Week 2 Case Study Instructions and Answer Sheet - MBA 7715

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Wilmington University *

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7715

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Statistics

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Feb 20, 2024

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Week 2 Case Study (Case Study #2) i Part 1 Based on your analysis and recommendations from Case Study #1, you decide to look at joint and individual significance for the three models from Case Study #1. Use the output of the regression models from Case Study # 1 to answer the questions below for Part 1 of Case Study #2. 1. Joint and Individual Significance for the Bays model a. Is there joint significance for the Bays model from Case Study #1 assuming alpha = 0.05? Write your answer in the box below. Yes, 4.95833328198758E-19 b. Is there individual significance for the Bays model from Case Study #1 assuming alpha = 0.05? Write your answer in the box below. Yes, 4.95833328198708E-19 2. Joint and Individual Significance for the Population model a. Is there joint significance for the Population model from Case Study #1 assuming alpha = 0.05? Write your answer in the box below. Yes, 1.3986194083991E-12 b. Is there individual significance for the Population model from Case Study #1 assuming alpha = 0.05? Write your answer in the box below. Yes, 1.3986194083991E-12 3. Joint and Individual Significance for the Bays and Population model (Multiple Regression) a. Is there joint significance for the Bays and Population model from Case Study #1 assuming alpha = 0.05? Write your answer in the box below. Yes, 2.28089896545713E-19 b. Is there individual significance for each variable for the Bays and Population model from Case Study #1 assuming alpha = 0.05? Write your answer in the box below. Yes. For Bays it is 2.29702060344379E-09 and for Population it is .0102239362883355 Part 2 You also receive some new information about the Bays variable. You will use the Bay Type worksheet in the QuickFix Vehicles Case Study Data.xlsx workbook along with the results from Case Study #1 for Part 2 of Case Study #2. If you compare the data in the Bay Type worksheet to the Bays and Population worksheet used in Case Study #1, you will notice that the Bay Type worksheet has the original number of bays divided into two variables, Oil Bays and Repair Bays . Using the new information, you decide to conduct some additional analyses to determine whether  the two types of bays are significant predictors of Vehicles Served ,  a model with Oil Bays , Repair Bays, and Population is a better fitting model than the model with Bays and Population from Case Study #1, and

 whether the effect of Oil Bays is different from the effect of Repair Bays . In the end, you will be deciding whether it is better to use bays as a single variable as in the Bays and Population worksheet or as two separate variables as in the Bay Type worksheet. Perform the steps listed below and provide answers to the questions. 1. Multiple Regression for Oil Bays, Repair Bays, and Population a. Run a multiple regression using Oil Bays, Repair Bays, and Population . Label your results in an Excel workbook using the prompt number. b. Write the regression equation for the Oil Bays, Repair Bays, and Population model using the variable names, intercept coefficient, and slope coefficients from the regression output. Write your answer in the box below. Vehicles Served = 24.2986056563214 * Oil Bays + 23.005240340071 * Repair Bays + 0.700871112247057 * Population + 218.072982412098 c. Interpret the slope coefficients for the model. Write your answer in the box below. Number of Vehicles Served increases by 24.2986056563214 for each additional Oil Bay assuming Repair Bays & Population is held constant. Number of Vehicles Served increases by 23.005240340071 for each Repair Bays assuming Oil Bays & Population are held constant. Number of Vehicles Served increases by 0.700871112247057 for each 1000 persons in the population assuming Oil Bays & Repair Bays are held constant. 2. Joint and Individual Significance for the Oil Bays, Repair Bays, and Population model (Multiple Regression) a. Is there joint significance for the Oil Bays, Repair Bays, and Population model assuming alpha = 0.05? Write your answer in the box below. Yes, 1.90183078739246E-18 b. Is there individual significance for each variable for the Oil Bays, Repair Bays, and Population model assuming alpha = 0.05? Write your answer in the box below. Yes. For Oil Bays it is 0.0491405942419776, for Repair Bays it is 0.000322369030137453 and for Population it is 0.0104099577048339. 3. Is the Oil Bays, Repair Bays, and Population model a better fit than the Bays and Population model from Case Study #1? Provide an explanation of how you reached your conclusion including the measure of goodness-of-fit that you used. Write your answer in the box below. No, it is not a better fit than the Bays and Population model as the Adjusted R square value for Bays and Populations model is slightly better than Oil Bays, Repair Bays and Population model. Adjusted R square for Bays and Population model = 0.346675351262382 Adjusted R square for Oil Bays, Repair Bays and Population model = 0.343362073045778 4. Using the Oil Bays, Repair Bays, and Population model as the unrestricted model and the Bays and Population model from Case Study #1 as the restricted model, conduct a partial F-test of the following hypotheses. You can use the partial F test tool provided in Canvas to assist with calculation of the partial F. Label your results in an Excel workbook using the prompt number.

H 0 : β Oil Bays = β Repair Bays H A : β Oil Bays ≠ β Repair Bays a. What is the value of the calculated partial F? Write your answer in the box below. 0.938475356 b. What are the degrees of freedom for the test? Write your answer in the box below. Degrees of freedom for Unrestricted model = 3 Degrees of freedom for restricted model = 2 c. Is the calculated partial F significant assuming alpha = 0.05? Indicate how you reached your conclusion. Write your answer in the box below. We will retain the null hypothesis as F Test value is greater than 0.05, meaning there is no difference between the effect of Oil Bays and Repair Bays. 5. Based on the analyses and conclusions from questions 3 and 4 above, do you recommend using the Oil Bays, Repair Bays, and Population model from Case Study #2 or Bays and Population model from Case Study #1? Indicate how you reached your conclusion. Write your answer in the box below. Bays and Population model is slightly better than the Oil Bays, Repair Bays and Population model as the adjusted square value was slightly higher for Bays and Population model. 6. In a separate Word document, write a concise summary report in APA format for the general manager. Your report should include an introduction, methodology, results, conclusions/recommendations, and references. The introduction must include a brief literature review (see template for instructions and details). The recommendation to the general manager should include whether the model from Case Study #2 is likely to be more useful for making predictions than the model from Case Study #1.

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i This case study is adapted from Exercises 17.1, problem 16, page 598 of Business Statistics: communicating with numbers , Jaggia and Kelly, Fourth Edition.

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