A Numerical Exploration of Transient Decay Mechanisms in Water Distribution Systems - Advances in Control and Automation of Water Systems - page 8

• Linear regression is used to model the value of a dependent scale variable based
on its linear relationship to one or more predictors.
• Nonlinear regression is appropriate when the relationship between the depen-
dent and independent variables is not intrinsically linear.
• Binary logistic regression is most useful in modeling of the event probability for
a categorical response variable with two outcomes.

The Auto regression procedure is an extension of ordinary least-squares re-
gression analysis specifically designed for time series. One of the assumptions
underlying ordinary least-squares regression is the absence of autocorrelation in
the model residuals. Time series, however, often exhibit first-order autocorrelation
of the residuals. In the presence of auto correlated residuals, the linear regression
procedure gives inaccurate estimates of how much of the series variability is ac-
counted for by the chosen predictors. This can adversely affect your choice of
predictors and hence the validity of your model. The auto regression procedure
accounts for first-order auto correlated residuals and provide reliable estimates
of both goodness-of-fit measures and significance levels of chosen predictor vari-
ables.

tABle 1.6 Regression Model Summary and Parameter Estimates Excluded Variables (Water
hammer condition).

Model Beta In t Sig. Partial Correlation Co- linearity Statistics

Tolerance

2 time .117(a) 1.574 .133 .348 .887

3 time .122(b) .552 .587 .122 1.000

flow .905(b) 9.517 .000 .905 1.000

distance -.913(b) -10.033 .000 -.913 1.000

4 time .189(c) 2.274 .035 .463 .995

flow .469(c) 3.533 .002 .630 .298

5 time .117(a) 1.574 .133 .348 .887

a Predictors in the Model: (Constant), distance, flow
b Predictor: (constant)
c Predictors in the Model: (Constant), distance
d Dependent Variable: pressure