MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![### Problem
The fish in my pond have a mean length of 10 inches with a standard deviation of 2 inches and a mean weight of 4 pounds with a standard deviation of 0.6 pounds. The correlation coefficient of length and weight is 0.9. If the length of a particular randomly selected fish is reported to be 15 inches, then what should we predict for the weight of that fish using simple linear regression?
### Options
- 5.35
- 2.52
- 6.55
- 2.5
- NONE OF THE OTHERS
### Explanation
To solve this problem, we can use the formula for the equation of the regression line:
\[ y = \bar{y} + r \cdot \frac{s_y}{s_x} \cdot (x - \bar{x}) \]
Where:
- \( x \) is the independent variable (fish length),
- \( \bar{x} \) is the mean of \( x \) (10 inches),
- \( s_x \) is the standard deviation of \( x \) (2 inches),
- \( y \) is the dependent variable (fish weight),
- \( \bar{y} \) is the mean of \( y \) (4 pounds),
- \( s_y \) is the standard deviation of \( y \) (0.6 pounds),
- \( r \) is the correlation coefficient (0.9).
Substitute the values into the equation to find the predicted weight of the fish.](https://content.bartleby.com/qna-images/question/03191458-7d30-4b7a-a32c-2a2b6b9a178c/7703d2ef-5bca-4c09-a264-23f18ff66d3b/i4epm3_processed.png)
Transcribed Image Text:### Problem
The fish in my pond have a mean length of 10 inches with a standard deviation of 2 inches and a mean weight of 4 pounds with a standard deviation of 0.6 pounds. The correlation coefficient of length and weight is 0.9. If the length of a particular randomly selected fish is reported to be 15 inches, then what should we predict for the weight of that fish using simple linear regression?
### Options
- 5.35
- 2.52
- 6.55
- 2.5
- NONE OF THE OTHERS
### Explanation
To solve this problem, we can use the formula for the equation of the regression line:
\[ y = \bar{y} + r \cdot \frac{s_y}{s_x} \cdot (x - \bar{x}) \]
Where:
- \( x \) is the independent variable (fish length),
- \( \bar{x} \) is the mean of \( x \) (10 inches),
- \( s_x \) is the standard deviation of \( x \) (2 inches),
- \( y \) is the dependent variable (fish weight),
- \( \bar{y} \) is the mean of \( y \) (4 pounds),
- \( s_y \) is the standard deviation of \( y \) (0.6 pounds),
- \( r \) is the correlation coefficient (0.9).
Substitute the values into the equation to find the predicted weight of the fish.
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