D.31 Answers: Correlation
Answers to exercises in Sect. 34.8.
Answer to Exercise 34.1:
Many correct answers.
Answer to Exercise 34.2:
1. \(R^2 = 0.881^2 = 77.6\)%.
About 77.6% of the variation in punting distance
can be explained by the variation in right-leg strength.
2. \(H_0\): \(\rho=0\) and \(H_1\): \(\rho\ne0\).
\(P\)-value very small.
Very strong evidence of a correlation in the population.
Answer to Exercise 34.3:
The plot looks linear; \(n = 25\);
variation doesn’t seem constant.
Answer to Exercise 34.4:
1. Very close to \(-1\).
2. \(r = -\sqrt{0.9929} = -0.9964\). (\(r\) must be negative!)
3. Very small. This is a very large value for \(r\) on a reasonable sized sample.
4. Yes.
Answer to Exercise 34.5:
1. Close to \(-1\), but not super close.
2. \(r = -\sqrt{0.6707} = -0.819\). (\(r\) must be negative!)
3. Very small. This is a large value for \(r\) on a reasonable sized sample.
(The \(P\)-value turns out to be 0.000104.)
4. Since \(n < 25\), the test may not be statistically valid.