Energy Project Financing : Resources and Strategies for Success

Appendix B 381

In the second case, where the model is used to estimate a particular
coefficient bk, the accuracy of the estimate is measured by the standard
error of the estimated coefficient. This standard error is also provided
by standard regression packages. The variance of the estimate ~ is the
expected value of

(b – b)^2 Eq. 4

where b is the true value of the coefficient, and b is the value esti-
mated by the regression. The standard error is the square root of the
variance.

Whether the quantity of interest is the predicted value of y or a par-
ticular coefficient bk, the accuracy measures provided by the standard
statistical formulas are valid characterizations of the uncertainty of the
estimate only if there are no important biases in the regression model.
Three statistical indices that can be used to evaluate regression
models are defined below (SAS 1990):

1. The Coefficient of Determination, R^2 (%):

R^2 = 1 –

Σ ypred,i– ydata,i^2

i = 1

n

Σ ydata– ydata,i^2

i = 1

n ×^1

Eq. 5

2. The Coefficient of Variation CV (%):

CV =

Σ ypred,i– ydata,i^2

i = 1

n

n – p

ydata ×^100 Eq. 6

3. The Mean Bias Error, MBE

MBE =

Σ ypred,i– ydata,i

i = 1

n

n – p

ydata ×^100 Eq. 7