In many fast-food restaurants, there is a strong correlation
between a menu item's fat content (measured in grams) and its
calorie content. Using all of the food menu items at a well-known
fast food restaurant, the fat content and calorie content were
measured. We decide to fit the least-squares regression line to the
data, with fat content (x, in grams) as the
explanatory variable and calorie content (y, in calories)
as the response variable. A summary of the data is provided
below:
r= 0.979 (correlation between x and y)
b= 11.36 (slope of the least square regression line)
a= 204.50 (intercept of the least square line)
Determine whether each of the following statements is true or
false (explain why either true or false):
a) 97.9% of the variation is explained by the regression
model
b) 95.8% of the response variable can be explained by the
explanatory variable
c) when there are 0 grams of fat, there will be approximately
204.5 calories