Math 533 - Managerial Statistics - Course Project Introduction ALLSEASONS is a Chicago company that specializes in residential heating and cooling systems. Their call center has 100 employees who handle both inbound and outbound calls to schedule appointments for service technicians. Call center employees can schedule any type of appointment but they are assigned to one of three specialized teams, as noted below. During the first week of September the call center managers gathered data on the following key variables. 1. 2. 3. 4. 5. 6. 7. ID number is the number assigned to employees on their ID/keycard APPOINTMENTS is the number of service appointments scheduled during the week OUTBOUND is the number of outbound calls the week INBOUND is the number of inbound calls the week MINUTES represents the average minutes per outbound call the week. MONTHS is the months of experience in the call center. TEAM specialty ... TUNEUP (1 hour) ... REPAIR (actual time + materials) ... INSTALL (quoted time + materials) This data can be found in a Minitab worksheet file posted in DocShare titled ALLSEASONS.mtw This project has 3 parts due at the end of Week2/Part A, Week6/Part B and Week7/Part C PART A: Exploratory Data Analysis 1. Download the ALLSEASONS.mtw dataset posted in DocShare. Use Minitab to analyze this data. 2. Select three variables. Use Minitab to analyze each variable by itself using numerical and then graphical techniques. Explain what you find from the Minitab output. Refer to the text for the types of graphs and numerical measures that you could employ. Caution: some may be appropriate for one variable but not another, nor are all necessary. Less is more and more is probably less so make your choices with care. Be sure to select an appropriate graph and measures of central tendency and of dispersion for each variable. 3. Select three pairs of variables. Use Minitab to analyze the connections/relationships between each pair. Here are the 9 pairings to choose from (APPOINTMENTS and OUTBOUND, APPOINTMENTS and INBOUND, APPOINTMENTS and MINUTES, APPOINTMENTS and MONTHS, APPOINTMENTS and TEAM, MINUTES and OUTBOUND, MINUTES and INBOUND, MINUTES and MONTHS, MINUTES and TEAM). Again, use Minitab to prepare both numerical and graphical measures. Refer to the text for the types of graphs and numerical measures that you could employ. Select the three pairs carefully. Some pairs may show clear relationships, while others may not. 4. Prepare your report using Microsoft Office. Begin with a one paragraph introduction IN YOUR OWN WORDS. Then explain your findings for each variable or pair of variables. Integrate your graphs and tables into your explanation. Remember to provide both graphical and numerical back up for your explanations in your paper. Be selective in what you include. Do not write a 20-page report on every detail about each variable/variable pair. Rather, you should explain in one paragraph what you see for each of the three individual variables you selected ... a total of 3 paragraphs. Repeat this for the 3 pairs of variables. So your paper should have at least 7 paragraphs. Each paragraph should discuss your findings from the one graph you selected for that variable ... one or two measures of central tendency and one or two measures of dispersion. All DeVry University policies are in effect, including the plagiarism policy. Part A is due by the end of Week 2 and is worth 100 total points. (See the grading rubric below.) Format for Part A Brief introduction (in your own words, DO NOT copy/paste) Discuss your findings for the 1st individual variable, using graphical and numerical methods. Discuss your findings for the 2nd individual variable, using graphical and numerical methods. Discuss your findings for the 3rd individual variable, using graphical and numerical methods. Discuss your findings for the 1st pair of variables, using graphical and numerical methods. Discuss your findings for the 2nd pair of variables, using graphical and numerical methods. Discuss your findings for the 3rd pair of variables, using graphical and numerical