Percent Temp H2toHeptane Contact
49.0 1300 7.5 0.0120
50.2 1300 9.0 0.0120
50.5 1300 11.0 0.0115
48.5 1300 13.5 0.0130
47.5 1300 17.0 0.0135
44.5 1300 23.0 0.0120
28.0 1200 5.3 0.0400
31.5 1200 7.5 0.0380
34.5 1200 11.0 0.0320
35.0 1200 13.5 0.0260
38.0 1200 17.0 0.0340
38.5 1200 23.0 0.0410
15.0 1100 5.3 0.0840
17.0 1100 7.5 0.0980
20.5 1100 11.0 0.0920
29.5 1100 17.0 0.0860
Ok, this is a problem in ridge regression.
The context is that of a chemical plant seeking to
estimate the percentage of conversion of one
chemical substance, n-heptane, to another, acetylene.
16 runs were made at various settings of Temperature,
H2 to n-heptane ratio, and contact time (in sec).
First off,
we want to standardize the three X variables (Percent
is the Y). Then, we want to fit a quadratic model:
P = T + H + C + T:H + T:C + H:C + T^2 + H^2 + C^2.
Compute the variance inflation factors for all of the
terms in the model. Do these suggest collinearity?
Plot the various X variables versus one another
(Temp, H2toHeptane, Contact).
Do you see collinearity? Produce a ridge trace plot
for k ranging from 0 to 0.5. Pick a value at which the
betas appear to have stabilized. Produce contour plots
for the percent yield (P) over the range
Temp in [1050 1370]
Contact in [0.01 0.10]
H2toHeptane at 12.44
using
a) the OLS estimates
b) the ridge trace values.
Which do you think is a more accurate representation?