Consider the simple linear regression model y = 50 + 10 x + e where e is NID (0, 16). Suppose that n = 2 0 pairs of observations are used to ? t this model

Generate 500 samples of 20 observations, drawing one observation for each level of x = 1 , 1.5, 2, . . . , 10 for each sample.

a. For each sample compute the least - squares estimates of the slope and intercept. Construct histograms of the sample values of ˆ ß 0 and ˆ ß 1. Discuss the shape of these histograms.

b. For each sample, compute an estimate of E ( y | x = 5). Construct a histogram of the estimates you obtained. Discuss the shape of the histogram.

c. For each sample, compute a 95% CI on the slope. How many of these intervals contain the true value ß 1 = 1 0? Is this what you would expect?

d. For each estimate of E ( y | x = 5) in part b, compute the 95% CI. How many of these intervals contain the true value of E ( y | x = 5) = 100? Is this what you would expect? Use R software.