A researcher is studying the relationship between the number of hours employees spend in professional training sessions per month (xx) and their job performance ratings (yy), scored out of 100100. A linear regression model is created to predict job performance based on training hours, and the resulting regression equation is y^=2.8x+65\hat{y}=2.8x+65. The researcher collects data from a sample of 1010 employees. Based on this data:Residual sum of squares (SSR): ∑(y−y^)2=82.4\sum (y - \hat{y}$$)^2 = 82.4$$Total sum of squares (SST): ∑(y−yˉ)2=240.0\sum (y - \bar{y}$$)^2 = 240.0$$What is the coefficient of determination $$r2r^2$$, and what does it tell us about the model?

r2=$$0.657r^2 = 0.657$$; 65.7%65.7\% of the variation in job performance is explained by training hours.

r2=$$0.343r^2 = 0.343$$; 34.3%34.3\% of the variation in job performance is explained by training hours.

r2=$$0.826r^2 = 0.826$$; 82.6%82.6\% of the variation in job performance is explained by training hours.

r2=$$0.286r^2 = 0.286$$; 28.6%28.6\% of the variation in training hours is explained by job performance.

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Problem 49Multiple Choice

A researcher is studying the relationship between the number of hours employees spend in professional training sessions per month ( $x$ ) and their job performance ratings ( $y$ ), scored out of $100$ . A linear regression model is created to predict job performance based on training hours, and the resulting regression equation is $\hat{y} = 2.8 x + 65$ . The researcher collects data from a sample of $10$ employees. Based on this data:
Residual sum of squares (SSR): $\sum (y - \hat{y})^{2} = 82.4$
Total sum of squares (SST): $\sum (y - \overset{ˉ}{y})^{2} = 240.0$
What is the coefficient of determination $r^{2}$ , and what does it tell us about the model?

$r squared equals 0.343$ ; $34.3 percent sign$ of the variation in job performance is explained by training hours.

$r squared equals 0.826$ ; $82.6 percent sign$ of the variation in job performance is explained by training hours.

$r squared equals 0.657$ ; $65.7 percent sign$ of the variation in job performance is explained by training hours.

$r squared equals 0.286$ ; $28.6 percent sign$ of the variation in training hours is explained by job performance.

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