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. Summary quantities are n = 14, Σyi = 572, g = 23,530, Σxi = 43, Σx2/i 157.42, and Σxtyt = 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 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.