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 R = 0.861. Using a = 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?

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

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

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

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

Number of bears is 8

The two variables are chest dimension of the bear and the weight of the bear

Linear correlation coefficient is 0.861 = R

Hence R²=0.7413

For option A I am unable to understand the question

Generally we test the hypothesis as

Null hypothesis = there exist linear relation ship beta=0

alternate hypothesis there does not exist linear relationship beta not equal to 0

Also there is no value of test statistics

B Hence 74% of the variation is explained by the chest dimension of the bear and the weight of the bear however 100-74=26% approximately cannot be explained.