Question

you generate a scatter plot using excel. you then have excel plot the trend line and report the equation and the $r^{2}$ value. the regression equation is reported as $hat{y}=-96.75x + 94.17$ and the $r^{2}=0.5776$. what is the correlation coefficient for this data set? (round to two decimals if needed.)

Explanation:

Step1: Recall the relationship between $r^2$ and $r$

The coefficient of determination $r^{2}$ is the square of the correlation coefficient $r$. So, $r=\pm\sqrt{r^{2}}$.

Step2: Determine the sign of $r$

The slope of the regression line $\hat{y}=-96.75x + 94.17$ is negative. When the slope of the regression line is negative, the correlation coefficient $r$ is negative.

Step3: Calculate $r$

Given $r^{2}=0.5776$, then $r =-\sqrt{0.5776}\approx - 0.76$.

Answer:

$-0.76$