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.