Questions on Correlation Concepts

#1
Hypothetically, say that I've found that the score for some physical health test (T) is strongly correlated to the time I spend working out in a gym (X). Then I break down the predictors into "times spent on treadmill", "time spent doing yoga", etc. and denote them as X1, X2, X3, etc. If the new regression of T gives nearly zero coefficients for X1, X2, X3, how should I explain this?

I find this intuitively sense-making. But I can't come up with a good way to explain it in terms of correlation. Please help? Thanks!
 

JohnM

TS Contributor
#2
It could be that:

the individual activities are highly correlated with each other, or

on an individual basis are not good predictors, but when summed together, the combined time is a good predictor