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 P14_41.xlsx contains data obtained from a carefully designed experiment involving these variables. Note that the assigned quality score can range from a minimum of 0 to a maximum of 100 for each manufactured product.
a. Estimate a multiple regression equation that includes the two given explanatory variables. Does the estimated equation fit the data well?
b. Add an interaction term between temperature and pressure (the product of these two variables) and run the regression again. Does the inclusion of the interaction term improve the model’s goodness of fit?
c. Interpret each of the estimated coefficients in the two equations. How are they different? How do you interpret the coefficient for the interaction term in the second equation?