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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A researcher finds a correlation of r = 0.60 between salary and the number of years of education for a group of 40-year-old men. How much of the variance in salary is explained by the years of education?

To determine
Amount of variance in salary is explained due to years of education.

Answer

The amount of variance explained by years of education is 36%.

Explanation

Given info:

Correlation between salary and the number of years of education for a group of 40-year-old mean is r=0.60.

Calculation:

Coefficient of determination:

The coefficient of determination is the portion of the total variation in the dependent variable that is explained by variation in the independent variable.

Here, coefficient of determination r2 determines the amount of variance in salary explained due to years of education.

If r=0.60, then

r2=0.36=36%

Thus, r2=36%

Thus, variance is calculated as 0.36. Hence, 36% amount of variance in salary is explained due to years of education.

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