An article in Concrete Research ("Near SurfaceCharacteristics of Concrete: Intrinsic Permeablility," Vol. 41,1989), presented data on compressive strength x and intrinsicpermeability y of various concrete mixes and cures. Summaryquantities are n = 14, Σ yi =572, Σ = 23,530, Σ xi =43,Σ = 157.42, and Σxiyi= 1697.80. Assume thatthe two variables are related according to the simple linearregression model.
(a) Calculate the least squares estimates of the slope andintercept. Estimate . Graph the regression line.
(b) Use the equation of the fitted line to predict whatpermeability would be observed when the compressive strength is x =4.3.
(c) Give a point estimate of the mean permeability when compressivestrength 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 correspondingresidual.