Picture two cyclists tested at multiple speeds, each under perfectly still conditions and while holding perfectly constant power on perfectly level ground. Also assume that the model is perfect, i.e., within a given individual the R^2 between modeled and predicted power is 1.00. Finally, assume that one cyclist is much heavier and less aerodynamic than the other. In this scenario:
1) the within-run variation in power is zero (assumed);
2) the between-run variation in power at a single speed is zero (corollary from first assumptions in first sentence);
3) R^2 between modeled and predicted power when you pool all of the data is less than 1.00.
IOW, as I said before the answer that you are seeking cannot be determined from the regression analysis, because the latter was performed by pooling averaged data across individuals.
1) the within-run variation in power is zero (assumed);
2) the between-run variation in power at a single speed is zero (corollary from first assumptions in first sentence);
3) R^2 between modeled and predicted power when you pool all of the data is less than 1.00.
IOW, as I said before the answer that you are seeking cannot be determined from the regression analysis, because the latter was performed by pooling averaged data across individuals.
Last edited by:
Andrew Coggan: Sep 7, 18 12:53