A researcher collects a random sample of data across stores containing information on different cereals. Using this sample information, the researcher hopes to make some inferences about the cereal market.

The data is in the table below. Details of the variables are as follows,

ratings average ratings of a particular cereal (consumers assign higher ratings to their preferred cereal)

mfr Manufacturer of the cereal type. There are three manufacturers in the data, "N", "K" and "G".

shelf The presentation mode of a cereal in the store, where, 1 is when it is presented on promotion shelf, 2 is when it is presented on the regular shelf, and 3 is when it is presented on the shelf closest to the cashier.

caloriesamount of calories per one serving.

vitaminaverage vitamin (in milligrams) per one serving measured in milligrams.

(a)Estimate a regression model with "ratings" as your dependent variable and the others as independent variables. Cut-and-paste your regression output. Remember to appropriately use "dummy variables" wherever required.

(b)Based on your regression results, what is the impact of calories and vitamins on the ratings of a cereal? Make a clear interpretation for each impact. (usea =0.05)

(c) Is there a difference in ratingsbased on the presentation mode (shelf)? Which type of presentation mode (shelf) results in maximum ratings?

rating	mfr	calories	vitamins	shelf
68.4	N	70.0	25.0	3
34	K	120.0	0.0	3
59.4	K	70.0	25.0	3
93.7	K	50.0	25.0	3
34.4	K	110.0	25.0	3
29.5	G	110.0	25.0	1
33.2	K	110.0	25.0	2
37	G	130.0	25.0	3
49.1	K	90.0	25.0	1
53.3	N	90.0	25.0	3
18	K	120.0	25.0	2
50.8	G	110.0	25.0	1
19.8	G	120.0	25.0	2
40.4	G	110.0	25.0	3
22.7	G	110.0	25.0	2
41.4	K	110.0	25.0	1
45.9	K	100.0	25.0	1
35.8	K	110.0	25.0	2
22.4	G	110.0	25.0	2
40.4	K	110.0	25.0	3
64.5	N	100.0	0.0	2
46.9	K	110.0	25.0	3
36.2	G	100.0	25.0	3
44.3	K	100.0	25.0	3
32.2	K	110.0	25.0	2
31.4	K	110.0	25.0	1
58.3	K	100.0	25.0	2
40.9	N	120.0	25.0	3
41	K	120.0	25.0	3
28	N	110.0	25.0	2
35.3	N	100.0	25.0	1
23.8	G	110.0	25.0	2
52.1	N	100.0	25.0	3
53.4	N	110.0	25.0	3
45.8	N	120.0	25.0	3
21.9	K	120.0	25.0	2
31.1	G	110.0	25.0	1
28.7	N	110.0	25.0	1
36.5	K	110.0	100.0	3
36.5	K	140.0	100.0	3
39.2	G	110.0	25.0	2
45.3	K	100.0	25.0	2
26.7	G	110.0	25.0	2
54.9	G	100.0	25.0	2
37.1	K	150.0	25.0	3
34.1	K	150.0	25.0	3
30.3	K	160.0	25.0	3
40.1	G	100.0	25.0	1
29.9	K	120.0	25.0	2
40.7	K	140.0	25.0	3
59.6	K	90.0	25.0	3
30.5	G	130.0	25.0	3
37.8	N	120.0	25.0	3
41.5	K	100.0	100.0	3
60.8	K	50.0	0.0	3
63	K	50.0	0.0	3
49.5	K	100.0	25.0	3
50.8	K	100.0	0.0	1
39.3	K	120.0	25.0	2
39.7	G	100.0	25.0	3
55.3	K	90.0	25.0	3
42	K	110.0	25.0	1
40.6	K	110.0	25.0	1
68.2	N	80.0	0.0	1
74.5	N	90.0	0.0	1
72.8	N	90.0	0.0	1
31.2	K	110.0	25.0	2
53.1	K	110.0	25.0	1
59.4	N	90.0	25.0	2
38.8	G	110.0	100.0	3
28.6	G	140.0	100.0	3
46.7	G	100.0	100.0	3
39.1	G	110.0	25.0	3
27.8	G	110.0	25.0	2
49.8	K	100.0	25.0	1
51.6	G	100.0	25.0	1
36.2	G	110.0	25.0	1