Deriving the OLS Estimators in Simple Linear Regression Model - Part 2

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This is the second video where I derive the OLS estimators in a simple linear regression model, this time I focus on deriving the second parameter in the model, Beta or the independent variable.

Part 1 found here:

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Much better than what my professor briefly presented as a derivation. Thanks

vicentefigueroatocornal

Thank you so much! This is the easiest explanation I have found of this exercise. Straight to the point and with a clear explanation.

Julian-semg

Nice and short derivation. Kudos for the lecturer!

berke-ozgen

Very well-explained. Thank you so much. Please keep on making more videos!

shireenkhan

Anybody wondering what happened at the and let me explain:

betahat = sum(from i = 1 to n) [ (yi - ybar)(xi - xbar) ] / sum(from i = 1 to n) [xi - xbar]

here nominator is simply the sample covariance between y and x, and denominator is the sample variance of the x.

then betahat = sample cov(y, x)/ sample var(x) => is the slope estimate of the regression that minimizes residuals.

BrunetteViking

What do you do with the summation at the end? I think the video cuts out early. Thank you for your help!

alaynabone

when you insert a^ why dont you factor in the -1 when re arranging the equation? @ 5:25

grantpezzolesi

Could you please explain, what you are doing with the sum operator ?

florianwotawa

Hi. Great video. It helped me understand OLS estimator better. But the video is not complete.

fruwheokeremute

Thank you for this video! I appreciate it

Feliciathegoat

i didnt understand why you are using Yi Instead of Y hat???
kindly u can clear me???

arsyed

Hie I have a question when you where you substituted alpha with yi did not make a mistake of forgetting to multiply the bracket replacing alpha with a negative be4 collecting like terms

sharonmapape

Hi. I have a question. When you divide the equation by 2, what happens to the negative sign? (at 10.08 minutes in the video)

sushmithags

This second part of the video series is really misleading as you did not clearly explain the summation at the end. Please reupload or remove this. It is not correct.

anmolmahajan

I would be great full if you assist me

sharonmapape

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