An engineer studied the effect of four variables on a dimensionless factor used to describe pressure drops in a screen-plate bubble column. Table B. 9 summarizes the experimental results.

a. Fit a multiple linear regression model relating this dimensionless number to these regressors.

b. Test for significance of regression. What conclusions can you draw?

c. Use $t$ tests to assess the contribution of each regressor to the model. Discuss your findings.

d. Calculate $R^{2}$ and $R_{\text {Adj }}^{2}$ for this model. Compare these values to the $R^{2}$ and $R_{\text {Adj }}^{2}$ for the multiple linear regression model relating the dimensionless number to $x_{2}$ and $x_{3}$. Discuss your results.

e. Find a $99 %$ CI for the regression coefficient for $x_{2}$ for both models in part d. Discuss any differences.

Transcribed Image Text:

x X2 X3 X4 y 2.14 10 034 1 28.9 4.14 10 0.34 1 31 8.15 10 0.34 1 26.4 2.14 10 0.34 0.246 27.2 4.14 10 0.34 0.379 26.1 8.15 10 0.34 0.474 23.2 2.14 10 0.34 0.141 19.7 4.14 10 0.34 0.234 22.1 8.15 10 0.34 0.311 22.8 2.14 10 0.34 0.076 29.2 4.14 10 0.34 0.132 23.6 8.15 10 0.34 0.184 23.6 2.14 2.63 0.34 0.679 24.2 4.14 2.63 0.34 0.804 22.1 8.15 2.63 0.34 0.89 20.9 2.14 2.63 0.34 0.514 17.6 4.14 2.63 0.34 0.672 15.7 8.15 2.63 0.34 0.801 15.8 2.14 2.63 0.34 0.346 14 4.14 2.63 0.34 0.506 17.1 8.15 2.63 0.34 0.669 18.3 2.14 2.63 0.34 1 33.8 4.14 2.63 0.34 1 31.7 8.15 2.63 0.34 1 28.1 5.6 1.25 0.34 0.848 18.1 5.6 1.25 0.34 0.737 16.5 5.6 1.25 0.34 0.651 15.4 5.6 1.25 0.34 0.554 15 4.3 2.63 0.34 0.748 19.1 4.3 2.63 0.34 0.682 16.2 4.3 2.63 0.34 0.524 16.3 4.3 2.63 0.34 0.472 15.8 4.3 2.63 0.34 0.398 15.4 5.6 1.25 0.34 0.554 15 4.3 2.63 0.34 0.748 19.1 4.3 2.63 0.34 0.682 16.2 4.3 2.63 0.34 0.524 16.3 4.3 2.63 0.34 0.472 15.8 4.3 2.63 0.34 0.398 15.4 5.6 10.1 0.25 0.789 19.2 5.6 10.1 0.25 0.677 8.4 5.6 10.1 0.25 0.59 15 5.6 10.1 0.25 0.523 12 5.6 10.1 0.34 0.789 21.9 5.6 10.1 0.34 0.677 21.3 5.6 10.1 0.34 0.59 21.6 5.6 10.1 0.34 0.523 19.8 4.3 10.1 0.34 0.741 21.6 4.3 10.1 0.34 0.617 17.3 4.3 10.1 0.34 0.524 20 4.3 10.1 0.34 0.457 18.6 2.4 10.1 0.34 0.615 22.1 2.4 10.1 0.34 0.473 14.7 2.4 10.1 0.34 0.381 15.8 2.4 10.1 0.34 0.32 13.2 5.6 10.1 0.55 0.789 30.8 5.6 10.1 0.55 0.677 27.5 5.6 10.1 0.55 0.59 25.2 5.6 10.1 0.55 0.523 22.8 2.14 112 0.34 0.68 41.7 4.14 112 0.34 0.803 33.7 8.15 112 0.34 0.889 29.7 2.14 112 0.34 0.514 41.8 4.14 112 0.34 0.672 37.1 8.15 112 0.34 0.801 40.1 2.14 112 0.34 0.306 42.7 4.14 112 0.34 0.506 48.6 8.15 112 0.34 0.668 42.4