Question

the excel file cereal data provides a variety of nutritional information about 67 cereals and their shelf location. Use regression analysis to find the best model that explains the relationship between calories and the other variables. Investigat the model assumptions and clearly explain your conclusion. Keep in mind the principle of parsimony!

DATA:

Cereal Data
Product	Cereal Name	Manufacturer	Calories	Sodium	Fiber	Carbs	Sugars
1	100% Bran	Nabisco	70	130	10	5	6
2	AlI-Bran	Kellogg	70	260	9	7	5
3	All-Bran w/Extra Fiber	Kellogg	50	140	14	8	0
4	Almond Delight	Ralston Purina	110	200	1	14	8
5	Apple Cinn Cheerios	General Mills	110	180	1.50	10.50	10
6	Apple Jacks	Kellogg	110	125	1	11	14
7	Basic 4	General Mills	130	210	2	18	8
8	Bran Chex	Ralston Purina	90	200	4	15	6
9	Bran Flakes	Post	90	210	5	13	5
10	Cap'n'Crunch	Quaker	120	220	0	12	12
11	Cheerios	General Mills	110	290	2	17	1
12	Cinnamon Toast Crunch	General Mills	120	210	0	13	9
13	Clusters	General Mills	110	140	2	13	7
14	Cocoa Puffs	General Mills	110	180	0	12	13
15	Corn Chex	Ralston Purina	110	280	0	22	3
16	Corn Flakes	Kellogg	100	290	1	21	2
17	Corn Pops	Kellogg	110	90	1	13	12
18	Count Chocula	General Mills	110	180	0	12	13
19	Cracklin' Oat Bran	Kellogg	110	140	4	10	7
20	Cream of Wheat	Nabisco	100	80	1	21	0
21	Crispix	Kellogg	110	220	1	21	3
22	Crispy Wheat & Raisins	General Mills	100	140	2	11	10
23	Double Chex	Ralston Purina	100	190	1	18	5
24	Froot Loops	Kellogg	110	125	1	11	13
25	Frosted Flakes	Kellogg	110	200	1	14	11
26	Frosted Mini-Whests	Kellogg	100	0	3	14	7
27	Fruit & Fibre	Post	120	160	5	12	10
28	Fruitful Bran	Kellogg	120	240	5	14	12
29	Fruity Pebbles	Post	110	135	0	13	12
30	Golden Grahams	General Mills	110	280	0	15	9
31	Grape Nuts Flakes	Post	100	140	3	15	5
32	Grape-Nuts	Post	110	170	3	17	3
33	Great Grains Pecan	Post	120	75	3	13	4
34	Honey Comb	Post	110	180	0	14	11
35	Honey Graham Ohs	Quaker	120	220	1	12	11
36	Honey Nut Cheerios	General Mills	110	250	1.50	11.50	10
37	Just Right Crunchy Nugget	Kellogg	110	170	1	17	6
38	Just Right Fruit &Nut	Kellogg	140	170	2	20	9
39	Kix	General Mills	110	260	0	21	3
40	Life	Quaker	100	150	2	12	6
41	Lucky Charms	General Mills	110	180	0	12	12
42	Mueslix Crispy Blend	Kellogg	160	150	3	17	13
43	Multi-Grain Cheerios	General Mills	100	220	2	15	6
44	Nut & Honey Crunch	Kellogg	120	190	0	15	9
45	Oatmeal Raisin Crisp	General Mills	130	170	1.50	13.50	10
46	Post Nat. Raisin Bran	Post	120	200	6	11	14
47	Product 19	Kellogg	100	320	1	20	3
48	Puffed Rice	Quaker	50	0	0	13	0
49	Puffed Wheat	Quaker	50	0	1	10	0
50	Quaker Oat Squares	Quaker	100	135	2	14	6
51	Raisin Bran	Kellogg	120	210	5	14	12
52	Raisin Squares	Kellogg	90	0	2	15	6
53	Rice Chex	Ralston Purina	110	240	0	23	2
54	Rice Krispies	Kellogg	110	290	0	22	3
55	Shrdded Wht Spn Size	Nabisco	90	0	3	20	0
56	Shredded Wheat	Nabisco	80	0	3	16	0
57	Shredded Wheat n Bran	Nabisco	90	0	4	19	0
58	Smacks	Kellogg	110	70	1	9	15
59	Special K	Kellogg	110	230	1	16	3
60	Strawberry Fruit Wheels	Nabisco	90	15	3	15	5
61	Total Corn Flakes	General Mills	110	200	0	21	3
62	Total Raisin Bran	General Mills	140	190	4	15	14
63	Total Whole Grain	General Mills	100	200	3	16	3
64	Trix	General Mills	110	140	0	13	12
65	Wheat Chex	Ralston Purina	100	230	3	17	3
66	Wheaties	General Mills	100	200	3	17	3
67	Wheaties Honey Gold	General Mills	110	200	1	18	8

Answer 1

Solution :

Regression analysis is done by keeping dependent variable as calories. Sodium, Fiber, Carbs, and Sugar are the independent variable

Regression is performed in the excel and results are as follows

Calorie = 21.89 + 0.024 * Sodium + 0.66 * Fiber + 3.43 * Carbs + 3.94 * Sugars

Conclusion: Significance value is 0.00 which is less than 0.01 so we can say that at 99% confidence level this model is valid.

Adjusted R square value is 0.72, which is good.