The data in Table B. 5 present the performance of a chemical process as a function of several controllable process variables.

a. Fit a multiple regression model relating $\mathrm{CO}_{2}$ product $(y)$ to total solvent $\left(x_{6}\right)$ and hydrogen consumption $\left(x_{7}\right)$.b. Test for significance of regression. Calculate $R^{2}$ and $R_{\text {Adj }}^{2}$.

c. Using $t$ tests determine the contribution of $x_{6}$ and $x_{7}$ to the model.

d. Construct $95 %$ CIs on $\beta_{6}$ and $\beta_{7}$.

e. Refit the model using only $x_{6}$ as the regressor. Test for significance of regression and calculate $R^{2}$ and $R_{\text {Adj. }}^{2}$. Discuss your findings. Based on these statistics, are you satisfied with this model?

f. Construct a $95 %$ CI on $\beta_{6}$ using the model you fit in part e. Compare the length of this CI to the length of the CI in part d. Does this tell you anything important about the contribution of $x_{7}$ to the model?

g. Compare the values of $M S_{\text {Res }}$ obtained for the two models you have fit (parts a and e). How did the $M S_{\text {Res }}$ change when you removed $x_{7}$ from the model? Does this tell you anything importaut about the contributiou of $x_{7}$ to the model?

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Run No. y X x2 x4 Xs X6 X7 36.98 5.1 400 51.37 4.24 1484.83 2227.25 2.06 11 12345678ODUCEMETER 13.74 26.4 400 72.33 30.87 289.94 434.90 1.33 10.08 23.8 400 71.44 33.01 320.79 481.19 0.97 8.53 46.4 400 79.15 44.61 164.76 24714 0.62 36.42 70 450 80.47 33.84 1097.26 1645.89 0.22 26.59 12.6 450 89.90 41.26 605.06 907.59 0.76 19.07 18.9 450 91.48 41.88 405.37 608.05 1.71 5.96 30.2 450 98.6 70.79 253.70 380.55 3.93 15.52 53.8 450 98.05 66.82 142.27 213.40 1.97 10 56.61 5.6 400 55.69 8.92 1362.24 2043.36 5.08 26.72 15.1 400 66.29 17.98 50765 761.48 0.60 20.80 20.3 400 58.94 17.79 377.60 566.40 0.90 6.99 48.4 400 74.74 33.94 158.05 237.08 0.63 45.93 5.8 425 63.71 11.95 130.66 1961.49 2.04 43.09 11.2 425 67.14 14.73 682.59 1023.89 1.57 15.79 27.9 425 77.65 34.49 274.20 411.30 2.38 21.60 5.1 450 67.22 14.48 1496.51 2244.77 0.32 35.19 11.7 450 81.48 29.69 652.43 978.64 0.44 19 26.14 16.7 450 83.88 26.33 458.42 687.62 8.82 20 8.60 24.8 450 89.38 37.98 312.25 468.28 0.02 21 11.63 24.9 450 79.77 25.66 307.08 460.62 1.72 22 9.59 39.5 450 87.93 22.36 193.61 290.42 1.88 23 4.42 29.0 450 79.50 21.52 155.96 233.95 1.43 24 38.89 5.5 460 72.73 17.86 1392.08 2088.12 1.35 25 11.19 11.5 450 77.88 25.20 663.09 994.63 1.61 26 75.62 5.2 470 75.50 8.66 1464.11 2196.17 4.78 27 36.03 10.6 470 83.15 22.39 720.07 1080.11 5.88