Question

4. Data are collected on the amount of fat (in grams) and calories in the french

fry orders at nine fast food restaurants. The least-squares regression line for the
data is û = 274.34 + 9.55x, where ŷ is the predicted number of calories and 2
is grams of fat. Which of the following is the correct interpretation of the slope
of the least-squares regression line?
(A) The calories increase by 9.55, on average.
(B) For every increase in fat, the calories increase as well.
(C) Every increase of 1 gram of fat causes an increase of 9.55 calories.
(D) For every increase of 1 gram of fat, the predicted calories increase by 9.55.
(E) For every increase of 1 calorie, the predicted grams of fat increase by 9.55.

Answer 1

Option D

Explanation:

The general equation of the line is y = mx + c

Where m is the slope and c is the initial value

Given: y = 274.34 + 9.55x

where y is the predicted number of calories and x is grams of fat

So, the slope of the line is 9.55 and the initial calories = 274.34

So, at x = 0 , y = 274.34

And at x = 1 gram , y = 274.34 + 9.55

And at x = 2 gram , y = 274.34 + 9.55 * 2

Which mean for every increase of 1 gram of fat, the predicted calories increase by 9.55.

So, the answer is option D