance request. Repair time (y, in hours) is believed to be related to the number of months since the last maintenance service, the type of repair problem (electrical or mechanical) and repairperson (Bob Jones or Dave Newton). Please use the following Minitab output to help you answer the questions. A regression analysis was conducted to predict the repair time (?, ?? ℎ????), given the number of months since the last maintenance service (?1), the type of repair (?2), and the repairperson (?3) who performed the service. Define a dummy variable ?2 for type of repair, ?2 = { 1 if a mechanical repair 0 if an electrical repair and define a dummy variable ?3 for repair person, ?2 = { 1 if Bob Jones performed the service 0 if Dave Newton performed the service Regression Analysis: Repair time versus x1, x2, x3 Regression Equation Repair time = 2.543 + 0.1644 x1 - 0.507 x2 + 1.222 x3 Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 2.543 0.315 8.07 0.000 x1 0.1644 0.0710 2.32 0.038 1.88 x2 -0.507 0.261 -1.94 0.075 1.09 x3 1.222 0.337 3.63 0.003 1.81 Model Summary S R-sq R-sq(adj) R-sq(pred) 0.508047 79.62% 74.91% 60.14% Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 3 13.1069 4.3690 16.93 0.000 x1 1 1.3849 1.3849 5.37 0.038 x2 1 0.9699 0.9699 3.76 0.075 x3 1 3.4035 3.4035 13.19 0.003 Error 13 3.3555 0.2581 Lack-of-Fit 9 2.7055 0.3006 1.85 0.290 Pure Error 4 0.6500 0.1625 Total 16 16.4624 a) Predict the repair time for a service for an electrical problem performed by Bob Jones with 9 months since the last maintenance occurred. b) Interpret the coefficients of the type of repair. c) Interpret the coefficients of the repairperson. d) At the 0.05 level of significance, test whether the estimated regression equation represents a significant relationship between the independent variables and the dependent variable. Make sure to show all the steps. [Hint: This is an overall significant test] e) Is the repair type significantly related to the repair time? Use α = 0.05, and make sure to show all the steps.