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) x = 40.35 grams (mean of the values of x) y = 662.88 calories (mean of the values of y) s_x = 27.99 grams (standard deviation of the values of x) s_y = 324.90 calories (standard deviation of the values of y) What is TRUE about the regression line in this example? A. When there are zero grams of fat, there will be approximately 200 calories. B. 97.9% of the variation is explained by the regression model. C. 95.8% of the response variables can be explained by the predictors. D. The point (40.35, 662.88) lies on the regression line.

Explanation / Answer

Here r = 0.979

So, Coefficient of determination = 0.979*0.979 = 0.958

So, 95.8% of the response variable can be explained by the predictors.

Option C is Correct

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