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

Question

You 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 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

Parameter Parameter estimate Std. err. of parameter est.

151.092 30.082

12.546 1.213

The quantity s = 43.5747 is an estimate of the standard deviation of the deviations in the simple linear regression model.

part I

The degrees of freedom for s are

a) 3. b) 12. c) 24. d) 26.

part II

The following results were obtained from software. r2 = 0.846 s = 43.5747

What is the correct interpretation for r2?

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

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

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

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

part III

The slope of the least-squares regression line is

a) 151.09.

b) 12.546.

c) 0.846.

d) None of the above

Explanation / Answer

Degree of freedom of S will be = 26-2 = 24

Option C is Correct

What is the correct interpretation for r2?

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

The slope of the least-squares regression line is

Option C is Correct. It is 12.546

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