The Well / Aquifer Model (Initial Test Results) - 20
Therefore, of the significant parameters measured in the first
series of tests, there is a total of 10 possible groupings of variables upon which
regression and correlation analysis can be performed. The regression, or estimation
of one variable (the dependent variable) on another (the independent variable), for
the 10 maximum combinations, is the subject of the following section. The degree of
relationship between the variables, or the indicator that tells how well the regression
equation describes or explains the relationship, is quantitatively measured using
correlation analysis.
For the variables in equation (32) only simple regression and
correlation was used. The purpose of the analyses was twofold:
- To verify existing known relationships (e.g.,
h vs V) and show that model analogy and test
procedures were valid.
- To establish new relationships by experimental observation and analysis which
could lead to better understanding the basic factors affecting well design.
Three types of simple regression were used to analyze the 25 test
results from the Santa Barbara and Silverado aquifers:
These three equations were fit to the observed test data using the
method of Least Squares. In order to quantitatively measure the degree of explained
or unexplained variations between the variables, the correlation coefficient (r) was
calculated, namely:
or
where:
Yest = estimated value of dependent variable.
= mean value = 
Y/N
Y = actual or measured value as obtained from test data
N = number of observations
From equation (35), the unexplained variation can be derived to be
The following analysis consists of calculations of simple regression
and correlation for all the variables of equation (32) as well as the unexplained
variation.
Back |
R & D Home |
Next