Question 14.11: dentifying a Regression Model from Chiller Performance Map D......

The cooling capacity and the compressor power at full load are regressed against the two fluid temperatures whose variations represent the usual operating range of this chiller. The results of the regression models are summarized in Table 14.13.
The equations of the fitted model with coefficient of determination R² and standard error (SE):
\dot{Q}_{cool} = 16.247  –  0.128 \times T_{ch,out} + 0.4155 \times T_{cd,in}
with Adjusted R² = 99.2 % and SE = 0.118 tons

and
\dot{W}_{comp} = 4.7969 + 0.124 \times T_{ch,out} + 0.1306 \times T_{cd,in}
with Adjusted R² = 99.1 % and SE = 0.074 kW
Note that first-order linear models are excellent with very high R² values, and all terms being statistically signicant at the 95% condence level as indicated by the Student’s t-value and the associated  probability values. A convenient visual manner of evaluating how well these models have captured the data is to generate x–y plots as shown in Figure 14.24.
Comments
The reader may find it rather surprising that rstorder linear models have captured the performance map data so well, while the DOE model advocates a second-order polynomial. The data in Tables 14.4 and 14.5 were extracted from actual manufacturer catalogs with anonymity being maintained by not citing the manufacturer or the equipment model number. We strongly suspect that the data are not actual measured data but synthetic data generated from simulation models developed by the manufacturers themselves from in-house testing. This is a commonly adopted procedure, and some amount of discretion is warranted especially in cases where this could compromise the results of an analysis. Note that the DOE models described earlier and the associated model coefficients are based on actual experimental tests and are not based on synthetically generated data.