# Beta - Cov(x,y)/Var(x) or SC(x,y)/SS(x)

#### nosit

##### New Member
Hello everyone,

Recently I am trying to understand formulas more in depth instead of just knowing them by heart.

When deriving the least squares estimators, which is Y=B0 +B1X, the B1 equals:

Σ (Xi - Xbar) (Yi-Ybar)/Σ (Xi - Xbar)^2

The thing is that this is apparently not Cov(x,y)/Var(x) because numerator and denominator are not being divided by "n-1" or simply by "n".

Therefore, why it is said Beta equals Cov(x,y)/Var(x) and not Sum of Cross products / Sum of Squares, aka SC(x,y)/SS(x)?

#### katxt

##### Active Member
Try sticking some n's in. two under the top and two under the bottom. You'll find it the same.

#### Dason

The good ol "multiply by 1" trick strikes again.

#### katxt

##### Active Member
Yes. I was a bit enthusiastic with n's perhaps. Only 1 needed at each level.

#### nosit

##### New Member
But when I start solving for B1, it starts in this way:

/B1 Σ (Yi - (B0 + B1.Xi))=0

So there is no "n" there, could you please explain me how do I add an "n" in a way that it makes sense?