Question: Many companies manufacture products that are at least partially produced using chemicals (e.g. Paint, gasoline and steel). In many cases, the quality of the finished product is a function of the temperature and pressure at which the chemical reactions take place. Suppose that a particular manufacturer wants to model the quality (Y) of a product as a function of the temperature (X1) and the pressure (X2) at which it is produced. The file P11_30.xls contains data obtained from a carefully designed experiment involving these variables. Note that the assigned quality score can range from a maximum of 100 to a minimum of 0 for each manufactured product.

a. Formulate a multiple regression model that includes the two given explanatory variables. Estimate the model using the given sample data.

b. Interpret each of the estimated coefficients in the multiple regression model

c. Consider adding a term to model a possible interaction between the two explanatory models. Reformulate the model and estimate it again using the given data. Does the inclusion of the interaction term improve the model’s goodness of fit.

d. Interpret each of the estimated coefficients in the revised model. In particular, how do you interpret the coefficient for the interaction term in the revised model.