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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 content were measured. We decide to fit the least-squares regression line to the data, with fat content ( x) as the explanatory variable and calorie content ( 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 117 grams of fat and 1520 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) ​ Refer to the example data point (117 grams, 1520 calories). What is the residual corresponding to this observation?   a. –14 calories   b. –4 calories   c. –10 calories   d. 4 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 content were measured. We decide to fit the least-squares regression line to the data, with fat content ( x) as the explanatory variable and calorie content ( 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 117 grams of fat and 1520 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) ​ Refer to the example data point (117 grams, 1520 calories). What is the residual corresponding to this observation?   a. –14 calories   b. –4 calories   c. –10 calories   d. 4 calories

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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  1. 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 content were measured. We decide to fit the least-squares regression line to the data, with fat content ( x) as the explanatory variable and calorie content ( 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 117 grams of fat and 1520 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)

    ​

    Refer to the example data point (117 grams, 1520 calories). What is the residual corresponding to this observation?

      a.
    –14 calories
      b.
    –4 calories
      c.
    –10 calories
      d.
    4 calories
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