Energy Project Financing : Resources and Strategies for Success

382 Energy Project Financing: Resources and Strategies for Success

where:

ydata, i data value of the dependent variable corresponding to
a particular set of the independent variables,

ypred, i predicted dependent variable value for the same set of
independent variables above,

ydata mean value of the dependent variable of the data set,

n number of data points in the data set.

p total number of regression parameters in the model.

Sampling Error—Sampling error refers to errors resulting from the fact
that a sample of units were observed rather than observing the entire
set of units under study. The simplest sampling situation is that of a
simple random sample. With this type of sample, a fixed number n of
units is selected at random from a total population of N units. Each unit
has the same probability n/N of being included in the sample. In this
case, the standard error of the estimated mean is given by:

SE y = –Nn

y 1 – y^2

i = 1Σ n – 1

n

⁄n

Eq. 8

For more complicated random samples, more complex formulas
apply for the standard error. In general, however, the standard error is
proportional to 1/√n). That is, increasing the sample size by a factor “f”
will reduce the standard error (improve the precision of the estimate)
by a factor of √f.

Combining Components of Uncertainty
If the savings (S) estimate is a sum of several independently esti-
mated components (C), then

S = C 1 + C 2 + C 3 + ... + Cp Eq. 9

the standard error of the estimate is given by