Question

The following table gives information on the amount of sugar (in grams) and the calorie count...

The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 13 varieties of Kellogg's cereal.

Sugar (grams)

6

15

12

11

8

6

7

3

7

14

20

5

13

Calories

120

200

150

110

130

80

200

120

120

190

190

130

120

Find the predictive regression equation of the number of calories on the amount of sugar.

Carry out all calculations exactly, and round the final answers to three decimal places.

y^=4.779+96.387x
y^=96.387+4.779x
y^=5.779+189.767x
y^=96.387-4.779x
y^=-189.767+5.779x

Homework Answers

Answer #1
X y (x-xbar)^2 (x-xbar)(y-ybar)

6
15
12
11
8
6
7
3
7
14
20
5
13

M: 9.7692

120
200
150
110
130
80
200
120
120
190
190
130
120

M: 143.0769

14.2071
27.3609
4.9763
1.5148
3.1302
14.2071
7.6686
45.8225
7.6686
17.8994
104.6686
22.7456
10.4379

SS: 282.3077

86.9822
297.7515
15.4438
-40.7101
23.1361
237.7515
-157.6331
156.213
63.9053
198.5207
480.0592
62.3669
-74.5562

SP: 1349.2308

Regression equation

Sum of X = 127
Sum of Y = 1860
Mean X = 9.7692
Mean Y = 143.0769
Sum of squares (SSX) = 282.3077
Sum of products (SP) = 1349.2308

Regression Equation = ŷ = bX + a

b = SP/SSX = 1349.23/282.31 = 4.779

a = MY - bMX = 143.08 - (4.78*9.77) = 96.387

ŷ = 4.779X + 96.387

So answer is

Option (b)

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