Imagine you have a dataset of rower lap-times with several predictor variables, such as weight, benchpress, deadlift, squat, nutrition quality, etc.
Now, let's say for a given rower, you want to reduce her lap time, but you can only train along ONE DIMENSION. How would you identify the best predictor to optimize? Assume only 1 standard deviation of improvement is possible.
I'm trying to think beyond brute force methods, here. Which family of machine learning algorithms would be best for this type of problem, and how would you attack it?