A Simple Regression Problem

Here's a regression problem for student readers of this blog.

Suppose that we estimate the following regression model by OLS:

                     y_i = α + β x_i + ε_i .

The model has a single regressor, x, and the point estimate of β turns out to be 10.0.

Now consider the "reverse regression", based on exactly the same data:

                    x_i = a + b y_i + u_i .

What can we say about the value of the OLS point estimate of b?

• It will be 0.1.
• It will be less than or equal to 0.1.
• It will be greater than or equal to 0.1.
• It's impossible to tell from the information supplied.

© 2013, David E. Giles

Thomas Bayes - 250 Years On

Two hundred and fifty years ago today a paper titled, "An Essay Towards Solving a Problem in the Doctrine of Chances", was presented to a meeting of the Royal Statistical Society in London. (Although, see here.)

The presenter - Richard Price. The author - (the late) Reverend Thomas Bayes.

Thus, we received "Bayes' Theorem".

A few days ago, the International Society for Bayesian Analysis held a celebratory conference to honour this momentous occasion in the history of statistical and scientific thinking.

Bayesian thinking has had a significant impact on the field of econometrics. My own Ph.D. dissertation (1975) was in Bayesian econometrics, and I was fortunate enough to have had Arnold Zellner as an external examiner.

I just wish I'd had access to the computational technology that's so freely available today!

© 2013, David E. Giles