In many fast food restaurants, there is a strong correlation between a menu item

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 (x) as the explanatory variable and (y) as the response variable. A scatterplot of the data (with regression line included) and a summary of the data are provided. One of the menu items is a hamburger with 107 grams of fat and 1410 calories.


r = 0.979 (correlation between x and y)
= 40.35 grams (mean of the values of x)
= 662.88 calories (mean of the values of y)
= 27.99 grams (standard deviation of the values of x)
= 324.90 calories (standard deviation of the values of y)

What is TRUE about the regression line in this example?

The point (40.35, 662.88) lies on the regression line. 97.9% of the variation is explained by the regression model. 95.8% of the response variables can be explained by the predictors. When there are zero grams of fat, there will be approximately 200 calories.

Explanation / Answer

Here,

r = 0.979

Hence, the coefficient of determination is

r^2 = 0.979^2 = 0.958

Hence,

OPTION C: 95.8% of the response variables can be explained by the predictors. [ANSWER]

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