380 Energy Project Financing: Resources and Strategies for Success
- assigning incorrect values for “known” factors.
- extrapolation of the model results outside their range of validity.
Non systematic errors are the random effects of factors not accounted
for by the model variables.
The most common models are linear regressions of the form
y = b 0 + b 1 x 1 + b 2 x 2 + ... + bp xp + e
Eq. 2
where:
y and xk, k = 1, 2, 3,..., p observed variables
bk, k = 0, 1, 2,..., p coefficients estimated by the regression
e residual error not accounted for by the
regression equation
Models of this type can be used in two ways:
- To estimate the value of y for a given set of x values. An impor-
tant example of this application is the use of a model estimated
from data for a particular year or portion of a year to estimate
consumption for a normal year. - To estimate one or more of the individual coefficients bk.
In the first case, where the model is used to predict the value of y
given the values of the xks, the accuracy of the estimate is measured by
the oot mean squared error r (RMSE) of the predicted mean. This accuracy
measure is provided by most standard regression packages. The MSE
of prediction is the expected value of:
(y|x – y|x)^2 Eq. 3
where y|x is the true mean value of y at the given value of x, and
y|x is the value estimated by the fitted regression line. The RMSE
of prediction is the square root of the MSE.