Hypothesis testing in linear regression part 1

[@hedgehog_fox]

Sometimes I wonder why I am still going to school when I can just watch Ben Lambert's video.

[@alanpereira7522]

Paying 9k year for University and here I am

[@ronak226]

the videos are amazing ! This is Quality content ! Great Work !

[@RealMcDudu]

I think the numerator has to be beta* - beta_true, because the t distribution requires a standard normal distribution in it's numerator.

[@kottelkannim4919]

In hope I am not misleading you, I guess it is the STANDARD t-distribution which requires a STANDARD normal R.V. populating the numerator (*). What I do not fully get is how beta* , defined as "a value we got from our LS estimators", serves as a statistic. I think it should be beta_LS_{hat}, much like denominator which contains a statistic. But then again, I do not completely follow the lecturer's intention using this notation. (*) www.statlect.com/probability-distributions/student-t-distribution

[@benjaminschatz4350]

Hey someone could explain to me why we don't use the estimation of var(Beta ls) to approximate the distribution of Beta hat instead of creating a t distribution ?

[@danxie3018]

whats the difference between beta_star and beta_hat?

[@totochandelier]

beta star is the application of beta hat on a particular sample . For one beta hat, you should have several beta star: one by sample . beta star is a number , beta hat is the ols estimator .

[@totochandelier]

if N is great enough, why don t we use a normal N(beta_true, sigma_tilda_square) for inference ?

[@kottelkannim4919]

What is sigma_tilda_square?

[@littlerainyone]

Question orthogonal to the video content: may I ask what sort of device you use for the screencasts? I plan to do some on-line tutoring and I have a Wacom tablet, but I find it quite difficult to write legibly with the Wacom pencil. It just isn't the same as paper. May I ask what you use? (I've already told you this, by the way, but the videos are fabulous).

[@rodguinea]

I was learning string theory and here I am (i.e. I ALWAYS end up in this channel lol)

[@pulkitprajapati1114]

Use simple notations and expressions

[@shosecor4986]

?