Question

(Production time) In a manufacturing study, the production times for 110 recent production runs were obtained. For each run, the production time (in hours) and the production size were recorded in the file "production time.txt". The researcher is interested in predicting the production time from the production size. Part 1 (a) Develop a simple linear regression model based on least squares that directly predicts Time from Size (that is, do not transform either the predictor nor the response variable). Ensure that you provide justification for your choice of model. (b) Describe any weaknesses in your model. Part 2 (a) Develop a simple linear regression model that predicts Time from Size (i.e., feel free to transform either the predictor or the response variable or both variables). Ensure that you provide detailed justification for your choice of model. (b) Describe any weaknesses in your model Part 3 Compare the model in Part 1 with that in Part 2. Decide which provides a better model. Give reasons to justify your choice.

production_time.txt is provided below which contains the data for the problem set above.

Time	Size
14.28	15
8.80	9
12.49	7
9.38	4
10.89	9
15.39	21
13.09	11
12.35	6
10.66	10
8.12	7
12.61	12
8.61	2
10.99	6
8.65	5
11.52	10
7.25	3
2.63	3
9.61	4
20.20	20
19.68	17
13.46	13
18.45	30
18.05	21
9.76	4
18.27	15
14.38	17
13.27	13
11.40	10
12.32	7
19.06	23
10.66	7
13.88	16
2.53	3
11.21	3
13.28	10
16.79	21
13.04	5
10.60	7
19.41	26
8.56	7
20.87	22
9.80	8
15.33	14
13.78	11
11.77	9
16.65	18
12.11	10
14.31	6
10.38	4
12.66	13
15.71	13
17.66	17
12.94	13
12.14	8
7.11	2
21.97	33
9.02	3
8.90	4
15.75	25
11.80	12
12.52	14
12.45	6
18.35	24
10.81	8
11.86	12
9.00	4
8.54	4
17.11	14
17.50	16
10.74	6
16.57	16
16.46	15
17.24	22
15.03	12
14.65	10
8.66	8
20.70	21
8.27	9
11.99	8
11.01	6
13.72	7
11.15	7
18.80	18
21.94	23
22.35	27
9.49	8
11.43	8
12.84	14
10.64	5
14.95	14
13.29	10
19.25	16
7.78	8
11.37	6
15.86	18
6.69	6
13.34	17
12.13	10
14.62	8
7.63	6
10.41	8
11.91	6
18.88	21
11.15	9
9.23	6
10.65	10
13.53	11
16.37	12
11.45	9
15.78	15

Answer 1

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