MB 3200 Homework #8 ****************************************************************************** Instructions: Solve all the problems. Problems #1, #3, and #4 carry 20 points each. Problems #2 and #5 carry 10 points each. Maximum score for this Homework is 80 points. Note: Use EXCEL as appropriate. Copy the tables into your report and finish up the rest (answering questions and conducting hypothesis tests) on paper and create a pdf file OR type in the answers into Excel or Word and submit the Excel file. But you must submit only a single file show the complete solution. DO NOT, I repeat, DO NOT try to solve the problems using calculator. Using Excel will save you a lot of time. Additional Suggestions/Instructions: 1) No need for typing. You can do your work by hand on paper. 2) If you use a regular A-4/Letter Size (8.5\"x11\") paper to do your Homework on one side, perhaps it will be easier for you to scan. LEAVE ONE-INCH MARGIN ALL AROUND SO THAT NOTHING GOES MISSING WHILE SCANNING. Ensure that in the scanned document the content on all pages is laid out Left to Right and Top to Bottom (whether the page is in Portrait or Landscape mode or in a combination there of). 3) Remember to write down your name on the report and number the pages. 4) Create a single scanned file. DO NOT SUBMIT MULTIPLE FILES. Verify and ensure everything with your report is in order so that when opened the layout is top to bottom. Word or pdf formats are acceptable. If you are using Excel ensure page setup is properly taken care of. 5) Name your report file contains in its name, "Your Full Name" and "Homework Number". 6) Upload your report file on Canvas and verify if everything is fine by opening up the uploaded file. It is your responsibility to ensure your report is uploaded properly. 7) Do not wait until the last minute. The deadline is strictly enforced by Canvas. No hardcopy submissions are accepted. No e-mail submissions are accepted. If the report does not appear in Canvas by the deadline, zero points will be recorded for you for that HW. No exceptions are entertained for any reason under any circumstance in this regard. 8) If anyone needs help with scanning, please stop by the Information Commons Help Desk by the second floor Rotunda and seek help. They will explain what you need to do and you will be able to scan your work. Their service is totally free of charge for you. Information Commons is open 9 a.m. - 9 p.m. Monday through Thursday; 9 a.m. - 5 p.m. on Friday; and 8 a.m. - 5 p.m. on Saturday. ****************************************************************************** 1 1. PC World rated four component characteristics for 10 ultraportable laptop computers: features; performance; design; and price. Each characteristic was rated using a 0-100 point scale. An overall rating, referred to as the PCW World Rating, was then developed for each laptop. The following table shows the performance rating, features rating, and the PCW World Rating for the 10 laptop computers. Model Thinkpad X200 VGN-Z598U U6V Elitebook 2530P X360 Thinkpad X300 Ideapad U110 Micro Express JFT2500 Toughbook W7 HP Voodoo Envy133 Performance 77 97 83 77 64 56 55 76 46 54 Features 87 85 80 75 80 76 81 73 79 68 PCW Rating 83 82 81 78 78 78 77 75 73 72 a) Perform Multiple Regression Analysis treating PCW World Rating as the dependent variable. b) Write down the estimated regression equation. c) Interpret the slope coefficients for each of the independent variables. d) Conduct Hypothesis tests on Regression and Individual coefficients at 0.05 level of significance. e) What are the values of Coefficient of Multiple Determination and Adjusted Coefficient of Multiple Determination? f) Comment on Goodness of Fit between the dependent variable and the two independent variables. g) What is the expected PCW Rating when Performance Rating is 65 and Features Rating is 82? 2. In a regression analysis involving 30 observations, the following estimated regression equation was obtained. y estimate = 17.6 + 3.8x1 - 2.3x2 + 7.6x3 + 2.7x4 a) Interpret b1, b2, b3, and b4 in this estimated regression equation. b) Estimate y when x1 = 9, x2 = 4, x3 = 2, and x4 = 3. 2 3. The owner of Showtime Movie Theaters, Inc., would like to estimate weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. Television Advertising ($1000s) Newspaper Advertising ($1000s) Weekly Revenue ($1000s) 3 3.5 2.5 5 2 4 2.5 3 3.3 2.3 4.2 1.5 2 1.5 2.5 2.5 98 97 97 99 93 98 95 97 Predictor Constant Television Advertising ($1000s) Newspaper Advertising ($1000s) S = 0.642587 R-Sq = 91.9% Analysis of Variance Source DF Regression ? Residual Error ? Total ? Coeff 86.230 2.2902 1.3010 SE Coef 1.574 0.3041 0.3207 T 54.79 7.53 4.06 P 0.000 0.001 0.010 R-Sq(adj) = 88.7% SS 23.435 ? 25.500 Source Television Advertising ($1000s) Newspaper Advertising ($1000s) MS ? ? DF 1 1 F ? P 0.002 Seq SS 16.640 6.795 a) Write down what the estimated regression equation is that relates weekly revenue equation with both television advertising and newspaper advertising as the independent variables. b) Interpret the slope coefficients for each of the independent variables. c) Complete the ANOVA Table d) Conduct Hypothesis tests on Regression and Individual coefficients at 0.05 level of significance. e) What are the values of Coefficient of Multiple Determination and Adjusted Coefficient of Multiple Determination? f) Comment on Goodness of Fit between the dependent variable and the two independent variables. g) How are R-Sq and R-Sq (adj) calculated? h) What is the gross revenue expected for a week when $3500 is spent on television advertising and $1800 is spent on newspaper advertising? 3 4. Refer to the Johnson Filtration problem introduced in this section. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a list showing which repairperson performed the service. The revised data follow. Repair Time in Hours 2.9 3 4.8 1.8 2.9 4.9 4.2 4.8 4.4 4.5 Months Since Last Service 2 6 8 3 2 7 9 8 4 6 Type of Repair Electrical Mechanical Electrical Mechanical Electrical Electrical Mechanical Mechanical Electrical Electrical Repairperson Dave Newton Dave Newton Bob Jones Dave Newton Dave Newton Bob Jones Bob Jones Bob Jones Bob Jones Dave Newton a) Ignore for now the months since the last maintenance service (x1) and the repairperson who performed the service. Develop the estimated simple linear regression equation to predict the repair time (y) given the type of repair (x2). Recall that x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical. b) Does the equation that you developed in part (a) provide a good fit for the observed data? Explain. c) Ignore for now the months since the last maintenance service and the type of repair associated with the machine. Develop the estimated simple linear regression equation to predict the repair time given the repairperson who performed the service. Let x3 = 0 if Bob Jones performed the service and x3 = 1 if Dave Newton performed the service. d) Does the equation that you developed in part (c) provide a good fit for the observed data? Explain. e) Develop the estimated regression equation to predict the repair time given the number of months since the last maintenance service, the type of repair, and the repairperson who performed the service. f) At the .05 level of significance, test whether the estimated regression equation developed in part (e) represents a significant relationship between the independent variables and the dependent variable. g) Is the addition of the independent variable x3, the repairperson who performed the service, statistically significant? Use = .05. What explanation can you give for the results observed? 5. Consider a regression study involving a dependent variable y, a quantitative independent variable x1, and a categorical independent variable with two possible levels (level 1, level 2). a) How many dummy variables are required to represent the categorical variable? b) Write a multiple regression equation relating x1 and the categorical variable to y. c) Interpret the parameters in your regression equation (Hint: Use the logic of \"Interpreting the Parameters\" on Text Book 12th Edition Pages 711 - 712). 4