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. R2=0.8812=77.6%.
About 77.6% of the variation in punting distance
can be explained by the variation in right-leg strength.
2. H0: ρ=0 and H1: ρ≠0.
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=−√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=−√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.