The concentration of $\mathrm{NbOCl}_{3}$ in a tube-flow reactor as a function of several controllable variables is shown in Table B.6.

a. Fit a multiple regression model relating concentration of $\mathrm{NbOCl}_{3}(y)$ to concentration of $\mathrm{COCl}_{2},\left(x_{1}\right)$ and mole fraction $\left(x_{4}\right)$.

b. Test for significance of regression.

c. Calculate $R^{2}$ and $R_{\text {Adj }}^{2}$ for this model.

d. Using $t$ tests, determine the contribution of $x_{1}$ and $x_{4}$ to the model. Are both regressors $x_{1}$ and $x_{4}$ necessary?

e. Is multicollinearity a potential concern in this model?

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Run No. y X2 x4 1234567890123AAKERA 0.000450 0.0105 90.9 0.0164 0.0177 0.000450 0.0110 84.6 0.0165 0.0172 0.000473 0.0106 88.9 0.0164 0.0157 0.000507 0.0116 488.7 0.0187 0.0082 0.000457 0.0121 454.4 0.0187 0.0070 0.000452 0.0123 439.2 0.0187 0.0065 0.000453 0.0122 447.1 0.0186 0.0071 0.000426 0.0122 451.6 0.0187 0.0062 0.001215 0.0123 4878 0.0192 0.0153 0.001256 0.0122 467.6 0.0192 0.0129 0.001145 0.0094 95.4 0.0163 0.0354 0.001085 0.0100 87.1 0.0162 0.0342 0.001066 0.0101 82.7 0.0162 0.0323 0.001111 0.0099 87.0 0.0163 0.0337 0.001364 0.0110 516.4 0.0190 0.0161 0.001254 0.0117 488.0 0.0189 0.0149 0.001396 0.0110 534.5 0.0189 0.0163 0.001575 0.0104 542.3 0.0189 0.0164 0.001615 0.0067 98.8 0.0163 0.0379 20 0.001733 0.0066 84.8 0.0162 0.0360 21 0.002753 0.0044 69.6 0.0163 0.0327 22 0.003186 0.0073 436.9 0.0189 0.0263 23 0.003227 0.0078 406.3 0.0192 0.0200 24 0.003469 0.0067 447.9 0.0192 0.0197 25 0.001911 0.0091 58.5 0.0164 0.0331 26 0.002588 0.0079 394.3 0.0177 0.0674 27 0.002635 0.0068 461.0 0.0174 0.0770 28 0.002725 0.0065 469.2 0.0173 0.0780