I’m a statistics student in my final year of undergrad. I just felt like checking out a video on covariationnas we begin PCA. This is by far the most clear it has ever been explained, and so succinctly! Well done, I feel I can think about it more clearly now.
This is literally the greatest explanation that I've ever heard. Beautifully animated and very straight to the point. The best video ever on this topic! You saved my life!😊
Some extra things that would be worth mentioning: 1) in the absence of linearity, the correlation itself may give you very little information. In some cases, data set with Corr = 0.9 might be closer to the one with Corr = 0, than to the other with Corr = 1. In other words, very weak trends (maybe not even worth mentioning) may give you high Corr value. 2) In random generated sets, certain degree of correlation may appear randomly, without a good reason. 3) Not only does correlation not imply causation, causation doesn't imply correlation as well. Take for example y = |x| for x \in [-1, 1]. Clearly y=f(x), yet Corr = 0.
TH-cam can't be serious that this video doesn't top their search result! Kudos to the channel. This video seriously deserves every compliment this world can offer. Keep up the great work thanks!
Your explanations are obvious, they remind me of all the knowledge that I had forgotten after my statistical class in the second year. I'm doing my capstone project, and your videos help me a lot. I appreciate your attribution.
Fantastic explanation, but one of the things that really sets this apart from some of the others I have seen is that you take time at the end to show the different values for different points. Really a great way to both help people visualize and check if they understood correctly.
The video looks more like an animation exercise rather than an educational video. The formulas are explained but the intuition behind them is as opaque as before. A few videos from 3Blue1Brown could be a good reference for this channel.
6:346:34 For example, let's say we observe a correlation between the number of ice cream cones sold at a beach and the number of drownings. There might indeed be a correlation, as both tend to increase during hot summer days. However, it would be incorrect to conclude that eating ice cream causes drownings or vice versa. Instead, there could be a third variable, such as temperature, that influences both variables independently.
Amazing intuition and excellent animation! Interestingly, the sign of correlation follows the monotony of sine function in each of the 4 quarters of the unit circle. In the top right quarter [0, 90deg] the sine function is monotonically increasing and correlation is positive, in the top left quarter [90, 180deg] the sine function is monotonically decreasing and correlation is negative and so on.
@@NormalizedNerd Ah! Actually not. In the bottom two the behavior is reversed! The sign of tangent in each quadrant would have been a better example. :)
that is exactly what i've been looking for for along time ,,, very clear and a big thumb for everything but espessially for the last visualization .....
how can (xi-x)(yi-y) be negative if variance is always positive? Did you mean to write x-variance and y-variance or did you mean to write x-deviation and y-deviation since I also noticed that you didn’t square the (xi-x) and (yi-y), which you would do for variance?
1:37 Hello sir can I know how you drew that type of Graph with Manim? I just want the name or line of the code about how you drew that kind of grid please sir!
The fact that I (a math teacher) learnt something new from this, means my students need to see it. Thumbs up my friend
You just made my day! ❤
I’m a statistics student in my final year of undergrad. I just felt like checking out a video on covariationnas we begin PCA. This is by far the most clear it has ever been explained, and so succinctly! Well done, I feel I can think about it more clearly now.
Could you explain why eigenvectors corresponding to largest eigenvalues maximize projected variance intuitively?
really asking
This is literally the greatest explanation that I've ever heard. Beautifully animated and very straight to the point. The best video ever on this topic! You saved my life!😊
Some extra things that would be worth mentioning:
1) in the absence of linearity, the correlation itself may give you very little information. In some cases, data set with Corr = 0.9 might be closer to the one with Corr = 0, than to the other with Corr = 1. In other words, very weak trends (maybe not even worth mentioning) may give you high Corr value.
2) In random generated sets, certain degree of correlation may appear randomly, without a good reason.
3) Not only does correlation not imply causation, causation doesn't imply correlation as well. Take for example y = |x| for x \in [-1, 1]. Clearly y=f(x), yet Corr = 0.
Great comment! May be I will make a dedicated video on Correlation in the future :D
TH-cam can't be serious that this video doesn't top their search result! Kudos to the channel. This video seriously deserves every compliment this world can offer. Keep up the great work thanks!
Your explanations are obvious, they remind me of all the knowledge that I had forgotten after my statistical class in the second year. I'm doing my capstone project, and your videos help me a lot. I appreciate your attribution.
The animations helped me get an idea of what I was calculating for this long :) Maths is beautiful✨
The best explanations and visualizations I've ever seen. Thank you for that!
