48% HO +: 0 7. Refer to the Old Faithful data introduced in Homework 2 Problem 3 (data file oldfaith). (a) Use simple linear regression methodology to obtain a prediction equation for Interval from Duration. Explain your result in a way that might be useful for nontechnical personnel who staff the Old Faithful Visitor's Center. (b) Find a range of values that we can be 95% confident contains the true expected waiting time following an eruption that lasts 250 seconds. In other words, find a 95% confidence interval for E(Interval Duration = 250). (c) An individual has just arrived at the end of an eruption that lasted 250 seconds, and wants to know a range of values (times in minutes) they can be 95% confident contains the time they will have to wait until the next eruption. Is the interval computed in part (b) an appropriate thing to tell this person? Explain. 8. In this problem you will conduct a simulation analysis to study (a) the sampling distributions of least squares estimators, and (b) the coverage probability of confidence intervals. The following R code simulates 1000 replicated data sets, each of size n = 100, sampled from a population in which YIX = I ~ Normal(10 + 2x, 52) . For each simulated data set, the estimates Bo and B1 and ? are computed. The distributions of these estimates for the simulated data sets approximate the sampling distributions, which are known to be ~Normalz [( 3.). 02 Sex + 12 and (n -2)62 02 ~ x? ( df = n - 2) with / and 82 independent. n