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?