Correcting the negative intercept in Linear Regression


Regression not speaking business well !

Often during Linear Regression modeling, we come across a negative intercept and it becomes quite difficult for us to explain the business sense of the same.

Suppose equation comes like :  Y = -100 + 23 (Media spend) + 13 (Discount)  ; in this case, client argues that the equation means that Sales would be  negative if there is no media spend and also discount is nil.

Doesn't make any sense, right ? How can we deal with such situation/equation ? Let me give you a tablet that can treat the model.


What is Intercept ?

In the equation of simple linear regression  >>  Y = mX + C, C is intercept. The only explanation that I consider to be perfect is " The value of Y @ X = 0".

But what is X can't be zero,  isn't the C unrealistic ? Yes, it is !

We generally don't bother about this in the modeling exercise as clients don't bother about equation. But these days people have got smart. So better be prepared.

Suggest me something !

In the situations, while your X can't be zero and your intercept is coming negative and you want to make it positive, Let me prescribe something ...

RX.

Instead of modeling Y on X, model it on X - Mean(X) ... so what would the new equation?

Y = m (X - mean(X)) + C

Now can you tell me, what is C ? Well, it is value of Y at X = mean(X), which is much more realistic scenario than X being 0. Also this trick ( with iterations) would help you treat the intercept to a positive horizon.



FYI !

Your model was not wrong while intercept was negative, it was only not much acceptable by business sense.


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