# 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.

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## 1 Answer

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.

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Yes, that's what I was suspecting with my partial understanding of logistic regression. But let's stretch my question a bit: what if I wanted to fit a model for different return targets rather than just an up or down outcome. Would I have to run a logistic regression for each target level and then compare each r-squared or are there SEMs that can solve for the best return target (in the variance sense) and direction? – Robert Kubrick Dec 20 '11 at 15:55
@RobertKubrick sounds like a discrete choice problem. You could create indicators for each relevant category and run multinomial logit. – Tal Fishman Dec 20 '11 at 15:57
It is, these questions have been a bit too beginner level for this site. Cross Validated is more open to beginners, I think. – Tal Fishman Dec 20 '11 at 16:03