Multivariate Regression Analysis of the Criterion Variables of Zc in the Space of Mahalanobis Variables of M.

Milos Popovic, Hana Valkova, Veroljub Stankovic, Dragan Popovic, Evagelia Boli, Vladimir Savic, Jasna Popovic

Abstract


Multivariate regression analysis of the criterion variables of Zc in the space of Mahalanobis variables of M can be defined as a solution to the problem Mb = Zc + E|trag(EtE) = minimum. As MtM = I, the solution that is easily obtained by differentiating the function trag (EtE) is b = MtZc = Rrr-1/2Rrc and the matrix of partial regression coefficients is, in fact, a matrix of ordinary prod¬uct - moment coefficients of correlation between the regressors transformed into Ma¬halanobis form and criterion variables. Of course, therefore, the asymptotic variance of coefficients bjp of matrix b is simply sjp2 = (1 - bjp2)2n-1, and the tests of hypotheses H0jp: bjp* = 0 are clearly fjp = bjp2((n - 2)(1 - bjp2)-1), because under H0jp: bjp* = 0 variables fjp have Fisher-Snedecor F distribution with 1 and n2 degrees of freedom Regression functions are now defined by the operation Y = Mb with a matrix of covariances G = YtY = btb = RcrRrr-1Rrc,s the diagonal elements of the matrix r2 = (rp2) = diag G are normal coefficients of determination; and since ZctY = RcrRrr-1Rrc = G, then rp elements of r matrix are ordinary multiple correlation coefficients, and tests of hypotheses H0p: rp* = 0 are defined by the functions fp = (rp2(1 - rp2)-1)((n - m - 1) m-1), because under H0p: rp* = 0 functions fp have Fisher-Snedecor F distribution with m and nm1 degrees of freedom.

Keywords: /multivariate / regression / analysis / criterion /variables /


Full Text:

PDF

References


Blažević, S., Katić, R, & Popović, D. (2005). The effect of motor abilities on karate performance. Collegium antropologicum 30 (2), 327-333.

Boli, E., Popović, D., Simić, M. & Stanković, V. (1998). The differences in the motor abilities of young basketball and handball players. 6th International Congress on Physical education and Sport, Exercise & society supplement issue No. 20 (pp. 147), Komotini, Greece

Momirovic, K. and Popovic, D. (2003) Construction and application of taxonomic neural networks. (Monograph) Multidisciplinary Research Center, Faculty of Physical Education, Leposavic, Serbia

Popović, D. (1980) Research methodology in Physical education, University of Nis, Scientific Youth, Nis.

Popovic, D. (1993):Programs and subprograms for the analysis of quantitative modifications. (Monograph) Multidisciplinary Research Center, Faculty of Physical Education, Pristina, Serbia

Popović, D. (1987) Motoric Abilities Relations and The Estimate of Successfulness of the Execution of Judo Techniqes. Proceedings of Fisu Cesu conference universiade 1987. No 1 pp (258-261). Zagreb, (Yugoslavia)

Popovic, D., Toskic, D., Boli, E. (2001). Influence of systematic training ih judo on the alternation of motor abilities. 9th International Congress on Physical education and Sport, Exercise & society supplement issue No. 28 (pp. 570), Komotini, Greece

Popović, D., Boli, E., Malacko, J., Dragić, B., Toskić, D. & Stanković, V. (2002). Relationship between abilities dependant upon moving regulation and upon energetic regulation. In M. Koskolou, N. Geladas, V. Klissouras (Eds), 7th Annual Congress of the ECSS, (pp. 1173), vol 2, Athens, Greece.

Popovic, D., Boli, E., Popovic, M., Savic, V., Popovic, J. and Bojovic, M. (2016) Determination of Differences in Motor Dimensions between Judo and Karate Athletes, Journal of Sports Science 4 (2016) 170-174.

Stanković, V., & Popović, D. (2012). The relations between the motor and cognitive abilities of adolescent females. Facta Universitatis. Series: Physical Education and Sport, 10 (3), 211-219

Stanković, V. & Popović D. (2010). The structure of the latent variables of motor abbilities of handball players of various competitive rankings. 5th International congres „Sport, stress, adaptation”, Sport & nauka, izvanreden broi 2010, čast 1, (pg. 85-91), Sofia, Bulgaria


Refbacks

  • There are currently no refbacks.