# Thread: Easy simple regression model

1. ## Easy simple regression model

Let $Y_i=\beta_0+\beta_1X_i+\epsilon_i$

I want to show that $E[b_0]=\beta_0$, where $b_0$ is an estimate of $\beta_0$

$b_0=\overline{Y}-b_1\overline{X}$

$E[b_0]=E[\overline{Y}]-\overline{X}E[b_1]$

$E[b_0]=\beta_0+\overline{X}\beta_1-\overline{X}\beta_1$

$E[b_0]=\beta_0$

Is this valid?

2. Originally Posted by noob mathematician
Let $Y_i=\beta_0+\beta_1X_i+\epsilon_i$

I want to show that $E[b_0]=\beta_0$, where $b_0$ is an estimate of $\beta_0$

$b_0=\overline{Y}-b_1\overline{X}$

$E[b_0]=E[\overline{Y}]-\overline{X}E[b_1]$

$E[b_0]=\beta_0+\overline{X}\beta_1-\overline{X}\beta_1$

$E[b_0]=\beta_0$

Is this valid?
You have not provided enough context. As it is it looks like you have effectivly assumed the answer, or at least imported other assumptions without telling us what they are.

You say $b_0$ is an estimate, but you appear to have a specific extimator in mind.

CB