5 For a sample of eight bears researchers measured the dista

5. For a sample of eight bears, researchers measured the distances around the bears\' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is R=0.972 Using =0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

A.

Yes, because the absolute value of the test statistic exceeds the critical value of 0.707.

B.

No, because the absolute value of the test statistic exceeds the critical value of 0.707

C.

Yes, because the test statistic falls between the critical values of 0.707 and 0.707.

D.The answer cannot be determined from the given information

Solution

if we look at critical values of r we find 0.707 for df=8-2=6 and alpha=0.05, and since this R=0.972 exceeds positive 0.707, we reject null, option (A) is correct.

Also, variation explained = r^2 = 0.972^2 =0.944784