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A researcher wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the age X (in months) and decides to fit a least-squares regression line to the data with X as the explanatory variable and Y as the response variable. He computes the following quantities. r = correlation between X and Y = 0.9 J = mean of the values of X = 6.5 M = mean of the values of Y = 6.6 sJ = standard deviation of the values of X = 3.6 sM = standard deviation of the values of Y = 1.2 Find the slope of the least-squares line.
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Answer :

The slope of the least-squares line is 0.3

How to find the slope of the least-squares line?

Given:

r = correlation between X and Y = 0.9

J = mean of the values of X = 6.5

M = mean of the values of Y = 6.6

sJ = standard deviation of the values of X = 3.6

sM = standard deviation of the values of Y = 1.2

To find the slope of the least-squares line in this case, you can use the following formula:

Slope = r × (sM / sJ)

Substituting the given values for r, sJ, and sM:

Slope = 0.9 × (1.2 / 3.6) = 0.3

Thus, the slope of the least-squares line is 0.3. This tells you the rate at which the average weight of children changes as their age increases by one month

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