# Regression Model Estimator

1. Feb 8, 2013

### mrkb80

1. The problem statement, all variables and given/known data
Assume regression model $y_i = \alpha + \beta x_i + \epsilon_i$ with $E[\epsilon_i] = 0, E[\epsilon^2] = \sigma^2, E[\epsilon_i \epsilon_j] = 0$ where $i \ne j$. Suppose that we are given data in deviations from sample means.

If we regress $(y_i-\bar{y})$ on $(x_i-\bar{x})$ without a constant term, what is the expected value of the least squares estimator of the slope coefficient?

2. Relevant equations

3. The attempt at a solution
I was thinking I could start with $S(\beta)=\Sigma (y_i-x_i \beta)^2$ and replace y and x with $(y_i-\bar{y})$ and $(x_i-\bar{x})$ and then take FOC to get the estimator.