Concept explainers
Pass the ball: The following table lists the heights (inches) and weights (pounds) of 14 National Football League quarterbacks in the 2016 season.
- Compute the least-squares regression line for predicting weight from height.
- Is it possible to interpret the y-intercept? Explain.
- If two quarterbacks differ in height by two inches: by how much would you predict their weights to differ?
- Predict the of a quarterback who is 74.5 inches tall.
- Kirk Cousins is 75 inches tall and weighs 214 pounds. Does he weigh more or less than the weight predicted by the least-squares regression line?
a.
To find: The least-square regression line for the given data set.
Answer to Problem 23E
The least square regression line of the given data set is,
Explanation of Solution
Following table with the heights and the weights of the national football quarterbacks in the season
Name | Height | Weight |
Aaron Rogers | 77 | 230 |
Cam Newton | 77 | 244 |
Russell Wilson | 71 | 206 |
Andrew Luck | 76 | 234 |
Drew Brees | 72 | 209 |
Blake Bortles | 77 | 232 |
Ben Roethlisberger | 77 | 241 |
Philip Rivers | 77 | 228 |
Eli Manning | 76 | 225 |
Tyrod Taylor | 73 | 217 |
Jamies Winston | 76 | 231 |
Carson Palmer | 77 | 235 |
Kirk Cousins | 75 | 214 |
Tom Brady | 76 | 225 |
Calculation:
The least-square regression is given by the formula,
Where
The correlation coefficient is given by the formula,
Let
The correlation coefficient can be obtained by the following table.
Hence, the correlation coefficient is,
Then, the coefficient
Therefore,
Conclusion:
The least square regression line is found to be,
b.
To explain:The possibility to interpret the
Answer to Problem 23E
The
Explanation of Solution
The least-square regression line has been computed as
Considering the
The
Conclusion:
There is no chance to a weight be a negative value. Therefore, this
c.
To calculate:The difference in the weight of two players when their heights differ by two inches.
Answer to Problem 23E
The difference of weight is found to be
Explanation of Solution
The least-square regression line has been computed as
Calculation:
Let the height of the shorter payer be
Also, the weight of the taller player should be,
Simplifying the obtained weight,
Therefore, the difference of two weights should be,
Interpretation:
As the calculation above, the weight difference for two inches change in the height is found to be
d.
To find:The predicted weight of a player whose height is
Answer to Problem 23E
The weight of a player whose height is
Explanation of Solution
Calculation:
By the computed least-square regression line, we can calculate the predictions for the weights of the players by substituting their heights into the formula.
Here, the height is said to be
Conclusion:
The weight of a player whose height is
e.
To find:Whether theactual weight of this player is greater than the predicted weight or not.
Answer to Problem 23E
The player weighs less than the predicted weight.
Explanation of Solution
The player is
Calculation:
When the height is said to be
The predicted weight is found to be
Conclusion:
Since
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