An article in Concrete Research [“Near Surface Characteristics of Concrete: Intrinsic Permeability” (1989, Vol. 41)] presented data on compressive strength x and intrinsic permeability y of various concrete mixes and cures. Summaryquantities are n = 14,Σy_i = 572, Σy_i² = 23,530,Σx_i = 43,  Σ x_i2 = 157.42, and Σx_iy_i = 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. 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.