# Can a regression formula be Y=A - BX

I'm new to statistics and I ran into this question, what I know is $$Y=A + BX$$ but in the question the value of $$B$$ is negative, is it normal for the $$B$$ value to be negative?

Here is the question, you don't have to answer it, I just added as a reference.

Estimate the value of $$Y$$ when $$X = 30$$ for the following regression equation: $$Y = 6.2 - 1.4 X$$.

## 2 Answers

$$B = -1.4$$ for you: $$Y = 6.2 + (-1.4)X$$. What this means is that same as if it were $$+1.4$$: that for every one-unit change in $$X$$, there is a $$B$$-unit change in $$Y$$. In this particular case, the change is that, for every one-unit change in $$X$$, $$Y$$ decreases by $$1.4$$ units.

$$B<0$$ is certainly acceptable. Consider a relationship like expected snowfall tomorrow as $$Y$$ and today's temperature as $$X$$.

• Your snowfall-temperature example is wrong, apart from that relation being very nonlinear, consider temperature $-15^\circ\text{C}$, there will not be snowing. Increase temperature with 10 degrees, expected snowfall will increase! – kjetil b halvorsen Jul 30 '20 at 0:44

Yes you can have negative weights. The simplest example of when this would happen is when you have a factor that has a negative correlation to the output Y. This would imply for every X unit increase, there should be a corresponding B * X decrease in Y. In your example, for every unit increase of X, Y should decrease by a factor of 1.4