I have to pull through a regression on a set of probabilities (so values between 0 and 1). Those probabilities are related to a binary variable, which I have to forecast exactly.
My code basically uses a logit transformation to make the probability data "wider" and then calculate the betas and the forecasts (based on out-of-sample information); then it makes a logit transformation and gives 1 or 0 to the forecasts if their value is over or below 0.5.
The R squared and other performance measures tell me that the regression works fine for in-sample data but those forecast really tell me another story (they float around 0.52-0.55).
Has anybody got any suggestion about this problem or how to better my procedure?
P.S. I already tried logistic regression (always with the >0.5 classification method) but I obtained same results.