I've been given the simple linear regression model:

$y_i = β_0 + β_1x_i + ε_i$

Under the assumptions of a simple linear regression model, the question they ask is:

Assuming the usual model assumptions hold, show that the least squares and maximum likelihood estimators of $(β_0 β_1)'$ coincide

What I can't seem to comprehend is the $(β_0 β_1)'$ part. I've never seen this before.

Can anyone explain what $(β_0 β_1)'$ means?

Also, how would this proof of LS and MLE differ from the usual $β_0$ and $β_1$ calculations?

Note. I'm not asking for the proofs, I simply want to understand what they are trying to ask.

  • 4
    $\begingroup$ I expect it's a formatting typo, and the intention is $(β_0, β_1)'$ (equivalently $(β_0\;\; β_1)^T$)- which denotes the transpose of the row vector $(β_0, β_1)$ -- that is a column vector, consisting of those two elements. $\endgroup$
    – Glen_b
    Commented Mar 12, 2014 at 23:13
  • $\begingroup$ Thanks, this makes a lot of sense now. I'm still trying to comprehend how to go about this solution, but with the "," in place, the question is much clearer now. $\endgroup$
    – Joe
    Commented Mar 12, 2014 at 23:25

1 Answer 1


They mean the vector with the intercept and the slope coefficients (not one multiplied by the other).

You need to show that the solution to minimizing the OLS objective function (sum of squared residuals) is numerically equivalent to the MLE one with normally distributed errors.


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