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ŠUMARSKI LIST 10-11/1974 str. 17     <-- 17 -->        PDF

Summary


EXAMPLE FOR ELECTRONIC DATA PROCESSING BY THE METHOD
OF STEPWISE REGRESSION


During 1970 were taken measurements of some characteristics in the progeny
test of European Larch on the experimental plot »Goić« near Jastrebarsko. Data
of measurement served as a material for the computation and finding of a multiple
linear equation as suitable as possible, using various working techniques in
the method of multiple stepwise regression. As a dependent variable (y) the height
of tree is used, and as independent variables (x) the following characteristics:
diameter b. h., number of branches per 1 m of length, diameter of the thickest
branch in the mid-crown, length of the thickest branch, diameter in the mid-
crown, insertion angle of branches and straightness of the stem. All computations
were performed on an IBM-computer of the Institute for Statistics, North Carorolina
University at Raleigh, USA, in 1971. In finding out the most favourable
linear equation by the method of multiple stepwise regression the following working
techniques were used: forward selection, backward elimination, stepwise,
maximum R-square improvement and minimum R-square improvement.


The method of multiple stepwise regression gave a very good insight into the
relations between the dependent variables and the independent ones, and into
the mutual relations within the independent variables (correlation coefficients).
Although this method is complicated when a great number of independent variables
are included into the model, the computations are much easier than when
the method of all possible regression equations is used. The number of combinations
in this method amounts to 2n. What working technique to use in applying
the method of multiple gradual regression is best lo leave to the user, for all of
them have their advantages and drawbacks. However, it ought to be stated that
in applying by means of the maximal and minimal determination coefficient (R4)
almost always the same equation should be selected.


In conclusion, it should be stated that the aim of this paper is to present
certain possibilities for using modern electronic systems in data processing by
means of methods of multiple regression, in the selection of the necessary number
of independent variables, disregarding the theoretical consideration of the problem
itself.