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 |
X | y | (x-xbar)^2 | (x-xbar)(y-ybar) |
6 M: 9.7692 |
120 M: 143.0769 |
14.2071 SS: 282.3077 |
86.9822 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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