An article in Concrete Research [“Near Surface

Chapter 11, Problem 3E

(choose chapter or problem)

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

                                                     \(n=14, \sum y_{i}=572, \sum y_{i}^{2}=23.530, \sum x_{i}=43\),

                                                        \(\sum x_{i}^{2}=157.42\), and \(\sum x_{i} y_{i}=1697.80\).

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. Estimate \(\sigma^{2}\), 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.

Equation Transcription:

Text Transcription:

x

y

n=14,sum y_i=572,sum y_i ^2=23.530,sum x_i=43

Sum x_i ^2=157.42

Sum x_i y_i=1697.80

Sigma ^2

x=4.3

x=3.7

x=3.7

y=46.1