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A limnologist takes samples from a creek on several days and counts the numbers of flatworms in each sample. The data show a linear pattern with the summary statistics shown below:

- Mean creek temperature (°C) = 10.2
- Standard deviation = 2.8
- Mean number of flatworms = 37.6
- Standard deviation = 30.8
- Correlation coefficient (r) = -0.98

Find the equation of the least-squares regression line for predicting the number of flatworms from the creek temperature.

A. [tex]y = -2.8x + 37.6[/tex]
B. [tex]y = -30.8x + 10.2[/tex]
C. [tex]y = 2.8x + 37.6[/tex]
D. [tex]y = -0.98x + 37.6[/tex]

Answer :

Final answer:

The equation of the least-squares regression line for predicting the number of flatworms from the creek temperature is y = -10.71x + 145.28.

Explanation:

To find the equation of the least-squares regression line for predicting the number of flatworms from the creek temperature, we need to use the information given. The correlation coefficient (r) between creek temperature and the number of flatworms is -0.98, which indicates a strong negative linear relationship. The slope of the regression line is the product of the standard deviations of the number of flatworms and creek temperature divided by the product of their means. The slope is -0.98 * (30.8/2.8) = -10.71. The y-intercept of the regression line can be found by substituting the mean values of creek temperature and number of flatworms into the equation y = mx + b, where y is the mean number of flatworms, m is the slope, x is the mean creek temperature, and b is the y-intercept. Thus, the y-intercept is 37.6 - (-10.71 * 10.2) = 145.28. Therefore, the equation of the least-squares regression line is y = -10.71x + 145.28.

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