Reference: Ref 5-2 In many fast food restaurants, there is a strong correlation

Question

Reference: Ref 5-2

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 (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)

Reference: Ref 5-2

Refer to the example data point (107 grams, 1410 calories). What is the residual corresponding to this observation? A. 10 calories (wrong) B. 10 grams C. 10 grams D. 10 calories 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) x= 40.35 (mean of the values of x) y= 662.88 calories (mean of the values of y) sx= 27.99 grams (standard deviation of the values of x) sy= 324.90 calories (standard deviation of the values of y) Reference: Ref 5-2 Refer to the example data point (107 grams, 1410 calories). What is the residual corresponding to this observation?

Explanation / Answer

First we need to find the least squares regression equation.

the slope of the equation = r*sy/sx

slope = 0.979*324.90/27.99

slope = 11.364

intercept of equation = ybar - slope*xbar

intercept = 662.88 - 11.364*40.35

intercept = 204.343

equation:

yhat = 11.364*x + 204.343

Now that we have the regression equation, we can put in the x value of 107 to get the predicted y value, yhat

yhat = 11.364*107 + 204.343

yhat = 1420

Then to find the residual:

residual = observed y - predicted y

residual = 1410 calories - 1420 calories

residual = -10 calories

answer: D -10 calories

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