Use the cereals data set included, at the book series website, for the following. Use regression to estimate rating based on fiber alone.

Based on the regression results, what would we expect a scatter plot of rating versus fiber to look like? Why? For the following exercises, use multiple regression to estimate rating based on fiber and sugars.

Cereal Data Set:

 

cereal
name	Manufacturer	type	calories per serving	grams of protein	grams of fat	milligrams of sodium	grams of dietary fiber	grams of complex carbohydrates	grams of sugars	milligrams of potassium	vitamins and minerals (% of FDA recommendation)	Display shelf	Weight in ounces per one serving	Number of cups in one serving	Rating of cereal
Apple Cinnamon Cheerios	General Mills	Cold	110	2	2	180	1.5	10.5	10	70	25	1	1	0.75	29.50954
Basic 4	General Mills	Cold	130	3	2	210	2	18	8	100	25	3	1.33	0.75	37.03856
Cheerios	General Mills	Cold	110	6	2	290	2	17	1	105	25	1	1	1.25	50.765
Cinnamon Toast Crunch	General Mills	Cold	120	1	3	210	0	13	9	45	25	2	1	0.75	19.82357
Clusters	General Mills	Cold	110	3	2	140	2	13	7	105	25	3	1	0.5	40.40021
Cocoa Puffs	General Mills	Cold	110	1	1	180	0	12	13	55	25	2	1	1	22.73645
Count Chocula	General Mills	Cold	110	1	1	180	0	12	13	65	25	2	1	1	22.39651
Crispy Wheat & Raisins	General Mills	Cold	100	2	1	140	2	11	10	120	25	3	1	0.75	36.1762
Golden Grahams	General Mills	Cold	110	1	1	280	0	15	9	45	25	2	1	0.75	23.80404
Honey Nut Cheerios	General Mills	Cold	110	3	1	250	1.5	11.5	10	90	25	1	1	0.75	31.07222
Kix	General Mills	Cold	110	2	1	260	0	21	3	40	25	2	1	1.5	39.24111
Lucky Charms	General Mills	Cold	110	2	1	180	0	12	12	55	25	2	1	1	26.73452
Multi-Grain Cheerios	General Mills	Cold	100	2	1	220	2	15	6	90	25	1	1	1	40.10597
Oatmeal Raisin Crisp	General Mills	Cold	130	3	2	170	1.5	13.5	10	120	25	3	1.25	0.5	30.45084
Raisin Nut Bran	General Mills	Cold	100	3	2	140	2.5	10.5	8	140	25	3	1	0.5	39.7034
Total Corn Flakes	General Mills	Cold	110	2	1	200	0	21	3	35	100	3	1	1	38.83975
Total Raisin Bran	General Mills	Cold	140	3	1	190	4	15	14	230	100	3	1.5	1	28.59279
Total Whole Grain	General Mills	Cold	100	3	1	200	3	16	3	110	100	3	1	1	46.65884
Triples	General Mills	Cold	110	2	1	250	0	21	3	60	25	3	1	0.75	39.10617
Trix	General Mills	Cold	110	1	1	140	0	13	12	25	25	2	1	1	27.7533
Wheaties	General Mills	Cold	100	3	1	200	3	17	3	110	25	1	1	1	51.59219
Wheaties Honey Gold	General Mills	Cold	110	2	1	200	1	16	8	60	25	1	1	0.75	36.18756
All-Bran	Kelloggs	Cold	70	4	1	260	9	7	5	320	25	3	1	0.33	59.42551
All-Bran with Extra Fiber	Kelloggs	Cold	50	4	0	140	14	8	0	330	25	3	1	0.5	93.70491
Apple Jacks	Kelloggs	Cold	110	2	0	125	1	11	14	30	25	2	1	1	33.17409
Corn Flakes	Kelloggs	Cold	100	2	0	290	1	21	2	35	25	1	1	1	45.86332
Corn Pops	Kelloggs	Cold	110	1	0	90	1	13	12	20	25	2	1	1	35.78279
Cracklin' Oat Bran	Kelloggs	Cold	110	3	3	140	4	10	7	160	25	3	1	0.5	40.44877
Crispix	Kelloggs	Cold	110	2	0	220	1	21	3	30	25	3	1	1	46.89564
Froot Loops	Kelloggs	Cold	110	2	1	125	1	11	13	30	25	2	1	1	32.20758
Frosted Flakes	Kelloggs	Cold	110	1	0	200	1	14	11	25	25	1	1	0.75	31.43597
Frosted Mini-Wheats	Kelloggs	Cold	100	3	0	0	3	14	7	100	25	2	1	0.8	58.34514
Fruitful Bran	Kelloggs	Cold	120	3	0	240	5	14	12	190	25	3	1.33	0.67	41.01549
Just Right Crunchy Nuggets	Kelloggs	Cold	110	2	1	170	1	17	6	60	100	3	1	1	36.52368
Just Right Fruit & Nut	Kelloggs	Cold	140	3	1	170	2	20	9	95	100	3	1.3	0.75	36.47151
Mueslix Crispy Blend	Kelloggs	Cold	160	3	2	150	3	17	13	160	25	3	1.5	0.67	30.31335
Nut&Honey Crunch	Kelloggs	Cold	120	2	1	190	0	15	9	40	25	2	1	0.67	29.92429
Nutri-Grain Almond-Raisin	Kelloggs	Cold	140	3	2	220	3	21	7	130	25	3	1.33	0.67