Week 1 Case Study answer sheet

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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 1 Case Study (Case Study #1) i The new general manager of QuickFix, a chain of quick service, no appointment auto repair shops, wants to predict monthly vehicles served at each of his locations to allow him to better stock each location with the necessary parts, engine oil and other supplies to meet customer needs. He hires you to develop a statistical model. He provides you with a data file with the monthly number of vehicles served, number of garage bays and population within a 5-mile radius for 200 shop locations. You will use the Bays and Population worksheet in the QuickFix Vehicles Case Study Data.xlsx workbook for this case study. To develop the model, you decide to perform the following steps. 1. Simple Regression for Bays a. Run a simple regression model using Bays to predict Vehicles Served . Label your results in an Excel workbook using the prompt number. Make sure to select all of the check box options at the bottom the regression tool pop-up. You will use them in Case Study 3. b. Write the regression equation for the Bays model using the variable names, intercept coefficient, and slope coefficient from the regression output. Write your answer in the box below. Vehicles Served = 29.40561 * Bays + 220.8869 c. Interpret the slope coefficient for the Bays model Write your answer in the box below. Number of Vehicles Served increases by 29.4056 for each additional bay. 2. Simple Regression for Population a. Run a simple regression model using Population to predict Vehicles Served . Label your results in an Excel workbook using the prompt number. Make sure to select all of the check box options at the bottom the regression tool pop-up. You will use them in Case Study 3. b. Write the regression equation for the Population model using the variable names, intercept coefficient, and slope coefficient from the regression output. Write your answer in the box below. Vehicles Served = 1.751718 * Bays + 285.3916 c. Interpret the slope coefficient for the Population model Write your answer in the box below. Number of Vehicles Served increases by 1.751718 for each 1000 persons in the population. 3. Multiple Regression for Bays and Population a. Run a multiple regression using both Bays and Population . Label your results in an Excel workbook using the prompt number. Make sure to select all of the check box options at the bottom the regression tool pop-up. You will use them in Case Study 3. b. Write the regression equation for the 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 = 23.3952 * Bays + 0.700798 * Population + 217.9244 c. Interpret the slope coefficients for the model. Write your answer in the box below.

Number of Vehicles Served increases by 29.4056 for each additional bay assuming population is held constant. Number of Vehicles Served increases by 1.751718 for each 1000 persons in the population assuming Bays are held constant. 4. Select the best fitting model and 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. Adjusted R square value of the multiple regression model having Bays and Population both as independent variables is greater than both the simple regression models. Hence, multiple regression model is better. 5. Write a sentence stating the percent of variation in Vehicles Served that is explained by the explanatory variables in the best fitting model. Write your answer in the box below. Adjusted R square value of the multiple regression model is highest. R square of that model is 0.35324, which means 35.32% variation is explained by the regression equation. 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 is likely to be useful for making predictions for his intended business purpose. To make the recommendation, consider how strong the relationship is between the response variable and explanatory variable(s).

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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