Regression Analysis (the Linear Least-Squares Methodology) - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 443

The denominator in the above equation ( n 2) represents the total number of degrees

of freedom excluding the two degrees of freedom already used up, namely the slope
and the intercept.

−

σ y is called the standard error of estimate .
The goodness of fit is ascertained in terms of the regression coefficient , which is
given by the following equation:

i y i , calcd −¯

y 2

r 2

= ,

i (y i −¯

y) 2

where y i , calcd is the value estimated from the regression equation, y i is the measured
value, and y is the mean of the measured values. In the case of an exact fit, r 2 will

be unity and will decrease in magnitude as the quality of the fit of the model to the
data diminishes. An r 2 of near zero indicates that the best estimate of the dependent
variable is not any better than the overall mean of the independent variable estimated
from the data. It is possible that a poor model can give a high r 2 and, alternatively, a
low r 2 can be displayed for a good model. Hence, the correlation coefficient should
only be taken as a general indicator of the goodness of the fit.

¯