s/ = ^ ^ (Yi - y) (A4) 



1=1 

 in which 



s = covariance between x and y 

 n = number of values in the data set 

 Xj^, Yi = corresponding values from the data sets to be correlated 

 X, y = mean values for the respective data sets 

 s^ = variance of x 

 Sy = variance of y 



3. Values of the correlation coefficient are in the domain -1 < r < 1. 

 A value of r = 1 implies a perfect linear relationship between the studied 

 variables, r = -1 indicates an inverse linear dependence, and r = means no 

 linear dependence. 



Coefficient of Determination 



4. In regression analysis, the parameters of a chosen functional rela- 

 tionship are estimated in an optimal way to provide the best fit with the 

 measured data according to a predetermined criterion. The criterion typically 

 used to optimize the parameter values is a minimization of the sum of the 

 squares of the difference between predicted and measured values of the 

 dependent variable. For example, if y is considered a function of the m 

 variables x^, X2, . . . ,x„ , the parameters in the function y(x;^, X2, . . . ,x^) 

 should be estimated to minimize the function R , defined as: 



i=l 



yT) (A5) 



where 



yP = value predicted with a regression equation 

 y™ = measured value 



A2 



