For a sample of eight bears researchers measured the distanc

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 requals 0.862. Using alpha equals 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. Is there a linear correlation between chest size and weight?

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

B. Yes, 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 negative 0.707 and 0.707.

D. The answer cannot be determined from the given information.

b. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

Solution

Yes, there a linear correlation between chest size and weight. B. Yes, because the absolute value of the test statistic exceeds the critical value of 0.707 .

The proportion of the variation in weight can be explained by the linear relationship between weight and chest size is:0.862^2=0.743