Least Squares Variance of Residuals Using Matrices and the Hat Matrix, H

[@EunjooSeo-f5b]

Michelle! Many thanks for your kind and systematic explanation👍

[@griddlebone44]

thanks! i ran across this statement about var(e) and could not understand why, found a nice explanation in your video

[@ezraezekielemmanuel1254]

Thanks for this great work presented In addition, In order not to be biased I would prefer to divide the error squared by n-k-1 degree of freedom especially when one explanatory variables are more than one. Thanks

[@michaelvendredi8274]

So well explained!!

[@jimturner4937]

I love your videos. You did lose me at 6:35 with I - H. I'm sure it has to do with my age and years out of school. Any help would be appreciated.

[@Stats4Everyone]

Happy to hear that you find my videos to be helpful! I wonder, are you referring to this step: Var ((I-H)y) = (I-H)Var(y)(I-H)' Here, (I-H) is a matrix of constants. However, variance has a similar property when there is a constant, a, multiplied by a random variable, y: Var(ay ) = a^2 * Var(y) Now, instead of "a" being a scalar, "A" is a matrix. This property is the same thing as: Var(Ay ) = A * Var(y) * A' This video might be helpful in explaining why Var(ay ) = a^2 * Var(y), which you can then extrapolate to Var(Ay ) = A * Var(y) * A' kzbin.info/www/bejne/a6ragH6cZ5qJgJIsi=dlk0tKXMV2z7zYhX

[@felipee2568]

very good!! thank you

[@nnicollydiva]

Hello! Could you explain why the var of Y is the same as the variance of e? You said it is because X is not random, but what does it imply? Thanks!

[@kristinperez6617]

Thank you!