Here's a regression problem for student readers of this blog.
Suppose that we estimate the following regression model by OLS:
yi = α + β xi + εi .
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:
xi = a + b yi + ui .
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