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- From: Mathematics, Statistics and Probability
- Posted on: Thu 21 Jan, 2016
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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
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