Introduction to Econometrics
Chapter 5 : Inference in the linear regression model with one explanatory variable
By Lund University
Inference means something like "a conclusion reached on the basis of evidence and reasoning". We now know how to estimate the parameters of the linear regression model (with one explanatory variable). However, these estimates are uncertain. In this section, we see what conclusions we can draw from all of this. But first, we must investigate a few more distributions (in addition to the normal distribution).
Some distributions
In order to prepare for the final section of this chapter, the section dealing with inference in the linear regression model, we need to discuss a couple of families of random variables. Specifically, we will look at the chi-square distribution, the t-distribution, and the F distribution and we will also look at the concept critical value.
The chi-square distribution
The t-distribution
The F-distribution
Critical values
Inference in the linear regression model
this section is an introduction to inference in the linear regression model. We will begin by looking at hypothesis testing as a general idea in statistics followed by hypothesis testing in the linear regression model. In this section we will only look at the t-test where we test if one of the unknown parameters is equal to some given value. Hypothesis testing is closely related to confidence intervals and we will look at confidence intervals for the beta parameters of the linear regression model.