Regression Analysis
Regression Analysis
Regression analysis is a statistical
technique that provides an equation
describing the nature of the relation
between two measured variables. In
simple regression, the equation predicts
the value of one of the variables (the
dependent variable, or “y”) on the basis
of the value of one other variable (the
independent variable, or “x”). In this
study, the dependent variables were the
median concentrations of sodium and
chloride in streams that supply water to
the Scituate Reservoir. The independent
variables were the densities of
Statemaintained and locally maintained
roads in the subbasins supplying
the streams. The simplest relation
between the two variables, that of a
straight line in which the value of the
dependent variable changes in linearproportion to a change in the value of
the independent variable, was assumed.
The resulting equation describes the
“bestfitting” straight line, in the sense
that the distances between the line and
each of the data points are minimized.
Simple regression analysis can also be used to measure the accuracy with
which the regression equation predicts values of the dependent variable
the basis of the value of the independent variable. This measure, known
as is the proportion of the variation in dependent variable that can be
accounted for by variations in the independent variable. For example,
an R2 of 0.62 for the equation relating median streamsodium concentration
to the density of Statemaintained roads in the subbasins supplying the
streams (fig. 4) indicates that 62 percent of the variation in sodium
concentration is accounted for by the variation in road density. A second
measure of the reliability of the regression equation is obtained by asking
whether or not the observed relation could have appeared by chance alone.
The pvalues presented in figures 46 give the probabilities that a linear
relation between the two variables could have arisen by chance. In all
cases, the probabilities are small (less than 0.01 percent) that the strong
positive relations between stream sodium and chloride concentrations and
the densities of Statemaintained roads are simply due to chance arrangements
of the data, whereas the probabilities that the observed relations involving
the two constituents and the densities of locally maintained roads are
due to chance are about 81 percent.
