8. The last term on the right side of this equation can be interpreted 

 as expressing the variation in the data not explained by the regression model 

 (Equation A5 normalized with the total variation in the data). Thus, if the 

 regression model fits the data perfectly, the second term will be zero, and 

 r^ = 1 . It is also recognized that the coefficient of determination varies 

 between and 1 since the sum of squares of the difference between measured 

 and predicted values is normalized by the total variation. 



Use in Present Study 



9. In the data analysis conducted in this study, correlation and 

 regression techniques were extensively used to investigate dependencies and 

 establish empirical relationships between variables. A correlation analysis 

 was first carried out irrespective of physical dimensions to identify vari- 

 ables which had marked influence on the quantity being studied. From this 

 information on dependencies, supplemented by physical considerations, regres- 

 sion equations involving pertinent variables were derived, in most cases 

 consisting of dimensionless groups formed by the studied variables. 



10. In some cases, nonlinear equations were used to develop functional 

 relationships between variables when it was not possible to transform the 

 equations to a linear form. A special computer solution procedure was 

 developed to obtain the optimal parameter values for these cases. Even if it 

 was possible to transform some regression equations to linear form, results 

 from the original nonlinear equation were used if an appreciable difference in 

 the optimal parameter estimates occurred. Also, to evaluate the performance 

 of the numerical model, coefficients of determination based on the difference 

 between calculated values and measured values were frequently used. 



A4 



