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.

$\backslash$table$[[$Factors$,$Response,Factor Levels$],[$A$,B,C,D,$Molecular Weight,$A,(C),100,120],[-,-,-,-,2400,B(\%),4,8],[+,-,-||,-,2410,C(min),20,30],[-,+,-,-,2315,D,(),60,75],[+,+,-,-,2510,,,],[-,-,+,-,2615,,,],[+,-,+,-,2625,,,],[-,+,+,-,2400,,,],[+,+,+,-,2750,,,],[-,-,-,+,2400,,,],[+,-,-,+,2390,,,],[-,+,-,+,2300,,,],[+,+,-,+,2520,,,],[-,-,+,+,2625,,,],[+,-,+,+,2630,,,],[-,+,+,+,2500,,,],[+,+,+,+,2710,,,]]$

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

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