Least Squares Regression Statistical Inference
Overview
When running an OLS regression, it is often useful to get an estimate of the likelihood that the results of the
regression are close to the true values. In particular, it is often useful to determine if a given coefficient is likely
to be different than zero.
This type of analysis utilizes the tools of
statistical inference
and
Hypothesis Testing to
provide confidence intervals around the calculated results.
Unfortunately, it is not possible to run a hypothesis test without making additional assumptions about the
distibution that created the dataset. The most common assumption is that
the model errors {% \epsilon %}
are normally distributed
(see
Normality assumption)
Statistics
The primary hypothesis tests run on an OLS regression are based on the following test statistics
- T-Statistic and P Value
- tests whether a single coefficient is non-zero
- F-Test
- tests whether at least one coefficient is non-zero
