Aren't visible the writings☝️☝️☝️

Aren't visible the writings☝️☝️☝️

Fantastic. Thanks for adding another worked example other than the binomial. It's always really helpful to see how these broad frameworks and approaches work for different situations, i.e. here different models.

Thank you!! This was super helpful! One question: what would the equation look like for teo proportions? Thank tou!

thanks

Thank you ❤

you saved my life

Thank you, very good explanation :). Greetings from germany

I am little bit confused because the intersection symbol not using in some part of video

Thank you very much🙏🏾. This was really helpful

Excellent proof. You are a savior

Unique video, but a few views and like. Please go on , don't stop okay, and also could you make video on Euler's number(e) please. once you did it put the link in reply!

Can't you solve this without using Excel? This isn't helpful for someone preparing for Exam

Anyone 2025?

thanks!

how you converted into 3 parts the integral parts?

great video nice it's so simple lol

Why aren't you summing over a in the discreet case and integrating over a as a support in the continous case?

I know that the expectation is but a Lebesgue integral, yet I can't help but ask what happens in these simplified definitions of the expected value for discrete and absolute continuous r.v.s when X is discrete and Y is continuous. What is E(X+Y), and what would be a logical explanation in simple terms regarding why the formula still holds?

muito obrigado!

thanks alot for this content

Tanks i am from Ethiopia

Thanks alot it helps alot❤❤

Excelente

one of the best stats channel on youtube. thank you very much for your effort! ❤

Thank you ❤❤❤

❤india,hai hind, nice concept

Hi I think it is important to just revise the common identities of matrix vector differentiation - when I studied my degree in statistics and when we did linear models - this was something I did not really understand until now.

If X~N(10, 4), X bar = (X1+X2+X3)/3; what’s var (X bar - X3)? If I compute var (X bar) + Var (X3)=4/3+4=16/3. But if I simplify X bar - X3 to (X1+X2-2X3)/3, then the variance becomes (4+4+4*4)/9=8/3. How come they are different? Thanks for your help!

If X~N(10, 4), X bar = (X1+X2+X3)/3; what’s var (X bar - X3)? If I compute var (X bar) + Var (X3)=4/3+4=16/3. But if I simplify X bar - X3 to (X1+X2-2X3)/3, then the variance becomes (4+4+4*4)/9=8/3. How come they are different? Thanks for your help!

Very helpful video. I only recently discovered that APY is not the same as monthly percentage, lol. Math is fun especially when it's about interest you earn. Thanks for the interesting video.

Nice

Thanks today is my test

Wonderful proof. Really easy to follow along. You have really mastered the art of explanation

When i calculate cov(Y, Y-hat) = E[Y.Y-hat] - E[Y]E[Y-hat] i get (B_0 + B_1X)^2 - (B_0 + B_1X)^2 = 0. I dont know what im doing wrong.

Amazing video! This completely cleared up my concept for ANOVA. and the $ trick is SO useful, i needed it, thank you!!

best channel for stats... thanks for posting

Brilliant! Thank you so much for the playlist so far. This video really helps link the prior more general theory to a more concrete example. However, I was wondering if you would also be showing how the variances of the betas are estimated for this model in this framework, and also whether a similar video would be possible where you focus on illustrating this framework for a GLM where the link isn't the identity and the weights aren't 1, so it's clearer how those more flexible parts work when "actually needed"?

how do we calculate ignificance f 5

this is an impactful

Am impressed of you

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The best reaching system to continue

Fantastic videos and series as always. One quick question: why is it okay in this proof (and subsequent videos) to just use the log of the density function and not the "full" likelihood function? I understand how the density function can be used as a likelihood function for the case when you have just one observation/z-value, but the "full" likelihood function is based on the product of n PDFs and would be different? What am I not getting here? Thanks.

This was such a great video! Thank you!

And very sexy voice too! 😊

Very helpful video!

thank you your tutorials are always helping me 😊

What program are you using for the virtual blackboard?

You might think of y = β0 + β1•x1 + β2•x2 + ... + e But it's better to see it as x1•β1 + x2•β2 + ... + e The *X* matrix is like our spreadsheet so that order is necessary for the dimensions to line up in the matrix multiplication. It's a bunch of known constants acting as the coefficients in a system of equations. Similar to the matrix equation *Ax* = *b* It's *Xβ* = *y* *β* is the variable vector transformed by *X*. Regression is about a linear combination of the β's. Given *Y* = *XB* + *e* E(*Y* | *X*) = *XB* + 0 The error term averages out to 0, i.e. we regress back to the (conditional) mean of Y. The product of a vector with its transpose collapses into the sum of its squared elements. *x’x* = Σx.i ² Variance is the average of squared deviations. (*x* - μ)’(*x* - μ) = Σi(x.i - μ)² Divide that by n for σ² , by n-1 for s². Similarly Cov(x1, x2) = Σi(x.i1 - μ1)(x.i2 - μ2) / n σ1,2= (*x1* - μ1)’(*x2* - μ2) / n Generalize it to (*X* - *M*)’(*X* - *M*) / n If the variables were mean centered first their means are 0. Therefore *M* = *0* and the covariance matrix is *X’X* divided by n or n-1.