Question:
The data in Table SE6 (page 649) consist of yield measurements from many runs of a chemical reaction. The quantities varied were the temperature in ?C (x1), the concentration of the primary reactant in % (x2), and the duration of the reaction in hours (x3). The dependent variable (y) is the fraction converted to the desired product.
a. Fit the linear model y = β0 + β1x1 + β2x2 + β3x3 + ε.
b. Two of the variables in this model have coefficients significantly different from 0 at the 15% level. Fit a linear regression model containing these two variables.
c. Compute the product (interaction) of the two variables referred to in part (b). Fit the model that contains the two variables along with the interaction term.
d. Based on the results in parts (a) through (c), specify a model that appears to be good for predicting y from x1, x2, and x3.
e. Might it be possible to construct an equally good or better model in another way?
TABLE SE6 Data for Exercise 6
Transcribed Image Text:
y X1 X2 X3 y X1 X2 X3 y X1 X2 X3 50 19 4.0 27.464 70 27 10.0 38.241 70 31 6.0 35.091 90 38 8.0 49.303 80 32 6.5 34.635 60 23 7.0 34.372 70 28 6.5 37.461 50 26 9.0 44.963 50 19 6.0 26.481 70 25 5.5 36.478 50 22 4.0 30.012 60 22 7.5 36.739 60 41.077 9.5 26 29 6.5 33.776 80 34 6.5 70 30 36.185 21 70 60 5.0 35.092 50 10.0 41.964 70 25 8.0 38.725 23 5.5 31.307 80 34 7.5 44.152 50 17 9.5 32.707 70 28 5.5 37.863 60 22 2.5 29.901 70 28 7.0 32.563 80 70 70 34 6.5 41.109 60 24 5.0 26.706 60 25 5.5 5.5 5.0 36.006 60 60 28.605 26 26 4.5 8.0 23 29 70 70 4.0 28.602 33.401 25 29 33.127 32.941 35.917 6.5 70 26 8.0 33.489 70 27 7.5 41.324 70 29 6.5 33.650 60 30 5.0 31.381 70 32 4.0 24.000 50 19 4.5 34.192 25 26 60 26 7.0 38.067 60 5.5 38.158 60 24 6.5 24.115 70 70 25 7.5 31.278 7.5 37.614 60 70 3.5 25.412 60 60 26 31 5.5 32.172 28 7.5 37.671 28 6.0 29.612 60 27 7.5 36.109 60 22 5.5 27.979 60 22 6.5 39.106 60 23 6.0 31.535 60 22 4.5 31.079 60 28 7.5 36.974 60 23 6.0 33.875 60 27 7.0 30.778 60 25 4.0 28.334 60 24 9.0 37.637 60 25 6.0 28.221 50 20 8.5 33.767 70 31 5.5 40.263 60 23 6.5 30.495 60 26 9.5 38.358 80 32 6.0 36.694 60 27 7.5 38.710 60 25 4.0 33.381 60 26 10.0 45.620 80 31 4.5 27.581 60 29 4.0 37.672 70 28 4.5 38.571 80 36 4.5 38.705 70 30 6.0 36.615 60 24 4.0 19.163 60 22 7.5 40.525 60 26 8.0 39.351 31.962 23.147 50 21 7.0 70 28 4.5 29.420 60 24 6.5 38.611 50 17 2.0 60 26 7.0 37.898 60 25 6.0 36.460 80 34 8.5 40.278 60 25 7.0 40.340 60 24 5.5 23.449 70 27 5.5 32.725 60 24 5.0 27.891 60 24 5.0 23.027 60 24 2.5 28.735 70 32 7.5 38.259 70 26 8.0 31.372