methods. Conclusion Part A: Grading Rubric Category Points % Description Three Individual Variables 12 points each 36% Findings from graphical and numerical analysis Three Pairs of Variables 15 points each 45% Findings from graphical and numerical analysis Communication Skills 19 points 19% Writing, grammar, clarity, logic, cohesiveness, adherence to the above format Total 100 points 100% A quality paper will meet or exceed all of the above requirements. Part B: Hypothesis Testing and Confidence Intervals Your manager has speculated the following: A. The average (mean) appointments per week is less than 30 per employee. B. The true population proportion of employees assigned to the Tuneup team is less than 55%. C. The average (mean) number of outbound calls made per week by employees on the install team is less than 80. D. The average (mean) minutes per call is greater than 10 minutes. 1. Use Minitab to analyze the ALLSEASONS.mtw dataset. Perform the hypothesis test for each of the four speculations to see if there is evidence to support your manager's belief in each case. Follow each step of the hypothesis testing procedure from the text using = .05, then explain your conclusion in simple terms. Also, be sure to compute the p-value and interpret. 2. Follow this up with computing 95% confidence intervals for each of the variables described in A-D and again interpreting these intervals. 3. Write a report to your manager about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical. 2 All DeVry University policies are in effect, including the plagiarism policy. Part B is due by the end of Week 6 and is worth 100 total points. (See the grading rubric below.) Format for Part B A. A 1-2 page summary report with an introduction followed by one paragraph explaining your findings for each of the four speculations (covering both the hypothesis test and the confidence interval) for a total of 5 paragraphs B. Appendix with all of the hypothesis testing steps for each speculation, as well as the confidence intervals. Include all Minitab output in your appendix. Part B: Grading Rubric Category Summary Report Appendix addressing each speculation Total Points % Description 20 points 20% one paragraph on each of the speculations 20 points each 80% hypothesis test and conclusion, confidence interval, and interpretation 100 points 100% A quality paper will meet or exceed all of the above requirements. PART C: Regression and Correlation Analysis Using Minitab, perform the regression and correlation analysis for the data on APPOINTMENTS (Y) and OUTBOUND (X) by answering the following questions. 1. Generate a scatterplot for APPOINTMENTS versus OUTBOUND, including the best fit line. Interpret. 2. Show and then explain in simple English the equation of the best fit line, which describes the relationship between APPOINTMENTS and OUTBOUND. 3. Determine the coefficient of correlation and interpret. Then interpret the coefficient of determination. 5. Test the utility of this regression model (use a two tail test with =.05). Interpret your results, including the p-value. 6. Based on the above, do you recommend using OUTBOUND to predict APPOINTMENTS? Explain. 7. Compute the 95% confidence interval for B1 (the population slope). Interpret this interval. 8. Using an interval, estimate and explain the average weekly appointments for weekly outbound calls that are 120. 9. Using an interval, predict the weekly appointments when weekly outbound calls are 120. Explain. 10. What can we say about the weekly appoints when weekly outbound calls are 150? Explain. 3 In an attempt to improve this model, build a multiple regression model predicting APPOINTMENTS based on INBOUND, OUTBOUND, MINUTES, and MONTHS. 11. Show and then explain in simple English the equation of the best fit line for a multiple regression model to predict APPOINTMENTS using the 4 variables noted above 12. Perform the global test for utility (F-Test). Explain your conclusion. 13. Perform the t-test on each independent variable. Explain your conclusions, and clearly state how you should proceed. In particular, state which independent variables should we keep, and which should be discarded. 