An experiment was conducted on a chemical process that produces a polymer. The four factors studied were temperature $(A),$ catalyst concentration $(B),$ time $(C),$ and pressure $(D).$ The response is the molecular weight of the polymer. The design matrix and response data are shown in the following table

a$)$ Estimate the main and two factor interaction effects. Which main effects and two$-$factor iteractions appear important?

b$)$ Write down a reggression model to predict molecular weight as a function of the important variables.