Bredahl, Maury E.

Mylander, Ann

English

Research Papers in Economics

Department of Agriculturaland AppliedEconomics
4
Staff Papers Series
Staff Paper P77-2 January 1977
THE ACCURACY OF REGRESSION PROGRAMS
UNIVERSHY OF MINNESOTA
by
Maury E. Bredahl and Ann Mylander
Universityof Minnesota
Institute of Agriculture, Forestryand Home Economics
St. Paul, Minnesota 55108THE ACCURACY OF REGRESSION PROGRAMS
UNIVERSITY OF MINNESOTA
Maury E. Bredahl and
A recent AJAE article compared the
produced by several regression packages
Menkhaus, and Penn. ] Erroneous results
Ann Mylander
accuracy of regression results
and computer systems [Boehn,
of large magnitude were
discovered prompting the authors to recommend
“Given the serious nature of the issue, perhaps the editor of
our journal should
from more than one
for publication.”
require authors to submit regression results
computer program prior to accepting papers
The accuracy test employed by Boehn et. al, was used to test the
accuracy of four computed programs used for economic research at the
University of Minnesota. By and large, accurate results were obtained
from the regression programs. However, an uninformed user of these
programs could very easily produce erroneous results. This paper
identifies key program parameters and options that researchers should
note in order to produce accurate results.
Multicolinearity. The referenced article suggests an exact speci-
fication of an equation (no random error) and highly correlated data.
The test equation is
Y=1+X+X2+X3+X4+ X5 (x =0, 1, 2,..., 20)The data constructed in this manner are highly correlated as evidenced
by the simple correlation coefficients given in Table 1.
Table 1. Simple Correlation Coefficients
X2 .971
x’ .922 .986
x’ .873 .960 .992
x’ .829 .929 .976 .995
x X2 x’ x’
Highly correlated data (price series for example) are often used in
estimation of supply or demand equations. As such, the ability of a
computer program to accurately compute regression coefficients and
associated standard errors is very important in agricultural economics
research.
Most often researchers examine the matrix of simple correlation
coefficients in order to identify multicolinearity. However, in many
cases, multicolinearity often involves several variables. Serious
multicolinearity results when an explanatory variable is an approximate
linear function of 2 or more other explanatory variables.
Regression packages which estimate regression equations in a step-
wise or forward selection procedure use measures of multicolinearity
as a criterion for including variables in the equation. Such computer
programs effectively regress each explanatory variable which is not
included in the equation on all explanatory variables already included
in the equation. The coefficient of determination (R2) is calculated,3
subtracted from one and the resultant value is termed the tolerance of
the excluded variable. The tolerance is a measure of the proportion
of the variation of an excluded explanatory variable not explained by
other variables in the equation. If the excluded explanatory variable
is orthogonal to (uncorrelated with) all included explanatory variables,
the tolerance would be 1. If, on the other hand, the excluded variable
is an exact linear combination of included variables, the tolerance
would be zero.
The stepwise or forward selection regression programs utilize an
arbitrary default value for the tolerance level for selecting variables
for an equation. If highly colinear data are being analyzed, that
arbitrary level may be exceeded and variables excluded from the
equation which should be included. Indeed, many of the erroneous
results reported in the referenced article we’re produced because the
tolerance level was violated and not because the regression programs
were inaccurate.
Accuracy of U of M Programs. Four U of M regression packages
were tested:
(1) ANALYZE (U of M Economics Dept.)
(2) SP22 (St. Paul Computer Center)
(3) BMD02R (Health Sciences Computing Center, UCLA)
(4) SPSS (Statistical Package for Social Sciences)
The computational methods used by each computer program are not discussed.
The estimated coefficients, standard errors, and standard error of the
estimates are given in Table 2.
The ANALYZE AND SP22 programs provided acceptable coefficient
estimates but standard errors and the estimated standard error of the4
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mestimate were not correct. The reported standard errors of the ANALYZE
program would have lead one to incorrect specification of the equation.
The SPSS and BMD02R program would give appropriate results if the
programs were used correctly. The BMD02R program utilizes a stepwise
regression procedure. If the default level for the tolerance is used,
erroneous results will be reported. The program excludes X3 from the
estimated equation because the tolerance level is violated, The correct
specification includes all variables. Therefore, estimated equations
which exclude a variable are necessarily incorrect. If the tolerance
level is decreased by the program user, correct results are obtained.
Much the same results are obtained from the SPSS computer program.
Unlike BMD02R, which automatically uses a stepwise procedure, SPSS
regressions may be run as exactly specified equations or in a stepwise
manner. If exact specification is used, the estimated coefficients and
standard errors are correct. If the optional stepwise procedure is
used, the tolerance level will be violated which excludes appropriate
variables and necessarily yields incorrect results.
Thus, the stepwise or forward selection regression packages should
be used sparingly in economic analysis. By and large, specification of
economic relationships should be based on theoretical considerations
and not on a “search” over a list of variables using stepwise or forward
selection procedures.
The ANALYZE and SP22 regression packages did not produce accept-
able estimated results. BMD02R produced correct results if the toler-
ance level was decreased. Because BMD02R always uses a stepwise regres-
sion procedure, errors due to default values of program parameters may6
consistently occur. The SPSS program produced correct estimates and
given the simplicity of program use would seem to be the regression
package to use for economic analysis at the U of M.References
Boehm, William T., D.,J.Menkhaus and J.B. Penn, Accuracy of Least Squares
Computer Programs: Another Reminder, A.J.A.E. , 58 (Nov., 1976), 7!;7-760.
Dixon, W.J., ed. BMD Biomedical Computer Programs. Health Sciences
Computing Center, University of California, Los Angeles, 1964.
Nie, Norman, D.H. Bent:and C.H. Hull, Statistical Package for Social
Sciences, New York: McGraw Hill Book Co., 1970.
Time Series Analyzer, Users Manual, mimeo, 1976.
University Computer Center, Statistical Package for the Social Sciences,
Version 6.0, University of Minnesota, August, 1975.

THE ACCURACY OF REGRESSION PROGRAMS: UNIVERSITY OF MINNESOTA

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