Concept explainers
a.
Find the least-squares regression line to predict the weights from heights.
a.
Answer to Problem 23E
The least-squares regression line to predict the weights from heights is
Explanation of Solution
Calculation:
The heights (inches) and weights (pounds) for some quarterbacks at a Combine are given.
Denote the heights as x and the weights as y.
Least-squares regression:
For an ordered pairs of values of variables, (x, y) with respective means
Regression:
Software procedure:
Step by step procedure to obtain regression using Minitab software is given as,
- Choose Stat > Regression > Regression > Fit Regression Model.
- In Responses, enter the numeric column containing the response data y.
- In Continuous Predictors, enter the numeric column containing the predictor variable x.
- Choose Results, select Regression equation and click OK.
- Click OK.
Output using MINITAB software is given below:
From the output, the least-squares regression line for the data set is found to be
b.
Explain whether it is possible to give an interpretation of the y-intercept of the regression line.
b.
Answer to Problem 23E
It is not possible to give an interpretation of the y-intercept of the regression line.
Explanation of Solution
Calculation:
Comparing the least-squares regression equation,
The y-intercept would mean that when the height of a quarterback is
However, it is practically impossible for the height of a quarterback to be 0 inches. The height would always take some non-zero positive value.
Hence, it is not possible to give an interpretation of the y-intercept of the regression line.
c.
Find the predicted difference in the weights of two quarterbacks, if their heights differ by 2 inches.
c.
Answer to Problem 23E
The predicted difference in the weights of two quarterbacks, if their heights differ by 2 inches is 3.18 pounds.
Explanation of Solution
Interpretation:
It is known that when the predictor variable values differ by the amount d, the corresponding response variable values differ by amount
Here,
From part a, the least-squares regression equation is:
Comparing this equation with the general form of the regression equation,
Thus,
Hence, the predicted difference in the weights of two quarterbacks, if their heights differ by 2 inches is 3.18 pounds.
d.
Find the weight of a quarterback whose height is 74.5 inches.
d.
Answer to Problem 23E
The weight of a quarterback whose height is 74.5 inches is 225.755 pounds.
Explanation of Solution
Calculation:
From part a, the least-squares regression equation is:
For a quarterback whose height is 74.5 inches,
Hence, the weight of a quarterback whose height is 74.5 inches is 225.755 pounds.
e.
Find whether the actual weight of Geno Smith is more or less than his predicted weight.
e.
Answer to Problem 23E
The actual weight of Geno Smith is less than his predicted weight.
Explanation of Solution
Calculation:
The actual height of Geno Smith is 74 inches and his actual weight is 218 pounds.
For Geno Smith, height is 74 inches, that is,
It is observed that the predicted weight of Geno Smith is 224.96 pounds, which is greater than his actual weight of 218 pounds.
Hence, the actual weight of Geno Smith is less than his predicted weight.
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Chapter 11 Solutions
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