# Linear regression and assets direction prediction

I have the following asset returns Y and the predictions for the same periods Y':

Y = { 10, 200, -1000, -1, -7 }
Y' = { 1, 2, -3, -4, -5 }


The OLR R-squared for these 2 vectors is 0.11 and the F-statistic 0.39, so clearly the explained variance is not very high. However variance analysis does not show that all the predicitions in Y' matched the same return direction than Y. To capture this point I would have to run a separate study counting each (Yn, Y'n) pair that has the same sign.

Are there better ways to fit a model and optimize the IVs coefficients for return direction? Ideally I would like to fit a model that gives more weigth to assets direction, then variance.

It sounds like all you need is to run a logistic regression, with the sign of $Y$ as your dependent variable instead of $Y$ itself. This will only give weight to the sign of the variable, and not to the magnitude. Once you have reformulated your question in more general terms (sign and magnitude of $Y$, rather than direction and volatility), you may be able to get further help from Cross Validated.