So clear. Thanks for explaining. Also the background music was super calming
Excellent video. Very intuitive and well explained! As someone who's both a student and a teacher of maths, I'm impressed from both angles!
Instantly subscribed. Please keep up the work! Amazing visualization.
I agree; this video was amazing! And you are so right- the video, in the end, was so good to see what the values look like at different plot points.
Fantastic explanation, but one of the things that really sets this apart from some of the others I have seen is that you take time at the end to show the different values for different points. Really a great way to both help people visualize and check if they understood correctly.
The video looks more like an animation exercise rather than an educational video. The formulas are explained but the intuition behind them is as opaque as before. A few videos from 3Blue1Brown could be a good reference for this channel.
Actually such a good video, the visual representations helped me finally get the inuition i was missing for covariance. Thank you!
6:34 6:34
For example, let's say we observe a correlation between the number of ice cream cones sold at a beach and the number of drownings. There might indeed be a correlation, as both tend to increase during hot summer days. However, it would be incorrect to conclude that eating ice cream causes drownings or vice versa. Instead, there could be a third variable, such as temperature, that influences both variables independently.
It's such a great explanation! Thank you so much!
what a beautiful animation, amazing video friend!
this is the kind of explanation we need . 🙂
Incredible explanation and visualization! Thank you!
Amazing intuition and excellent animation! Interestingly, the sign of correlation follows the monotony of sine function in each of the 4 quarters of the unit circle. In the top right quarter [0, 90deg] the sine function is monotonically increasing and correlation is positive, in the top left quarter [90, 180deg] the sine function is monotonically decreasing and correlation is negative and so on.
Thanks mate!
Is this observation true for bottom two quadrants?
@@NormalizedNerd Ah! Actually not. In the bottom two the behavior is reversed! The sign of tangent in each quadrant would have been a better example. :)
great video ! i really appreciate the effort you put into this
great video! you really helped me to understand in 7 minutes what my proffesor could not in 1 hour! thanks!
the visual is sick!! amazing
This is so well explained. Thank you so much
Great video. You really did explain the concept in a very elegant way.
thank you sir, great teaching and visualizations. 👍😊
Great video, thank you! I finally understand covariance. Very helpful and beautiful visualizations as I study for my statistics final :)
that is exactly what i've been looking for for along time ,,, very clear and a big thumb for everything but espessially for the last visualization .....
Thanks for this video, you really helped me understand covariance visually.
First time I comment a video of a math explanation in years, wow very good!
Great video , thanks!!
It's crazy learning correlation without telling you about covariance
well explained !
Thank you
thank you clearly explained.
thanku so much man
Excellent explanations!
thank you it is clear!
amazing video, so happy I came across it
Thanks!
Thsnk you much. Please more statistics.
Very helpful thank you!
Can't wait for your channel to get discovered
Well explained.
super good animaitions and music
your definition about covariance is partially correct covariance also shows the strength of the relationship but not the linear relationship
It’s truly intuitive … is there a way I can connect with you?
Beautiful
Very intuitive, thanks!
Brilliant animations, thanks
Thanks mate!!
Good animation, well explained, thanks for sharing 👍
well explained
Brilliant!
eloquently explained
how can (xi-x)(yi-y) be negative if variance is always positive? Did you mean to write x-variance and y-variance or did you mean to write x-deviation and y-deviation since I also noticed that you didn’t square the (xi-x) and (yi-y), which you would do for variance?
thankyou
Damm next level teaching
Do you use manim?
very good video!
Sick
Can you tell me why we perform eigen decomposition to the covariance matrix in PCA ?
This is art
thanks!!!
That is beautiful 😢
amazing and satisfying
Perfect!
amazing video
great video!
Please do degrees of freedom
Amazing
hello, anyone can explain what is the yellow dot lines ? what does it represent?
This video is well explained than my teacher
1:37 Hello sir can I know how you drew that type of Graph with Manim? I just want the name or line of the code about how you drew that kind of grid please sir!
For creating the grid you need to use NumberPlane object.
@@NormalizedNerd Thanks man
tyvm
Best explanation..👍..sir, please make videos on regression line.....🙏
Thanks!!
this is the best thin ever!
I recognise a lot of 3Blue1Brown's animation and audio style here ^^ nevertheless, thanks for the helpful video
Yeah, I'm using his python library!
Thank you..
Limpid. Great job.
Thanks a lot :D
holy shit that was incredible
Nice animation
super video
Eventually somebody did it ! :)
Lovely animations, 3B1B style c:
Thanks a lot! Yup using his library.
wow