Regression - finding alpha and beta

This one really has me stumped.

I have a variable X that can have the values of 0 and 1. I have a sample of n_{1} observations where X=0 and n_{2} observations where X=1. Ybar1 is the mean value for the n_{1 }observations where X=0; Ybar2 is the mean value of Y for the n_{2} observations where X=1. For the OLS regression: Y=alpha + betaX + e, I need to somehow find the values of alpha and beta in terms of n_{1} and n_{2}.

This is what I think I know:

When X=0, Ybar1 is 0 so Y=alpha in the n1 case.

When X=1, Ybar2 is 1 so Y=alpha+beta in the n2 case.

I asked for help from the professor and he wrote "You can show it with matrices or with the scalar version of the bivariate regression model. If you choose the latter, split your data and do the computations where n1 are the 1...n1 cases where X is coded as 0 and n1+1...n = n2 cases are the ones where X is coded as 1. You are basically splitting up the summation of the covariances and variances over these two subset so data cases", but I honestly do not know what any of that really means.

Re: Regression - finding alpha and beta

Hey drabbie.

Can you just state your model and the conditions for your model and if you are using categorical or contingent rules, please specify the nature of those rules.

Re: Regression - finding alpha and beta

Oh wow, I don't know what that means either :(

The model given to us was a simple bivariate regression: Y=alpha + betaX + e

Beyond that, all that was given was the n1 observations where X=0 and n2 observations where X=1. And to find alpha and beta in terms of n1 and n2.

Since I don't know what categorical or contingent rules are, I'm assuming there are none.

Re: Regression - finding alpha and beta

Recall that the mean of x = n2/(n1+n2).

Try looking at the formulas for point estimates of alpha and beta, and convert the expressions for the mean, variance and other attributes of x into terms involving n1 and n2 (I gave you a starting point with x_bar = n2/(n1+n2))