Question

question number 8. suppose you find that the correlation coefficient for a set of data is 0.835. what is the coefficient of determination and what does it mean? o 0.835; this means that 83.5% of the variation of y is explained by the lsrl of y on x. o 0.697; this means that 69.7% of the variation of y is explained by the lsrl of y on x. o 0.697; this means that we are 69.7% accurate with our prediction of the lsrl equation. o 0.835; this means that we are 83.5% accurate with our prediction of the lsrl equation. o none of the above

Explanation:

Step1: Recall coefficient of determination formula

The coefficient of determination $R^{2}$ is the square of the correlation coefficient $r$. Given $r = 0.835$, then $R^{2}=r^{2}$.

Step2: Calculate $R^{2}$

$R^{2}=(0.835)^{2}= 0.697225\approx0.697$. The coefficient of determination represents the proportion of the variance in the dependent - variable ($y$) that is predictable from the independent - variable ($x$). In other words, it means that 69.7% of the variation of $y$ is explained by the least - squares regression line (LSRL) of $y$ on $x$.

Answer:

0.697; This means that 69.7% of the variation of y is explained by the LSRL of y on x.