For a sample of eight bears researchers measured thedistance

For a sample of eight bears, researchers measured thedistances around the bears\' chests and weighed the bears. Minitab was used to find that the value of the linear correlationcoefficient is r=0.945. Using ?=0.05 determine if thereis a linear correlation between chest size and weight. Whatproportion of the variation in weight can be explained by thelinear relationship between weight and chest size?

1) is there a linear correlation between chest size andweight?

a) No, beacuse the absolute value of the test statistics exceed the crtical value of 0.707

b) Yes, becuase he absolute value of the test statistics exceed the critical value of 0.707

c) Yes, because the test statistics falls between -0.707 and 0.707

d) the answer can not be determined

2) what proportion of the variation in weight can be explainedby the linear relationship between weight and chest size?

Solution

From the table with n=8 and significance level 0.05, the critical value is 0.707 (degrees of freedom 6)
0.872 exceeds this value so the correlation is significant. There is a linear correlation between chest size and weight.

r^2 = (0.872)^2 = 0.7604

About 76% (or proportion of 0.76) of the variation in weight can be explained by the linear relationship between weight and chest size.