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: ρ0. 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.