# Condition Number in Single Variable Regression

I've calculated a single variable linear regression using OLS (in the python statsmodels library).

The model has a large condition number, and suggests there may be multicollinearity.

I don't understand how there can be multicollinearity in a single variable model (unless it is multicollinearity the intercept, I guess implying too many of my data points are equal to 1?).

Either way, my understanding of condition numbers, especially as they pertain to regression models, is fuzzy, and wikipedia seems rather blank on the subject.

• Try centering your independent variable $x$, and see what happens the condition number. Since you just have a two-dimensional design, the condition number will be closely related the to dot product of $\mathbf{x} \mathbf{1} = \sum x$. How does that change when you center $x$? Nov 14, 2014 at 0:46
• @AndrewM If I saw something along those lines as an answer, I'd upvote it. Nov 14, 2014 at 2:56

Answered in comments: Try centering your independent variable $x$, and see what happens the condition number. Since you just have a two-dimensional design, the condition number will be closely related the to dot product of $\mathbf{x} \mathbf{1} = \sum x$. How does that change when you center $x$? – Andrew M