# Question: Many companies manufacture products that are at least partially produced

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.

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.

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