Question
In: Statistics and Probability
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) 5 15 12 11 8 6 7 2 7 14 20 5 13 Calories 130 200 160 110 130 80 210 120 120 190 190 110 120 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.
Solutions
Expert Solution
| Line of Regression Y on X i.e Y = bo + b1 X | ||||
| X | Y | (Xi - Mean)^2 | (Yi - Mean)^2 | (Xi-Mean)*(Yi-Mean) |
| 5 | 130 | 21.302 | 191.717 | 63.906 |
| 15 | 200 | 28.994 | 3153.249 | 302.366 |
| 12 | 160 | 5.686 | 260.945 | 38.52 |
| 11 | 110 | 1.917 | 1145.565 | -46.863 |
| 8 | 130 | 2.61 | 191.717 | 22.367 |
| 6 | 80 | 13.071 | 4076.337 | 230.83 |
| 7 | 210 | 6.84 | 4376.325 | -173.019 |
| 2 | 120 | 57.994 | 568.641 | 181.598 |
| 7 | 120 | 6.84 | 568.641 | 62.367 |
| 14 | 190 | 19.225 | 2130.173 | 202.366 |
| 20 | 190 | 107.84 | 2130.173 | 479.289 |
| 5 | 110 | 21.302 | 1145.565 | 156.214 |
| 13 | 120 | 11.456 | 568.641 | -80.71 |
calculation procedure for regression
mean of X = ∑ X / n = 9.6154
mean of Y = ∑ Y / n = 143.8462
∑ (Xi - Mean)^2 = 305.077
∑ (Yi - Mean)^2 = 20507.69
∑ (Xi-Mean)*(Yi-Mean) = 1439.231
b1 = ∑ (Xi-Mean)*(Yi-Mean) / ∑ (Xi - Mean)^2
= 1439.231 / 305.077
= 4.718
bo = ∑ Y / n - b1 * ∑ X / n
bo = 143.8462 - 4.718*9.6154 = 98.485
value of regression equation is, Y = bo + b1 X
Y'=98.485+4.718* X
orchestra answered 2 years agoRelated Solutions
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. Calories is the dependent variable.
Calculate the r-sqr, correlation coefficient, and explain each
value.
Index
1
2
3
4
5
6
7
8
9
10
11
12
13
Sugar (grams)
4
15
12
11
8
6
7
2
7
14
20
3
13
Calories
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200
140
110
120
80
190
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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. Calories is the dependent variable.
Calculate the r-sqr, correlation coefficient, and explain each
value.
Index 1 2 3 4 5 6 7 8 9 10 11 12 13
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