Simple Linear Regression: Checking Assumptions with Residual Plots

An investigation of the normality, constant variance, and linearity assumptions of the simple linear regression model through residual plots.

The pain-empathy data is estimated from a figure given in:

Singer et al. (2004). Empathy for pain involves the affective but not sensory components of pain. Science, 303:1157--1162.

The Janka hardness-density data is found in:

Hand, D.J., Daly, F. , Lunn, A.D., McConway, K., and Ostrowski, E., editors (1994). The Handbook of Small Data Sets. Chapman & Hall, London.

Original source: Williams, E.J. (1959). Regression Analysis. John Wiley & Sons, New York. Page 43, Table 3.7.

[l]

I'M GIVIN THIS VIDEO THE BIG CHECK MARK

[plzrjmh]

this was posted 11 years ago T-T and has the best explanations and videos on statistics I have ever found, thank you so much for all your hard work and legacy, i hope you know you're my savior.

[jbstatistics]

"think you guys should get more views..."

Thanks! (And I'll take as a compliment that you said "you guys", since this is a one man show.) Getting lots of views isn't very high on my priority list -- I'm just trying to provide the best resources for my students that I can. (I haven't done any promotion, and I don't allow ads on the videos.)

There are many students in intro stats in North America and around the world, and I'm glad that some of them find my videos helpful.

[nkululekoshabane]

One of the best, if not the best, video on regression analysis I've seen. Thank you very much for creating it. Your service is highly appreciated.

[GuppyPal]

This is exactly what I have needed. My professor goes over these plots but has been doing statistics at a high level so long that I think it's hard for him to relate to someone who is new to it. I really needed someone to just explain it all from start to finish, and you did that. Thank you so much! Your videos are so, so helpful. Sincerely, a first year statistics graduate student.

[doodelay]

"The residual plot removes that increasing trend and then re-scales the y axis, so it's a little bit easier to see these issues.. sometimes in the residual plot." Now that is some serious insight. Thank you so much and this video was superb with really excellent examples!

[jbstatistics]

I'm glad you find them useful John. Best of luck in your course!

[raseshgupta]

I was struggling to understand the assumptions in simple linear regression through other sources. This video has made it clear

[valeriereid]

Thank you for this excellent lecture. It certainly helps.

[snakeb]

Excellent methods used to help students learn in this vid. This is the future of education!

[jbstatistics]

We often simply rely on an appropriate sampling design or experimental design to ensure independence. But if, say, we have recorded the observations in some sort of time order, then plots of the residuals through time can give us some indication of whether the residuals are correlated.

[Maha_s]

Prof Balka knocks it out of the park every time! We miss your videos. Could you do some videos on multiple linear regression? Hope you come back soon with new vids!

[deniskapliy]

Small...and then they're big...and then they're small...and then they're big..

Great video, pretty simplistic, but very useful, thank you!

[vasili]

Very good videos about simple linear regression. Thank you very much for creating them!

[shayd]

JB thank you so much you have helped me more than you'll ever know! My only suggestion to you would be to create playlists for associated topics. Other than that your teaching methods are incredible! Thanks!

[johncasey]

I'm so fricking glad these videos align well with my UIUC stats class. Much appreciated!

[hichamitani]

Thank you
Need more like these videos on outliers in residuals

[muhammadusama]

The more I watch your video, the more I hate my uni. Much love man

[hritwick]

you are great man . thanks for your content . I am forever great full to you .

[dedraryqui]

very clear, easy understandable video