Question

The coefficient of absorption (COA) for a clay brick is the ratio of the amount of cold water to the amount of boiling water that the brick will absorb. An article presents measurements of the (COA) and the pore volume (in cm³/g) for seven bricks. The results are presented in the following table

Pore Volume	COA
1.750	0.8
1.632	0.78
1.594	0.77
1.623	0.75
1.495	0.71
1.465	0.66
1.28	0.63

a. Compute the least-squares line for predicting COA from pore volume. Round the answers to three decimal places

Y= 0.103+0.404X (already got and checked this)

b.Compute the error standard deviation estimate s. Round the answer to four decimal places

c. Compute a 95% confidence interval for the slope. Round the answers to three decimal places

d. Find a 95% confidence interval for the mean COA for bricks with pore volume 1.5 cm³/g. Round the answers to three decimal places

e. Find a 95% prediction interval for the COA of a particular brick whose pore volume is 1.5 cm³/g. Round the answers to three decimal places.

Answer 1

a,b] Regression Analysis: COA versus Pore volume

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.0216328 90.52% 88.63% 82.12%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 0.1035 0.0908 1.14 0.306
Pore volume 0.4037 0.0584 6.91 0.001 1.00

Regression Equation

COA = 0.1035 + 0.4037 Pore volume

c,d,e]

95% confidence interval for the slope

Lower 95.0%	Upper 95.0%
0.254	0.554

Prediction for COA

Regression Equation

COA = 0.1035 + 0.4037 Pore volume

Variable Setting
Pore volume 1.5

Fit SE Fit 95% CI 95% PI
0.709021 0.0086521 (0.687, 0.731) (0.649, 0.770)