A chemical engineer is investigating how the amount of conversion of a product from a raw material (y) depends on reaction temperature (x1) and the reaction time (x2). He has developed the following regression models:

1. y= 100+2(x1)+4(x2)

2. y= 95+1.5(x1)+3(x2)+2(x1x2)

Both models have been built over the range 0.5<=x2<=10.

a) What is the predicted value of conversion when x2=2? Repeat this calculation for x2=8. Draw a graph of the predicted values for both conversion models. Comment on the effect of the ineraction term in model 2.

b) Find the expected change in the mean conversion for a unit change in the mean conversion for a unit change in temperature x1 for model 1 when x2=5. Does this quantity depend on the specific value of reaction time selected? Why?

c) Find the expected change in the mean conversion for a unit change in temperature x1 for model 2 when x2=5. Repeat this calculation for x2=2 and x2=8. Does the result depend on the value selected for x2? Why?