Practice Exam Questions 2 For each of the following short scenarios, describe briefly and specifically how you would respond to the issue raised: 1. What are the purposes of looking at each of leverage, studentized residuals and Cook’s D? 2. You expected from theory, that a particular X variable of the 5 you have in the equation should have a direct relationship with Revenues, your dependent variable. However, when you look at your regression results you see a negative slope with a significant P-value of .002. What problem does this suggest and what would you do about it? 3. You are at the final stages of a revenues forecasting project and now need to forecast revenues using values for your independent variables for the next 4 quarters. Specify the two very different ways for obtaining values for these independent variables for the next 4 quarters. 4. One of your models involves transforming sales by taking a natural log. Why can you no longer use the standard error as a means of choosing a ‘best’ model? What should you use in this case? 5. The normal probability plot in Tools-Data Analysis- Regression gives you a normal probability plot of the dependent variable and it shows the dependent variable to be normal. Is that sufficient to satisfy the normality assumption in regression? If not, what should you do? 1 Data is available in Appendix A on household income for households sampled from 4 regions in a large city in the Western United States. 6. We wish to determine whether or not a significant relationship exists between income and region. (a) Set up specific hypotheses that reflect the type of relationship for situations like this and (b)use Appendix A to help you write up a statement of how confident you are, and (c) Check the assumptions that are needed to do this test. 7. Use the post hoc analysis to help you write up a series of statements detailing how confident you are about which areas have significantly higher incomes than which other areas. Appendix B details a seasonal and trend analysis of 20 quarters of revenues from Lowe’s Home Improvement ($Millions) 8a. Describe the type and strength of the trend in Lowe’s revenues. b. Describe the seasonal nature of Lowe’s revenues. c. Calculate a seasonal forecast for the 21st quarter (a first quarter) using the results of a and b above. 2 Appendix C and following Appendices deal with forecasting revenues for Lowe’s. Definitions for all the variables are found at the bottom of page 6. 9. Look at Appendix C. Explain why the VIF process is used and what you would do as a next step in this process. 10. Look at Appendix D. The dependent variable is seasonally adjusted revenues for Lowe’s Home Improvement. a. Interpret the numbers 0.5556 and 1.2902 across from GDP. Make sure you use the proper units and interpret the numbers in terms of revenues and GDP. b. Does a relationship exist between revenues and housing starts (HSN1F)? Set up appropriate hypotheses and write a conclusion stating your confidence. c. Interpret the number 1.3617 for HSN1F. Make sure you use the proper units. 11. Look at Appendix E. (a) What assumption does this plot address? (b). Does the assumption hold? (c) This plot comes from an equation that has a negative coefficient for MRIME. If you were to use the ladder approach and wanted a better fitting model what would your next step be? Be very specific. 3 12. Look at Appendix F. The dependent variable in the left equation is adjusted revenues and the right is the natural log of adjusted revenues. Being careful of units, interpret the slope for GDP in each equation. 13. Look at Appendix G. This plot comes from Model D. What assumption does it address? Does this assumption hold? 14. Look at Appendix H. This plot comes from Model D. What assumption does it address? Does this assumption hold? If you could ask for other statistical evidence, what would you ask for? 15. Since this data is time series, the D-W statistic is appropriate. In Model D, the D-W statistic was 1.1. What does this say about the independence assumption? How might you make this a better model? 4 16. For the following charts: State whether or not the process is in control or out of control, and describe the reason(s) why using Rules 1, 2 and 3. 