In a chemical engineering experiment dealing with heat

Chapter 12, Problem 12.65

(choose chapter or problem)

In a chemical engineering experiment dealing with heat transfer in a shallow fluidized bed, data are collected on the following four regressor variables: fluidizing gas flow rate, lb/hr (\(x_1\)); supernatant gas flow rate, lb/hr (\(x_2\)); supernatant gas inlet nozzle opening, millimeters (\(x_3\)); and supernatant gas inlet temperature, \(^{\circ}F\) (\(x_4\)). The responses measured are heat transfer efficiency (\(y_1\)) and thermal efficiency (\(y_2\)). The data are as follows:

Consider the model for predicting the heat transfer coefficient response

\(y_{1i} = \beta_0+\sum _{j=1} ^4 \beta_j x_{ji}+\sum _{i=1} ^4 \beta_{jj}x^2 _{ji} +\sum \sum _{j \neq 1} \beta_{jl}x_{ji}x_{li}+ \epsilon_i,\ \ \ \ i = 1,\ 2,\ .\ .\ .\ ,\ 20.\)

(a) Compute PRESS and \(\sum _{i=1} ^n |\ y_i - \hat y_{i,\ - i}\ |\) for the least squares regression fit to the model above.

(b) Fit a second-order model with \(x_4\) completely eliminated (i.e., deleting all terms involving \(x_4\)). Compute the prediction criteria for the reduced model. Comment on the appropriateness of \(x_4\) for prediction of the heat transfer coefficient.

(c) Repeat parts (a) and (b) for thermal efficiency.