You can visit the official website of any large restaurant chainto examine the nutritional data for menu items. For fast-foodrestaurants, many menu items are high in fat, so most of theircalorie content comes from fat (rather than carbohydrate orprotein). Here we investigate the relationship between amount offat in a menu item (Fat, measured in grams) and the number ofcalories (Calories).

In order to predict the number of calories in a menu item given itsfat content, we use the simple linear regression model Caloriesi = + Fati + i ,

where the deviations i are assumed to be independent and Normallydistributed, with mean 0 and standard deviation .

At one major fast-food restaurant chain, there were 26 items listedunder the heading of Sandwiches (which includes hamburgers,chicken sandwiches, and other sandwich selections) on the menu. Wefit the model described above to the data using the method of leastsquares. We treat these 26 menu items (which came from onerestaurant) as a sample from the population of all sandwich itemsat 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

1. The response variable in this study is

a. number of calories

b. fat content (grams of fat)

c. the slope,

d. 12.546

(my answer = a)

2. The quantity s = 43.5747 is an estimate of the standard deviation of the deviations in the simple linear regression model. The degrees of freedom for s are

a. 3

b. 12

c. 24

d. 26

(not sure)

3.The slope of the lease-squares regression line is

a. 151.09

b. 12.546

c. 0.846

d. None of the above

(my answer = b)

4. Suppose the researchers test the hypotheses Ho: = 0, Ha: > 0

The value of the t statistic for this test is

a. 10.343

b. 5.023

c. -5.023

d. -10.343

(not sure)

5. The P-value corresponding to the test of the hypotheses in Question 4 is

a. more than 0.02

b. between 0.001 and 0.02

c. between 0.0005 and 0.001

d. less than 0.0005

(not sure)

6. A 95% confidence interval for the mean number of calories per gram of fat in sandwich menu items at fast-food restaurants is

a. 99.627 to 202.553

b. 89.007 to 213.172

c. 10.169 to 14.923

d. 10.042 to 15.050

(not sure)

7. The sample correlation between calories and fat in fast-food sandwich menu items is

a. 0.716

b. 0.920

c. -0.920

d. -0.716

(not sure)

Suppose we're interested in using software to predict the calorie content of menu items with 25 grams of fat. the following output summarizes. Use it to answer 8 & 9.

8. If were trying to estimate w/ 95% confidence, the mean number of calories in all menu items with 25 grams of fat, the appropriate interval is

a. 329.5 to 599.9 calories

b. 432.2 to 497.3 calories

c. 432.2 to 599.9 calories

d. None of the above

(my answer = b)

9. If were trying to estimate w/ 95% confidence, the mean number of calories in a particular menu item with25 grams of fat, the appropriate interval is

a. 329.5 to 599.9 calories

b. 432.2 to 497.3 calories

c. 432.2 to 599.9 calories

d. None of the above

(my answer = a)

Predicted calories	Stdev. predict	95.0% CI	95.0% PI
464.7	15.8	(432.2, 497.3)	(329.5, 599.9)