Regersijski modeli v biatlonu

Članek je raziskovalne narave. S pomočjo testiranj slovenske reprezentance biatloncev in tekačev na smučeh so predstavljeni različni modeli, izdelani v programskem jeziku R. Izdelava modelov temelji na teoriji mešanih linearnih modelov in uporabi treh metod - metode najmanjših kvadratov, navadne in restringirane metode največjega verjetja. Za preverjanje ustreznosti modelov so uporabljene različne mere, kot najpomembnejši pa je upoštevan determinacijski koeficient multiple regresije. Poudarek je na napovedi maksimalne porabe kisika tekmovalcev, kjer se kot statistično značilne spremenljivke izkažejo mišičje, višina in starost testirancev. Model tekmovalne uspešnosti je predstavljen zgolj kot zanimivost, saj bi bilo za zanesljive sklepe potrebno pridobiti veliko več podatkov. Na podlagi podatkov, pridobljenih iz 24-ih minut testiranja na tekoči preprogi se da pojasniti več kot 80% variabilnosti v doseženem času testiranja, maksimalni vrednosti ventilacije, porabe kisika in srčnega utripa. Vse dobljene modele bi se dalo izboljšati z večjo skupino testirancev.

Regression models in biathlon

This article is based on real-life data that was gathered from tests of members of Slovenian national teams of biathletes and cross country skiers. We presented different kinds of models which were implemented in programming language R. Most of the time we employ Gaussian linear mixed models. Estimations were made with three different types of methods - least squares method, maximum likelihood method, and restricted maximum likelihood method. For testing goodness of fit of the investigated models we use different measures, most importantly the coefficient of determination. The emphasis is on prediction of the maximum rate of oxygen consumption. We find that muscular mass, height, and age of a competitor are statistically important covariates for this prediction. The model of competitive success is presented only as an interesting fact. For accurate findings much more data should be available. From results gathered from 24 minutes of measuring on the treadmill we can explain over 80% of variability of maximum testing time, maximum ventilation, maximum rate of oxygen consumption, and maximum heart rate. All models could be improved with more tests and participants.