THE FLORIDA STATE UNIVERSITY ARTS AND SCIENCES ...

where, M is the slope of the linear regression for the given linear regression and C is the
intercept.
If we consider the slope and the intercept as random variables we can then use the Monte
Carlo method to generate various sets of slopes and intercepts. Since there is a
relationship between all the slopes and intercepts for each subset we can generate various
‘M’ and then obtain ‘C’ based on ‘M’. The direct linear relationship between the slopes
and the intercepts of each class which can be expressed as
C = I - S * M
---- Equation 3.2
1
1
where I1 is the intercept and S1 is the slope once the individual slopes and intercepts of
each linear regression from a given database are plotted.
Substituting the value of C from Equation 3.2 in Equation 3.1 we obtain,
R dn
= M ∗ Oc − S ∗ M + I
---- Equation 3.3
1
1
Thus by generating several values of M we may obtain several possible values of Rdn for
a given value of OC. As long as the random sample set is large enough the mean of the
randomly generated denitrification rate will be representative of the population mean.
Hence by averaging out the values we could theoretically get a value that is close to the
actual value true of Rdn. While this may not necessarily give us an exact value of Rdn we
can still estimate a range within which the denitrification rate will occur.. In order to have
as much useful information as possible, all the generated denitrification rates can be
converted to a histogram and the range of the denitrification rate may provided,
accompanied with a probability of occurrence within the specified range.
The methodology may be summarized as follows
106