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###### Statistics

1. (10 points) Trosset chapter 15.7 exercise 5.

Assume that the population of all sister-brother heights has a bivariate normal distribution and that the data in Table 14.4 were sampled from this distribution.(please see attached)

(a) Compute the sample coefficient of determination, the proportion of variation “explained” by simple linear regression.

(b) Let alpha =0.05.Do these data provide convincing evidence that knowing a sister's height (x)helps one predict her brother's height (y)?

(c) Construct a 0.90-level confidence interval for the slope of the population regression line for predicting y from x.

(d) Suppose that you are planning to conduct a more comprehensive study of sibling heights. Your goal is to better estimate the slope of the population regression line for predicting y from x. If you want to construct a 0.95-level confidence interval of length 0.1, then how many sister-brother pairs should you plan to observe?

If applicable use R language to solve the problem