Say we took a sample of fast food items and found a line of best fit to predict

Question

Say we took a sample of fast food items and found a line of best fit to predict the number of calories the item has based on the grams of fat it contains: yhat = 11.73x + 193.85.  

-What is the slope coefficient and how do we interpret it?

a)193.85, for every 1g increase in fat we expect the number of calories to increase by 193.85.

b)11.73, for every 11.73g increase in fat we expect the number of calories to increase by 1.

c)193.85, if an item had 0g fat we expect the number of calories to be 193.85.

d)11.73, for every 1g increase in fat we expect the number of calories to increase by 11.73.

-Using the regression line from #2, what is the residual for a Crispy Chicken Sandwich that has 25g of fat and 500 calories?

-We found the coeffiecent of determinant to for the regression line in #2 to be .95, interpret this value

-

Explanation / Answer

(1) d)11.73, for every 1g increase in fat we expect the number of calories to increase by 11.73.

(2) Calories = 11.73 * 25 + 193.85 = 487.1

Residual = 500 - 487.1 = 12.9

(3) 95% of the variation in calories can be explained by the variation in the fat content, using this model.

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