14. Is this multiple regression model better than the 1 variable model that we generated? Explain. All DeVry University policies are in effect, including the plagiarism policy. Part B is due by the end of Week 6 and is worth 100 total points. (See the grading rubric below.) Format for report A. Provide an introduction, then summarize your findings from 1-14 in a report that is NO MORE than two pages in a manner that is understandable to someone who does not know statistics. B. Appendix that addresses points 1-14 with appropriate output, graphs, and interpretations. Be sure to number each point 1-14. Part C: Grading Rubric Category Points % 5 points each 65% addressed with appropriate output, graphs, and interpretations Question 13 15 points 15% addressed with appropriate output, graphs, and interpretations Summary 20 points 20% writing, grammar, clarity, logic, cohesiveness, adherence to the above format Total 100 points 100% A quality paper will meet or exceed all of the above requirements. Questions 1-12 and 14 Description 4 ID Number APPOINTMENTS OUTBOUND INBOUND 2505 33 108 2508 21 71 2515 31 102 2520 32 123 2523 29 117 2530 34 121 2535 20 63 2538 31 109 2545 29 98 2550 24 86 2553 33 118 2560 27 82 2565 30 77 2568 39 135 2575 28 86 2580 29 105 2583 19 61 2590 29 86 2595 25 72 2598 36 122 2605 26 91 2610 30 86 2613 37 130 2620 24 90 2625 26 89 2628 30 107 2635 31 129 2640 32 102 2643 27 87 2650 30 111 2655 29 105 2658 35 115 2665 31 101 2670 38 128 2673 24 76 2680 24 75 2685 33 108 2688 31 107 2695 28 90 2700 29 91 2703 27 81 2710 24 71 2715 34 114 2718 26 94 2725 27 71 2730 24 68 2733 22 66 MINUTES MONTHS TEAM 64 8.2 6 TUNEUP 32 12.5 5 INSTALL 55 11.2 4 TUNEUP 72 8.5 4 TUNEUP 73 10.3 3 TUNEUP 82 7.9 3 TUNEUP 16 15.7 4 INSTALL 58 9.9 4 REPAIR 54 9.4 2 REPAIR 47 10.9 4 INSTALL 71 7.7 5 TUNEUP 31 11.5 1 INSTALL 33 12.5 3 REPAIR 96 9.0 3 TUNEUP 39 12.8 1 TUNEUP 54 8.4 4 TUNEUP 17 13.0 3 INSTALL 47 12.0 2 REPAIR 25 13.7 2 REPAIR 71 14.1 3 TUNEUP 47 13.8 2 INSTALL 47 11.1 2 TUNEUP 83 8.7 2 TUNEUP 39 14.2 1 INSTALL 45 10.5 4 REPAIR 68 10.2 5 REPAIR 82 10.1 2 REPAIR 51 11.9 4 TUNEUP 43 10.8 4 REPAIR 72 11.1 3 TUNEUP 58 10.5 1 TUNEUP 64 10.6 4 TUNEUP 57 12.0 4 REPAIR 89 7.3 3 TUNEUP 29 9.9 1 INSTALL 24 13.2 2 INSTALL 64 11.4 6 TUNEUP 68 6.7 1 TUNEUP 43 13.5 4 REPAIR 40 10.6 3 REPAIR 37 9.5 4 INSTALL 32 12.4 3 INSTALL 67 12.7 1 TUNEUP 43 10.0 5 INSTALL 27 15.7 4 REPAIR 29 13.8 2 REPAIR 19 13.9 5 INSTALL 2740 2745 2748 2755 2760 2763 2770 2775 2778 2785 2790 2793 2800 2805 2808 2815 2820 2823 2830 2835 2838 2845 2850 2853 2860 2865 2868 2875 2880 2883 2890 2895 2898 2905 2910 2913 2920 2925 2928 2935 2940 2943 2950 2955 2958 2965 2970 2973 31 30 29 35 24 28 30 27 29 30 26 28 33 27 31 31 28 30 33 30 21 36 32 20 24 27 31 28 39 36 35 26 28 25 27 20 21 25 25 32 26 36 28 23 29 28 32 25 120 106 92 119 80 94 104 79 105 112 87 92 100 99 126 90 95 97 110 115 67 121 111 65 86 96 97 103 115 115 113 80 96 86 88 63 64 89 83 125 76 138 93 69 98 89 115 94 69 62 53 72 29 50 65 32 54 68 48 45 49 55 87 43 44 53 71 68 16 77 72 18 35 52 58 56 64 71 74 33 45 42 49 16 13 45 44 78 25 94 54 22 47 45 76 47 10.6 9.5 11.5 8.3 7.5 9.0 10.3 11.3 7.6 10.3 13.5 13.4 12.1 9.1 9.6 16.4 8.9 6.7 7.6 13.8 5.8 6.9 9.5 5.6 11.3 10.1 10.3 12.9 10.4 7.5 8.8 11.0 14.3 10.2 12.1 5.8 5.7 9.7 15.2 5.5 14.8 8.0 7.3 15.0 11.8 10.1 11.9 11.9 5 TUNEUP 6 REPAIR 3 TUNEUP 3 TUNEUP 2 INSTALL 2 TUNEUP 4 TUNEUP 3 INSTALL 3 REPAIR 3 REPAIR 3 REPAIR 2 REPAIR 3 TUNEUP 5 REPAIR 4 TUNEUP 3 TUNEUP 4 TUNEUP 5 TUNEUP 2 TUNEUP 3 REPAIR 5 TUNEUP 5 TUNEUP 3 TUNEUP 6 TUNEUP 2 REPAIR 3 REPAIR 3 TUNEUP 2 REPAIR 2 TUNEUP 3 TUNEUP 2 TUNEUP 3 INSTALL 3 TUNEUP 3 INSTALL 3 REPAIR 5 TUNEUP 6 TUNEUP 5 REPAIR 3 INSTALL 3 TUNEUP 4 REPAIR 2 TUNEUP 4 REPAIR 3 INSTALL 4 TUNEUP 2 TUNEUP 3 TUNEUP 4 REPAIR 2980 2985 2988 2995 2999 28 31 31 31 24 91 93 107 107 83 40 49 68 60 32 9.8 17.1 8.0 11.3 13.2 2 REPAIR 1 TUNEUP 2 TUNEUP 1 TUNEUP 4 INSTALL Descriptive Statistics: MONTHS Variable Mean StDev Minimum Median Maximum Range MONTHS 3.220 1.299 1.000 3.000 6.000 5.000