in many fast food restaurants, there is a strong correlation between a menu item
ID: 3441240 • Letter: I
Question
in many fast food restaurants, there is a strong correlation between a menu item's fat content (measured in grams) and its calorie content. We want to investigate this relationship. Using all of the food menu items at a well-known fast food restaurant, the fat content and calorie contents were measured. We decide to fit the least-squares regression line to the data, with fat content (x) as the explanatory variable and (y) as the response variable. A scatterplot of the data (with regression line included) and a summary of the data are provided. One of the menu items is a hamburger with 107 grams of fat and 1410 calories.
r = 0.979 (correlation between x and y)
= 40.35 grams (mean of the values of x)
= 662.88 calories (mean of the values of y)
= 27.99 grams (standard deviation of the values of x)
= 324.90 calories (standard deviation of the values of y)
The intercept of the least-squares regression line is:
Explanation / Answer
As we can see in the graph, the line intersected the y axis somewhere between 0 and 500, but nearer to 0 than 500.
Among the choices, it must be that the answer is
OPTION D: 204.50 [ANSWER]
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