Many companies manufacture products that are at least partially produced using chemicals. 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 P10_39.xlsx contains data obtained from a designed experiment involving these variables. Note that the quality score can range from a minimum of 0 to a maximum of 100 for each product.
a. Estimate a multiple regression equation that includes the two given explanatory variables. What do the results in the ANOVA table indicate about this regression?
b. Use a partial F test with a 5% significance level to decide whether it is worthwhile to add second order terms (X21, X22 , and X1X2) to the regression equation in part a.
c. Which regression equation is the most appropriate one for modeling the quality of the product? Keep in mind that a good statistical model is usually parsimonious.