Consider the "cabbages" data set provided with this exam; the data itself is in cabbages.csv and the docu- mentation is provided in cabbages.txt. 1. Using symbols (e.g., = + + , which is the basic model for an ANOVA), write a simple linear model describing the relationship between weight of a head of cabbage and its ascorbic acid content. What do each of the symbols represent? 2. Using only basic math functions, such as sums and exponents, and simple summary statistics, such as means, and the ordinary least squares procedure, estimate the coefficients in this model from the data provided. 3. Using your software of choice, show that you have calculated the coefficients correctly. 4. Provide a figure that helps visualize the relationship between head weight and ascorbic acid in this data. This figure should look professional: include proper axis labels in words (not variable names), a title, appropriate shapes and colors, and so on. 5. Can you improve your model by considering the cultivar and planting date of each cabbage? Using software to estimate coefficients, compare the simpler model you wrote above with the more compli- cated model considering more information. What measures or values did you use to compare the two models? Which model is better, and why? 6. Interpret the coefficient associated with the cultivar of the head of cabbage. 7. How would you interpret the coefficients associated with the planting date? Why is there more than one? What does each coefficient estimate mean?

	Cult	Date	HeadWt	VitC
1	c39	d16	2.5	51
2	c39	d16	2.2	55
3	c39	d16	3.1	45
4	c39	d16	4.3	42
5	c39	d16	2.5	53
6	c39	d16	4.3	50
7	c39	d16	3.8	50
8	c39	d16	4.3	52
9	c39	d16	1.7	56
10	c39	d16	3.1	49
11	c39	d20	3	65
12	c39	d20	2.8	52
13	c39	d20	2.8	41
14	c39	d20	2.7	51
15	c39	d20	2.6	41
16	c39	d20	2.8	45
17	c39	d20	2.6	51
18	c39	d20	2.6	45
19	c39	d20	2.6	61
20	c39	d20	3.5	42
21	c39	d21	2.2	54
22	c39	d21	1.8	59
23	c39	d21	1.6	66
24	c39	d21	2.1	54
25	c39	d21	3.3	45
26	c39	d21	3.8	49
27	c39	d21	3.2	49
28	c39	d21	3.6	55
29	c39	d21	4.2	49
30	c39	d21	1.6	68
31	c52	d16	2	58
32	c52	d16	2.4	55
33	c52	d16	1.9	67
34	c52	d16	2.8	61
35	c52	d16	1.7	67
36	c52	d16	3.2	68
37	c52	d16	2	58
38	c52	d16	2.2	63
39	c52	d16	2.2	56
40	c52	d16	2.2	72
41	c52	d20	4	52
42	c52	d20	2.8	70
43	c52	d20	3.1	57
44	c52	d20	4.2	58
45	c52	d20	3.7	47
46	c52	d20	3	56
47	c52	d20	2.2	72
48	c52	d20	2.3	63
49	c52	d20	3.8	54
50	c52	d20	2	60
51	c52	d21	1.5	78
52	c52	d21	1.4	75
53	c52	d21	1.7	70
54	c52	d21	1.3	84
55	c52	d21	1.7	71
56	c52	d21	1.6	72
57	c52	d21	1.4	62
58	c52	d21	1	68
59	c52	d21	1.5	66
60	c52	d21	1.6	72