Econometric Theory/Inference

Inference is essentially the process of creating a hypothesis of the parameters that describe a population by testing the sample parameters (such as $$\hat \alpha$$ and $$\hat \beta$$) that we already have from a sample of the population.

For example, you have a sample of size N, and you have created a model that can be used to predict changes in the units of the sample. The parameters of this model would be estimates of the actual parameters (such as $$\alpha$$ and $$\beta$$) for the entire population. Inference is the process used to determine, statistically, what the parameters would be for the whole population.

There are two basic ways of checking estimates for the purposes of statistical inference
 * Interval estimation
 * Hypothesis testing

To successfully use these methods, one must know two things:
 * The probability distribution of the true parameter values ($$\alpha$$ and $$\beta$$) must be known.
 * The formulae used must use data that can be found in the sample data (we can't successfully use unknown parameters in a function).