The following table shows the fat content (in grams) and calories for a sample of granola bars.

Fat (in grams)                         Calories
7.6    . . . . . . . . . . . . . . . . . . . . . . .    370
3.3    . . . . . . . . . . . . . . . . . . . . . . . 106.1
18.7  . . . . . . . . . . . . . . . . . . . . . . . 312.4
3.8    . . . . . . . . . . . . . . . . . . . . . . . 113.1
5        . . . . . . . . . . . . . . . . . . . . . . . 117.8
5.5     . . . . . . . . . . . . . . . . . . . . . . . 131.9
7.2     . . . . . . . . . . . . . . . . . . . . . . . 140.6
6.1     . . . . . . . . . . . . . . . . . . . . . . . 118.8
4.6     . . . . . . . . . . . . . . . . . . . . . . . 124.4
3.9      . . . . . . . . . . . . . . . . . . . . . . . 105.1
6.1      . . . . . . . . . . . . . . . . . . . . . . .    136
4.8      . . . . . . . . . . . . . . . . . . . . . . .    124
4.4      . . . . . . . . . . . . . . . . . . . . . . . 119.3
7.7      . . . . . . . . . . . . . . . . . . . . . . . 192.6

a. Use technology to make a scatterplot of the data. Use fat as the independent variable (x) and calories as the dependent variable (y). Does there seem to be a linear trend to the data?

b. Compute the correlation coefficient and the regression equation, using fat as the independent variable and calories as the dependent variable.

c. What is the slope of the regression equation? Interpret the slope in the context of this problem.

d. What is the y-intercept of the regression equation? Interpret the y-intercept in the context of this problem or explain why it would be inappropriate to do so.

e. Find and interpret the coefficient of determination.

f. Use the regression equation to predict the calories in a granola bar containing 7 grams of fat.

g. Would it be appropriate to use the regression equation to predict the calories in a granola bar containing 25 grams of fat? If so, predict the number of calories in such a bar. If not, explain why it would be inappropriate to do so.

h. Looking at the scatterplot there is a granola bar in the sample that has an extremely high number of calories given the moderate amount of fat it contains. Remove its data from the sample and recalculate the correlation coefficient and regression equation. How did removing this unusual point change the value of r and the regression equation?