An article in Concrete Research ("Near Surface Characteristics of Concrete: Intrinsic," Permeability Vol. 41, 1989) presented data on compressive strength x and intrinsic permeability y of various concrete mixes and cures. The following data are consistent with those reported. ∑yi = 572, ∑y2i = 23,530, ∑xi= 43, ∑x2i= 157.42 and ∑ xiy i= 1697.80

Assume that the two variables are related according to the simple linear regression model.

Required:
a. Calculate the least squares estimates of the slope and intercept. Estimate σ². Graph the regression line.
b. Use the equation of the fitted line to predict what permeability would be observed when the compressive strength is x = 4.3.
c. Give a point estimate of the mean permeability when compressive strength is x = 3.7.
d. Suppose that the observed value of permeability at x = 3.7 is y = 46.1. Calculate the value of the corresponding residual.