Question

In many fast food restaurants, there is a strong correlation between a menu item’s fat content (measured in grams) and its calorie content. We want to investigate this relationship. Using all of the food menu items at a well-known fast food restaurant, the fat content and calorie contents were measured. We decide to fit the least-squares regression line to the data, with fat content being used to predict calorie content.

The data collected gave the following values: Mean Fat content= 38.35 grams; Mean Calorie content= 642.88 calories; Standard deviation of the fat content= 23.99 grams; Standard deviation of the calorie content= 304.90 calories; r = 0.949

a. Find the equation of the least-squares regression line.

b. One of the items on the menu is a hamburger that has 87 grams of fat and 1080 calories. Calculate the residual corresponding to this data point.

Answer 1

Solution:

Given: To fit the least-squares regression line to the data, fat content being used to predict calorie content.

Thus let y = dependent variable = calorie content and x = independent variable = fat content

Thus we have:

Mean Fat content= 38.35 grams;

Mean Calorie content= 642.88 calories;

Standard deviation of the fat content= 23.99 grams;

S_x = 23.99

Standard deviation of the calorie content= 304.90 calories;

S_y = 304.90

r = 0.949

Part a) Find the equation of the least-squares regression line.

Regression equation is :

where

and

thus

Part b. One of the items on the menu is a hamburger that has 87 grams of fat and 1080 calories. Calculate the residual corresponding to this data point.

That is: x = Fat Content = 87 and y = Calorie Content = 1080

we have to find residual

where

Thus