Many companies manufacture products that are at least partially produced using chemicals

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?

Product	Quality (Y)	Temperature (X1)	Pressure (X2)	X1 X2
1	71.3	90	60	5400
2	73.0	80	60	4800
3	70.9	90	60	5400
4	73.2	100	55	5500
5	97.4	90	55	4950
6	63.4	90	50	4500
7	69.8	100	55	5500
8	42.5	100	60	6000
9	61.6	90	50	4500
10	46.4	100	50	5000
11	71.2	80	60	4800
12	46.6	100	50	5000
13	72.5	100	55	5500
14	93.7	80	55	4400
15	49.1	100	50	5000
16	50.7	80	50	4000
17	38.7	100	60	6000
18	90.9	80	55	4400
19	74.5	80	60	4800
20	41.4	100	60	6000
21	93.8	90	55	4950
22	68.8	90	60	5400
23	63.4	90	50	4500
24	49.4	80	50	4000
25	50.8	80	50	4000
26	90.9	80	55	4400
27	92.1	90	55	4950

11 years ago

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many_companies_manufacture_products_that_are_at_least_partially_produced_using_chemicals.xlsx