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Provide bias to regression model to reduce total cost of mistakes
I am running a linear regression model to predict a monetary sum. If I miss the target by more than 15% however there is a fine imposed which is dependent on the direction in which I miss my target. So if I underestimate values by 15% or more, I have to pay a €500 fine, if I overestimate values by 15% or more, I have to pay a €1000 fine. Currently my model correctly predcits 3/4ths of the database.
However I this leaves me with a significant cost, which is equally distributed on both predicting too high and predicting too low. I would like to modify the model to take this price differential into account to reduce the cost of the misses. This means I would rather undershoot than overshoot my target since that is cheaper.
Currently I have two columns generated, which define if I overshoot (true,False) or undershoot (true, false) the target by 15% or more. Is there any way I could do this? I know this will probably reduce the accuracy of the model, but getting total cost down is important from a business point of view.