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

$H_1$ :

$\rho\ne0$ .

$t=6.16$ ;

$P$ -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.