Regression through origin - closed form of slope estimator? [duplicate]

I am following up on discussion in this threat. I am interested in the case when we have a linear regression model through the origin $(0,0)$. $$y=\beta_1 x_1 + \epsilon.$$ How can the OLS slope estimator for $\beta$ be dervied and written in closed form?

• Please clarify a few things: In linear regression, one usually also has an error term. Is this the case here? Also, what estimator do you mean? The ordinary least squares estimator? Or any other? Or simply, any? One could estimate $\beta$ with a constant (say, 1) and that would be close form, but possibly not what you're after...
– Momo
Aug 18 '15 at 16:09
• Thanks, I made the edits to specify that there is an error term and that I mean an OLS estimator. I would be okay with an answer using a different (ML, WLS) estimator, but OLS seems fine for starters. In fact I am interested in the closed form solution for the simple linear regression model for which the Gauss Markov assumptions hold, but where the models does not have an intercept. Aug 18 '15 at 16:13
• I believe the answer you need is in the linked thread. Please read it. If you still have a question afterwards, come back here & edit your Q to state what you've learned & what you still need to know. Then we can provide the information you need without simply duplicating material elsewhere that already didn't help you. Aug 18 '15 at 16:15