An article in Concrete Research presented data on compressive strength x and intrinsic permeability y of various concrete mixes and cures. Summary quantities are n = 14, Σ y i = 572, = 23,530, Σ x i =...

An article in
Concrete Research
presented data on compressive strength
x
and intrinsic permeability
y
of various concrete mixes and cures. Summary quantities are
n
= 14, Σy

_i
= 572,
= 23,530, Σx

_i
= 43,
= 157.42, and Σx

_i

y

_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.

(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.