ou can visit the official Web site of any large restaurant chain to examine the

Question

ou can visit the official Web site of any large restaurant chain to examine the nutritional data for menu items. For fast-food restaurants, many menu items are high in fat, so most of their calorie content comes from fat (rather than carbohydrate or protein). Here we investigate the relationship between the amount of fat in a menu item (“Fat,” measured in grams) and the number of calories (“Calories”). To predict the number of calories in a menu item given its fat content, we use the simple linear regression model Calories = + (Fat) where the deviations are assumed to be independent and Normally distributed, with mean 0 and standard deviation .

At one major fast-food restaurant chain, there were 26 items listed under the heading of “Sandwiches” (which includes hamburgers, chicken sandwiches, and other sandwich selections) on the menu. We fit the model described above to the data using the method of least squares. We treat these 26 menu items (which came from one restaurant) as a sample from the population of all sandwich items at all fast-food restaurants. This assumption is probably dubious. The following results were obtained from software.

r2 = 0.846
s = 43.5747

What is the CORRECT interpretation for r2?

84.6% of the variation in number of calories is predicted by the fat content (in grams)

92.0% of the variation in fat content (in grams) is predicted by the number of calories

92.0% of the variation in number of calories is predicted by the fat content (in grams)

84.6% of the variation in fat content (in grams) is predicted by the number of calories

84.6% of the variation in number of calories is predicted by the fat content (in grams)

92.0% of the variation in fat content (in grams) is predicted by the number of calories

92.0% of the variation in number of calories is predicted by the fat content (in grams)

84.6% of the variation in fat content (in grams) is predicted by the number of calories

Explanation / Answer

Option B is Correct.

  84.6% of the variation in number of calories is predicted by the fat content (in grams).

Explanation:

From the given information

r2 = 0.846
s = 43.5747

So as r2 in percentage is 84.6% which will be the variation in no.. of calories

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