For a sample of eight bears, researchers measured the distances around the bears

Question

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 0.947. 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. Is there a linear correlation between chest size and weight? 0 A. O B. No, 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 C. Yes, because the absolute value of the test statistic exceeds the critical value of 0.707 0 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? L (Round to three decimal places as needed.)

Explanation / Answer

The proportion of the variation in weight that can be explained by the linear relationship here is computed as:

= r2 = 0.9472 = 0.897

Therefore 0.897 is the required proportion here.

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