For a sample of eight bears, researchers measured the distance around the bears\

Question

For a sample of eight bears, researchers measured the distance around the bears' chests and weighted the bears. Minitab was used to find that the value of the linear correlation coefficient is r = 0.771. Using alpha = 0.05 determine if there is a linear correlation between chest size an 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. Yes, because the absolute value of the test statistic exceeds the critical value of 0.707. B. Yes, because the test statistic falls between the critical values of -0.707 and 0.707 C. No, because the absolute value of the test statistic exceeds the critical value of 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?

Explanation / Answer

Here critical value of r will be calculated by critical value of t for dF = 8-2 =6 and significance level = 0.05

t6,0.05 = 2.447

so as formula,

r = t/ sqrt [n-2 +t2] = 2.447/ sqrt (6 + 2.4472) = 2.447/ sqrt(11.9878) = 0.707

OPtion b is correct.Because, the test statistic falls between the critical values of -0.707 and 0.707.

(B) R- square R2 = (0.771)2 = 0.5944

so , there are 59.444% of the variation in weight can be explained by the linear relationship between weight and chest size.

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