Problem 2 Let r be the compressive strength and y be the intrinsic permeability of various concrete mixes and cures. Summary quantities are n = 15, Elly,- = 572, 2:21:13}? = 23,530, Ell-1:110 = 43, 2;, 32,2 = 157.42, and 2;, my, = 1697.80. Assume that the two variables are related according to the simple linear regression model. (a) Calculate the least squares estimates of the slope and intercept. (b) Use the equation of the tted line to predict what permeability would be observed when the compressive strength is a: = 4.3. (c) Give a point estimate of the mean permeability when compressive strength is at = 3.7. (d) Suppose that the observed value of permeability at a: = 3.7 is y = 46.1. Calculate the value of the corresponding residual. (e) Test for signicance of regression using or = 0.05. Find the Pvalue for this test. Can you conclude that the model species a useful linear relationship between these two variables? (f) Estimate 02 and the standard deviation of Bl. (g) What is the standard error of the intercept in this model