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. summary quantities are n = 14,
∑yi=572,∑y2i=23,530,∑xi=43,∑x2i=157 .42and∑xiyi=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.