6. Regression Analysis

MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013
Instructor: Peter Kempthorne

This lecture introduces the mathematical and statistical foundations of regression analysis, particularly linear regression.

License: Creative Commons BY-NC-SA

[zhuangjiwang]

This lecture, compared with the previous ones, provides a great example for the importance of using blackboard in math courses.

[SeikoVanPaath]

Timestamps:
0:02:40 Overview
0:29:10 Ordinary Least Squares (OLS) Estimates
0:45:54 Gauss-Markov Theorem
0:54:47 Generalized Least Squares (GLS) Estimates
0:58:17 Normal Regression Models
1:19:25 Maximum Likelihood Estimation

[phillustrator]

This lecture convinced me that no amount of money you pay will guarantee you good teachers.

[lessmoneylessproblems]

Holy, who knew that linear regression could get so complex.

[burnbush]

Awesome content at least my knowledge of matrices and statistics has been broadened on a larger scope. Thanks.

[caverac]

@30:30 There's a mistake in the slides: the last term in the sum should be \beta_{p}, not \beta_{i, p}

[liuauto]

The slides ruined the lectures. This is a math course. Writing on the board can save more time than talking and hand waving

[KARABNAS]

This a good example of how a course in maths should not be. Especially the notation is so dodgy - Random matrix X is referred to the matrix of realizations of X all the time. Ridiculous

[SergeiIakhnin]

Good content, but should have really been handled in two lectures. A lot of time is spent on the basics, and then all of the more advanced details are simply glossed over due to a lack of time.

[fustilarian]

I miss Choongbum. This guy shouldn't be allowed to teach -.-

[danielduranloosli]

That was a brutally dense lecture with almost no real-life analogies. At that pace, you would need to be a linear algebra god to actually have the time to think about the statistical interpretations and applications of the expressions you are following.
Also, no use of much-needed graphs or technology whatsoever.

[chunlangong]

All his slides are in the textbook. Why the students in the classroom?

[btugh]

52:07 another typo? shouldn’t it be E[f’y]=f’E[y]?

[WallaceRoseVincent]

Anyone interested in working through the course together?

[lochestnut]

can anyone help me prove that:
if \epsilon ~ N_n(0_n, \sigma^2 \Sigma),
then \Sigma^(-0.5) \epsilon ~ N_n(0_n, \sigma^2 I_n)

[amandinelevecq]

Now I remember why I didn't like statistics and chose maths at university 😄

[okwrzmi]

The previous lecturer did not cope with his work

[CaseyVanBuren]

These slides seem riddled with mistakes, indices are lost or flipped or added where they shouldn't be. I was expecting more from MIT

[dankole]

With regression analy. The order of the fit justifies weighting. Seems to me neural networks are a much better subject to fits. Both are worthwhile. Neural nets provide options for rapid changes and simulation.

[michalroesler]

what it means and why it's there (y - theoretical y)^t * (y - theoretical y). why ^t is there?? what it means?