This paper introduces a new piecewise regression methodology
that can be used when linear regression fails to represent data.
Effort can be saved to determine the best non-linear model
shape using this methodology. Therefore, in this paper a
nonlinear relationship is introduced using only one independent
variable by a simple and direct way. The new approach depends
on dividing the data set into several groups and then estimating
the best line or segment for each group to perform a continuous
broken line. The locations of breakpoints are determined by
minimizing the sum of squared errors while the number of
segments is determined by maximizing the adjusted coefficient
of determination. The proposed approach can be used in many
transportation applications such as trip generation models,
zonal trip rates, nonlinear correlation coefficient, accident
modeling, and traffic characteristics models. The proposed
approach was tested against many practical examples and found
that it can describe most of the transportation relationships
properly and can decrease the number of variables used in the
transportation modeling process. The proposed approach can be
extended in the future to get the nonlinear relationship using
more than one independent variable to cover the rest of
transportation applications. |
