Question

the regression of price on size of homes had r² = 31.6%. answer the questions below. a) what is the correlation between size and price? r = (round to three decimal places as needed.)

Explanation:

Step1: Recall the relationship between $R^{2}$ and correlation coefficient $r$.

The relationship is $R^{2}=r^{2}$. Given $R^{2} = 0.316$.

Step2: Solve for $r$.

We have $r=\pm\sqrt{R^{2}}=\pm\sqrt{0.316}$. Since the sign of the correlation (positive or negative) is not given by $R^{2}$ alone, and in the context of price - size relationship of homes, we assume a positive correlation (larger homes usually cost more). So $r=\sqrt{0.316}\approx0.562$.

Answer:

$0.562$