The following table shows the design matrix and response data for an experiment that studies the effect of two factors A and B on the response time (y) in a chemical process.

Run A B y

1 1 1 54

2.1 1 47

3.1 1 32

4 1 1 45

5.0 0 40

6 00 38

7 0 0 42

(a) Estimate the main effect of A.

(b) Estimate the AB interaction.

(c) Estimate the variance 2 .

(d) What are the pure error degrees of freedom?

(e) Is the AB interaction significant at 5% level? Show your work.

(f) Is the curvature effect significant at 5% level? Show your work.

Here is part of the t table showing the upper percentage points of the t distribution.

df 12 3 4 5 67 89 10

= 0.05 6.314 2.92 2.353 2.132 2.015 1.943 1.895 1.86 1.833. 1.812

= 0.025 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228