Question

The amounts of sugar (grams of sugar per gram of cereal) and calories (per gram of cereal) were recorded for a sample of 16 different cereals. The linear correlation coefficient is r= 0.765 and the regression equation is y ^ = 3.46 + 1.01 x , where x represents the amount of sugar. The mean of the 16 amounts of sugar is 0.295 grams and the mean of the 16 calorie counts is 3.76.

What is the best predicted calorie count for a cereal with a measured sugar amount of 0.40 g?

Answer 1

The best predicted calorie count for a cereal with a measured sugar amount of 0.40 g is 3.864

Explanation:

Consider the provided information.

he linear correlation coefficient is r= 0.765 and the regression equation is
`\hat y= 3.46 + 1.01* x`

The mean of the 16 amounts of sugar is 0.295 grams and the mean of the 16 calorie counts is 3.76.We need to find the best predicted calorie count for a cereal with a measured sugar amount of 0.40 g

Substitute x = 0.40 in the given equation.

`\hat y= 3.46 + 1.01* 0.40`

`\hat y= 3.46 + 0.404`

`\hat y= 3.864`

Hence, the best predicted calorie count for a cereal with a measured sugar amount of 0.40 g is 3.864