Estimate the learning curve from production and cost data. Data is given below:

1. Estimating the simple learning curve
   • Using the data provided, create any new variables needed to estimate the learning curve as a simple regression. What is the dependent (Y) variable? What is the regressor (X)?
   • Plot the relationship between your X and Y variables and discuss.
   • Run the learning curve regression and interpret the results, referring to the table of output. What does the regression tell you about any learning effect? Use words that a layperson could understand.
2. Taking another look
   • The production manager believes that cost efficiency has improved due to experience in production (learning). But she notes that unit costs are also directly a function of current production, and that because production ramped up over time, there may be a confounding effect on the learning curve estimate. Explain briefly what she might have in mind. Which direction would the bias go- that is, is the simple regression's learning effect overestimated or underestimated? Might the bias go in either direction? If so, what about costs would determine the direction of the bias?
   • Address the manager's concern using multiple regression to control for the confounding effect. Explain what variable or variables you add to the simple learning curve and why.
   • Interpret the results and compare the estimated learning effect with what was obtained in #1 (simple regression). Include and refer to regression tables. Was the manager correct? Explain what is going on.
3. Yet another look
   1. An engineer suggests that learning occurs simply with the passage of time, not with output experience. Add a regressor to your regression from #2 to test his conjecture. Discuss the table of results. Is the engineer correct? Explain carefully.

Requirements:

• Using the data delivered in the downloadable above, deliver a report in the form of a Word or PDF document
• In discussing regression results, always interpret the the estimates in words (such as, "this coefficient indicates that a 1% increase in price is associated with a 5% reduction in quantity, other variables held constant"), make sure to consider both economic (size of effect) and statistical significance, and discuss goodness of fit (adjusted R-squared).
• Make comparisons between regression results where called for, and cite specific evidence from results to answer the questions.

Data:

Monthly production and cost data for a machine
Variable	Definition
month	sequence of months since beginning of production
q	quantity produced in that month
cost	total cost of all units produced in that month, in dollars

month	q	cost
1	21	333540.94
2	51	408674.53
3	51	620608.19
4	9	210845.23
5	55	492494.75
6	22	216455.23
7	13	184409.75
8	40	182010.69
9	14	213098.23
10	10	201228.41
11	16	158400.41
12	15	169656.97
13	24	194213.42
14	20	251545.22
15	41	394777.06
16	21	177385.17
17	35	293163.13
18	58	552672.00
19	51	361720.44
20	46	536971.00
21	54	517110.81
22	50	325373.31
23	37	257186.95
24	28	185652.08
25	37	189189.78
26	61	414943.06
27	45	368184.84
28	29	310034.03
29	49	236670.09
30	60	339970.34
31	36	295902.66
32	67	654628.13
33	46	294579.50
34	35	246857.25
35	68	478070.38
36	48	490993.69
37	56	351727.47
38	40	425364.00
39	59	581216.50
40	34	204943.53
41	50	250813.28
42	51	434830.97
43	28	146158.95
44	41	246549.03
45	41	392116.75
46	63	445888.22
47	53	349943.03
48	61	391099.13
49	60	584898.31
50	33	285947.72
51	61	591917.81
52	47	368670.22
53	39	387581.47
54	51	232734.94
55	60	421448.41
56	32	303257.28
57	41	325229.72
58	64	297445.78
59	42	155247.91
60	63	426471.69