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 $H_1$: $\rho \ne 0$. $t=6.16$; $P$-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 35.5: 1. $b_0$: When someone spends no time on sunscreen application, an average of 0.27g has been applied; nonsense. $b_1$: Each extra minute spent on application adds an average of 2.21g of sunscreen: sensible. 2. The value of ${\beta }_0$ could be zero… which would make sense. 3. $\hat{y}=0.27+(2.21\times 8)=17.95$; an average of about 18g. 4. About 64% of the variation in sunscreen amount applied can be explained by the variation in the time spent on application. 5. $r=\sqrt{0.64}=0.8$, and need a positive value of $r$. A strong and positive correlation between the variables.