Estimating the Variance of the Error Term in the Simple Linear Regression Model

We have seen how to estimate the beta parameters in the Simple Linear Regression model, but there is one more parameter in that model that needs to be estimated. That parameter is the variance of the error terms, and deriving that estimator is what we’re going to do in this lecture video.

Here is an outline of the topics covered in this video:

Quantify the Total Variability of the Response Variable
Partition the Total Variability of the Response Variable
Partition the Total Degrees of Freedom Available to Us
Quantify the Proportion of Variability in the Response Accounted for by the Fitted Model
Provide the Expected Values of the Sums of Squares
Define Mean Squares from the Sum of Squares and Find their Expected Values
Obtain an Unbiased Estimator of the Variance of the Model Error Term

Next lecture in this series:    • F Test of the Null Hypothesis that th...  
Previous lecture in this series:    • Sampling Distributions of the Least-S...  
First lecture in this series:    • Introduction to Linear Regression  

Here is the textbook we are using:
Title: "Introduction to Linear Regression Analysis 5th Edition"
Authors: Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining.
ISBN-13: 978-0470542811
ISBN-10: 0470542810
Link on Amazon: https://www.amazon.com/Introduction-R...

Software Packages Used:
Get access to SAS for free: https://www.sas.com/en_us/software/on...
Minitab: https://www.minitab.com/en-us/

Music Title: Urban Morning
Music Artist: Prigida
Music URL: https://tunetank.com/track/us/urban-m...

Timecodes

0:00 Introduction
0:19 Outline
1:20 Quantifying the Total Variability in the Response
3:00 Partitioning the Total Variability in the Response
10:24 Partitioning the Total Degrees of Freedom
13:55 Proportion of Variability in the Response Accounted for by the Fitted Model
15:09 Expected Values of the Sums of Squares
17:26 Mean Squares and their Expected Values
19:07 Summary
20:00 Funky Outro Music
21:27 Related Lecture Videos