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Week 5 Case Study (Case Study #4)^[i]

As you continue to look for a better predictive model, you decide to try some non-linear models. You decide to run the following models. You will use the Bays and Population worksheet in the QuickFix Vehicles Case Study Data.xlsxworkbook for this case study.

1. Quadratic Multiple Regression for Bays, Bay², and Population
   1. Run a quadratic regression model using Bays, Bays² and Population. Label your results in an Excel workbook using the prompt number.
   2. Write the regression equation for the quadratic model using the variable names, intercept coefficient, and slope coefficients from the regression output. Write your answer in the box below.

1. Logarithmic Multiple Regression for ln(Bays) and Population
   1. Run a logarithmic regression model using ln(Bays) and Population. Label your results in an Excel workbook using the prompt number.
   2. Write the regression equation for the logarithmic model using the variable names, intercept coefficient, and slope coefficients from the regression output. Write your answer in the box below.

1. Exponential Multiple Regression for Bays and Population
   1. Run an exponential regression model using Bays and Population. Remember that an exponential model uses the natural log of the y-variable. In this case, it would be ln(Vehicles Served). Label your results in an Excel workbook using the prompt number.
   2. Write the regression equation for the exponential model using the variable names, intercept coefficient, and slope coefficients from the regression output. Write your answer in the box below.

1. Select the best fitting non-linear model and provide an explanation of how you reached your conclusion including the measure of goodness-of-fit that you used. Remember that the exponential model requires that some of the goodness-of-fit measures need to be corrected. You can use the R squared correction tool provided in Canvas to assist with the correction. Write your answer in the box below.

1. Is the best fitting non-linear 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.

1. Based on the data that we have at this point in the case study, what model would you recommend using? Provide an explanation for your choice. Write your answer in the box below.

1. 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 revised recommendation to the general manager should include any additional information about the usefulness of a non-linear model from Case Study #4. If one of the non-linear models is a better fit, make sure to be clear with the manager about how much better the non-linear model is.

^[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.

Vehicles Served	Bays	Population in Thousands
200	3	15
351	3	22
382	3	35
294	3	52
223	3	47
309	3	26
302	3	45
369	3	25
312	3	16
289	3	10
304	3	11
233	3	15
313	3	48
285	3	51
298	3	16
224	3	34
403	3	22
282	3	12
299	3	36
200	3	15
366	3	22
385	3	35
291	3	52
238	3	47
308	3	26
289	3	45
368	3	25
312	3	16
292	3	10
306	3	11
226	3	15
301	3	48
278	3	51
283	3	16
233	3	34
404	3	22
278	3	12
301	3	36
214	4	30
250	4	37
288	4	42
352	4	45
345	4	48
410	4	62
259	4	63
331	4	54
401	4	29
425	4	37
428	4	58
407	4	19
340	4	50
340	4	38
328	4	41
427	4	51
330	4	29
410	4	42
339	4	57
427	4	60
403	4	24
216	4	30
254	4	37
289	4	42
359	4	45
347	4	48
399	4	62
245	4	63
316	4	54
394	4	29
421	4	37
438	4	58
410	4	19
339	4	50
355	4	38
314	4	41
433	4	51
315	4	29
396	4	42
332	4	57
437	4	60
392	4	24
325	5	25
317	5	29
344	5	36
376	5	39
369	5	44
494	5	72
377	5	26
273	5	66
273	5	63
436	5	25
377	5	34
358	5	65
355	5	32
370	5	71
357	5	69
357	5	25
353	5	27
293	5	35
366	5	28
373	5	62
457	5	42
317	5	25
316	5	29
345	5	36
379	5	39
376	5	44
498	5	72
369	5	26
287	5	66
284	5	63
440	5	25
372	5	34
373	5	65
366	5	32
368	5	71
346	5	69
359	5	25
356	5	27
282	5	35
363	5	28
372	5	62
448	5	42
318	6	49
354	6	54
512	6	77
464	6	74
402	6	50
468	6	66
485	6	64
400	6	47
380	6	57
397	6	38
394	6	37
321	6	40
395	6	44
378	6	76
459	6	62
392	6	36
393	6	36
380	6	60
397	6	44
318	6	49
363	6	54
513	6	77
453	6	74
387	6	50
480	6	66
475	6	64
391	6	47
374	6	57
382	6	38
380	6	37
323	6	40
389	6	44
382	6	76
463	6	62
394	6	36
403	6	36
374	6	60
385	6	44
495	7	56
325	7	57
509	7	93
491	7	86
520	7	57
336	7	79
328	7	86
416	7	85
508	7	67
332	7	46
432	7	84
430	7	63
411	7	51
356	7	72
503	7	81
416	7	74
335	7	45
408	7	46
418	7	45
416	7	58
509	7	56
330	7	57
523	7	93
506	7	86
535	7	57
333	7	79
318	7	86
412	7	85
518	7	67
330	7	46
446	7	84
432	7	63
420	7	51
347	7	72
488	7	81
421	7	74
350	7	45
414	7	46
416	7	45
430	7	58