This bachelor's thesis is based on real-life data that was gathered from tests of members of Slovenian representative 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 tissue, 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 a good model 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.