An extension of a multiple regression prediction model to multiple response variables is presented. An algorithm using least sum of Euclidean distances between the multivariate observed and model-predicted response values provides regression coefficients, a measure of effect size, and inferential procedures for evaluating the extended multivariate multiple regression prediction model.
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References
1.
Anderson-SprecherR. (1994) Model comparisons and R2. The American Statistician, 48, 113–117.
2.
BerryK. J.MielkeP. W.Jr. (1998) Least sum of absolute deviations regression: Distance, leverage, and influence. Perceptual and Motor Skills, 86, 1063–1070.
3.
CohenJ.CohenP. (1975) Applied multiple regression/correlation analysis for the behavioral sciences. Hillsdale, NJ: Erlbaum.
4.
D'AndradeR.DartJ. (1990) The interpretation of r versus r2 or why percent of variance accounted for is a poor measure of size of effect. Journal of Quantitative Anthropology, 2, 47–59.
5.
DarlingtonR. B.WeinbergS. L.WalbergH. J. (1973) Canonical variate analysis and related techniques. Review of Educational Research, 43, 433–454.
6.
DraperN. R. (1984) The Box-Wetz criterion versus R2. Journal of the Royal Statistical Society, Series A, 147, 100–103.
7.
GraybillF. A.IyerH. K. (1994) Regression analysis: Concepts and applications. Belmont, CA: Duxbury.
8.
HahnG. J. (1973) The coefficient of determination exposed!Chemtech, 3, 609–612.
9.
HealyM. J. R. (1984) The use of R2 as a measure of goodness of fit. Journal of the Royal Statistical Society, Series A, 147, 608–609.
10.
KaufmanE. H.TaylorG. D.MielkeP. W.Jr.BerryK. J. (2002) An algorithm and Fortran program for multivariate LAD (l1 of l2) regression. Computing, 68, 275–287.
11.
KvålsethT. O. (1985) Cautionary note about R2. The American Statistician, 39, 279–285.
12.
MielkeP. W.Jr. (1987) L1, L2 and L3 regression models: Is there a difference?Journal of Statistical Planning and Inference, 13, 430.
13.
MielkeP. W.Jr.BerryK. J. (2001) Permutation methods: A distance function approach. New York: Springer-Verlag.
14.
MielkeP. W.Jr.BerryK. J. (2002a) Data dependent analyses in psychological research. Psychological Reports, 91, 1225–1234
15.
MielkeP. W.Jr.BerryK. J. (2002b) Multivariate multiple regression analyses: A permutation method for linear models. Psychological Reports, 91, 3–9. [Erratum. Psychological Reports, 91, 2.]
16.
OzerD. J. (1985) Correlation and the coefficient of determination. Psychological Bulletin, 97, 307–315.
17.
PedhazurE. J. (1997) Multiple regression in behavioral research: Explanation and prediction. (3rd ed.) New York: Harcourt.
18.
StevensJ. (1986) Applied multivariate statistics for the social sciences. Hillsdale, NJ: Erlbaum.