6.00 5.00 4.82 4.00 3.00 2.00 1.34 1.00 0.00 0 0 10 20 30 40 1.85 1.75 1.7221 1.65 1.55 1.45 1.35 1.33277 1.25 1.15 1.05 0.95 0.94345 0.85 0 10 20 30 40 50 The following situations call for the use of a control chart. Look at each situation and decide which type of control chart is appropriate for the situation. 17. Customers are surveyed leaving the teller window to find out if their transaction was satisfactory. They sample 50 customers each day and record the number of unsatisfactory transactions. What chart is called for? 18. A chart is constructed by looking at a sample of 25 applications for a consumer loan. Each application is checked thoroughly to see how many questions on the application are not filled out properly. You are to analyze the data but you have only the number of questions not filled out properly. What chart is called for? 19. A mail-order clothing retailer is interested in improving the time of its customer service agents who enter customer orders into the computerized record system. A manager records how long it takes to enter an order in a daily sample of 15 customer orders. He does this over the course of one month’s time. . What type of chart should they use? 5 Appendix A One factor ANOVA Mean 70,179.3 60,203.1 45,758.8 51,021.5 58,639.5 n 18 8 10 12 48 ANOVA table Source SS Treatment 4,772,087,278.83 Error 10,014,453,691.09 Total 14,786,540,969.92 Std. Dev 15,997.59 16,211.27 14,843.42 12,937.56 17,737.17 NE NW SE SW Total df MS 3 1,590,695,759.6 44 227,601,220.3 47 F 6.99 p-value .0006 NE 70,179.3 Post hoc analysis p-values for pairwise t-tests SE SW NW NE 45,758.8 51,021.5 60,203.1 70,179.3 SE 45,758.8 SW 51,021.5 NW 60,203.1 .4196 .0497 .0002 .1893 .0014 .1268 SW 51,021.5 NW 60,203.1 1.33 3.41 1.56 Tukey simultaneous comparison t-values (d.f. = 44) SE 45,758.8 SE 45,758.8 SW 51,021.5 0.81 NW 60,203.1 2.02 NE 70,179.3 4.10 critical values for experimentwise error rate: 0.05 0.01 NE 70,179.3 2.67 3.31 NE NW SE SW Skewness -0.178 0.012 1.011 -0.146 Kurtosis -1.111 -2.093 -0.574 -0.047 Appendix B: 22 quarters of revenues from Lowe’s Home Improvement ($Millions) 2007 2008 2009 2010 2011 mean: adjusted: Calculation of Seasonal Indexes 1 2 3 0.961 1.008 1.138 0.962 1.008 1.144 0.939 1.009 1.126 0.961 1.029 1.149 1.013 1.139 0.956 1.014 1.140 0.956 4 0.886 0.891 0.908 0.876 0.890 0.890 Low e's Revenues and Adjusted Revenues 8100 7600 7100 6600 6100 5600 5100 4600 4100 3600 3100 y = 202.95x + 2713.2 R2 = 0.9873 0 5 10 15 20 6 Appendix C and Following appendices deal with forecasting revenues for Lowe’s and uses data as follows: Adjusted –Seasonally adjusted revenues $Millions GDP – Gross Domestic Product $Billions DPI – Disposable Personal Income $Billions CCONF – Consumer Confidence Index CPI – Consumer price index MORTG – Mortgage interest rate in percent MPRIME – Prime interest rate in percent UNRATE – Unemployment rate in percent HSN1F – Single Family new housing starts (thousands) PERMITS – Building permits (thousands) Appendix C: Regression output variables coefficients Intercept -19,619.8011 GDP 0.7690 DPI -0.0194 CCONF 7.8018 CPI 81.5912 MORTG -37.5298 MPRIME -38.1043 UNRATE 316.5112 HSN1F 1.3720 PERMITS 0.00038802 Appendix D Regression output variables coefficients Intercept -17,697.1195 GDP 0.9229 CPI 60.2911 UNRATE 399.8557 HSN1F 1.3617 std. error 0.3205 0.5798 7.6670 48.8790 87.1693 50.4449 140.6777 0.7371 0.0013 t (df=12) p-value 2.399 -0.033 1.018 1.669 -0.431 -0.755 2.250 1.861 0.302 confidence interval 95% lower 95% upper .0336 0.0707 1.4673 .9739 -1.2827 1.2438 .3290 -8.9032 24.5069 .1209 -24.9069 188.0893 .6744 -227.4553 152.3957 .4646 -148.0143 71.8056 .0440 10.0007 623.0217 .0873 -0.2339 2.9779 .7680 -0.00241320 0.00318925 std. error t (df=15) p-value 0.1723 16.4430 35.7735 0.4717 5.356 3.667 11.177 2.887 .0001 .0023 1.13E-08 .0113 VIF 184.050 484.516 21.473 486.851 17.631 38.980 50.716 12.467 1.402 144.232 mean VIF confidence interval 95% lower 95% upper 0.5556 25.2436 323.6063 0.3563 1.2902 95.3386 476.1051 2.3671 7 Appendix E MPRIME Residual Plot 200 2 150 y = 15.563x - 211.6x + 667.3 2 R = 0.2057 Residuals 100 50 0 -504.00 6.00 8.00 10.00 -100 -150 Appendix F Y=Adjusted Coefficients Intercept -130009.4 MPRIME -205.5678 Ln(GDP) 14842.41 Y = Ln AdjustedCoefficients Intercept 5.255698 LnMPRIME -0.164521 GDP 0.00036 Appendix G Residuals vs Predicted 200 150 100 50 0 2000 -50 3000 4000 5000 6000 7000 8000 -100 -150 Appendix H Normal Probability Plot of Residuals 1.63 1.13 0.63 0.13 -0.37 -0.87 -1.37 -1.87 -109.40 -59.40 -9.40 40.60 90.60 140.60 8