Covariance Clearly Explained!

Поделиться
HTML-код
  • Опубликовано: 23 дек 2024

Комментарии • 98

  • @BrianAmedee
    @BrianAmedee 3 года назад +90

    The fact that I (a math teacher) learnt something new from this, means my students need to see it. Thumbs up my friend

  • @GMoDiLLa
    @GMoDiLLa 8 месяцев назад +15

    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.

    • @pewpewhuang4162
      @pewpewhuang4162 8 месяцев назад

      Could you explain why eigenvectors corresponding to largest eigenvalues maximize projected variance intuitively?
      really asking

  • @YourNerdGal
    @YourNerdGal Год назад +15

    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!😊

  • @oskarvavtar4990
    @oskarvavtar4990 3 года назад +50

    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.

    • @NormalizedNerd
      @NormalizedNerd  3 года назад +12

      Great comment! May be I will make a dedicated video on Correlation in the future :D

  • @thecheckplease2357
    @thecheckplease2357 2 года назад +8

    RUclips 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!

  • @AsafJerbi
    @AsafJerbi 15 дней назад

    The best explanations and visualizations I've ever seen. Thank you for that!

  • @hariind86
    @hariind86 Год назад +7

    The animations helped me get an idea of what I was calculating for this long :) Maths is beautiful✨

  • @happyslug
    @happyslug 21 день назад

    So clear. Thanks for explaining. Also the background music was super calming

  • @ReubenSilveira6
    @ReubenSilveira6 Год назад +2

    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!

  • @robertturley2974
    @robertturley2974 9 месяцев назад

    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.

  • @thisukainol
    @thisukainol 7 месяцев назад +1

    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.

  • @luvshell1
    @luvshell1 Год назад +1

    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.

  • @veronicatellnes6424
    @veronicatellnes6424 4 месяца назад

    Actually such a good video, the visual representations helped me finally get the inuition i was missing for covariance. Thank you!

  • @jepp1572
    @jepp1572 2 года назад +1

    Instantly subscribed. Please keep up the work! Amazing visualization.

  • @Cringeupdates
    @Cringeupdates 11 месяцев назад +2

    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.

  • @ChristosMilarokostas
    @ChristosMilarokostas 3 года назад +4

    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
      @NormalizedNerd  3 года назад +1

      Thanks mate!
      Is this observation true for bottom two quadrants?

    • @ChristosMilarokostas
      @ChristosMilarokostas 3 года назад +1

      @@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. :)

  • @nicolesamuel1838
    @nicolesamuel1838 10 месяцев назад

    great video! you really helped me to understand in 7 minutes what my proffesor could not in 1 hour! thanks!

  • @zakaboudich2972
    @zakaboudich2972 Год назад +1

    what a beautiful animation, amazing video friend!

  • @dineshkumare1750
    @dineshkumare1750 Год назад +2

    this is the kind of explanation we need . 🙂

  • @tomhaswell6283
    @tomhaswell6283 10 месяцев назад

    Incredible explanation and visualization! Thank you!

  • @Echoooo-ex7zf
    @Echoooo-ex7zf 25 дней назад

    It's such a great explanation! Thank you so much!

  • @montanalee3560
    @montanalee3560 Год назад

    Great video, thank you! I finally understand covariance. Very helpful and beautiful visualizations as I study for my statistics final :)

  • @wenwenbai
    @wenwenbai Год назад

    Great video. You really did explain the concept in a very elegant way.

  • @Muneh14
    @Muneh14 Год назад

    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 .....

  • @melodylin5058
    @melodylin5058 10 месяцев назад

    the visual is sick!! amazing

  • @7ezem345
    @7ezem345 Год назад +1

    great video ! i really appreciate the effort you put into this

  • @dimitrismylonas4159
    @dimitrismylonas4159 Год назад

    Thanks for this video, you really helped me understand covariance visually.

  • @SENSE.WORLDWIDE
    @SENSE.WORLDWIDE 9 месяцев назад

    First time I comment a video of a math explanation in years, wow very good!

  • @kadidiasaboudoumbia4797
    @kadidiasaboudoumbia4797 9 месяцев назад

    This is so well explained. Thank you so much

  • @rishabhnarula1999
    @rishabhnarula1999 Год назад

    thank you sir, great teaching and visualizations. 👍😊

  • @mainakmukherjee3444
    @mainakmukherjee3444 Год назад

    Can you tell me why we perform eigen decomposition to the covariance matrix in PCA ?

  • @neethinnandakumar4303
    @neethinnandakumar4303 2 года назад

    Can't wait for your channel to get discovered

  • @isaaccheng1111
    @isaaccheng1111 3 месяца назад

    hello, anyone can explain what is the yellow dot lines ? what does it represent?

  • @rajvanshmalhotra931
    @rajvanshmalhotra931 4 месяца назад

    your definition about covariance is partially correct covariance also shows the strength of the relationship but not the linear relationship

  • @EpicGamer-ux1tu
    @EpicGamer-ux1tu 5 месяцев назад

    It's crazy learning correlation without telling you about covariance

  • @komudamatata5492
    @komudamatata5492 Год назад

    amazing video, so happy I came across it

  • @ryanpereira9238
    @ryanpereira9238 9 месяцев назад

    Well explained.

  • @ggxue
    @ggxue Год назад

    thank you clearly explained.

  • @parisarezaei6274
    @parisarezaei6274 6 месяцев назад

    Great video , thanks!!

  • @PritishMishra
    @PritishMishra 3 года назад

    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!

    • @NormalizedNerd
      @NormalizedNerd  3 года назад +1

      For creating the grid you need to use NumberPlane object.

    • @PritishMishra
      @PritishMishra 3 года назад

      @@NormalizedNerd Thanks man

  • @MOHDIMRAN-zc4ev
    @MOHDIMRAN-zc4ev Год назад

    thanku so much man

  • @MrJeepiez
    @MrJeepiez Год назад

    super good animaitions and music

  • @lucasluzzi
    @lucasluzzi Год назад

    This is art

  • @Copley417
    @Copley417 2 года назад

    Excellent explanations!

  • @michelleelizabeth9956
    @michelleelizabeth9956 Год назад

    Good animation, well explained, thanks for sharing 👍

  • @bello3137
    @bello3137 5 месяцев назад

    well explained !

  • @OmarAmil
    @OmarAmil Год назад

    Thank you

  • @nourredinekebaili
    @nourredinekebaili 11 месяцев назад

    thank you it is clear!

  • @luataina5253
    @luataina5253 3 года назад

    Very intuitive, thanks!

  • @Dubai_life_
    @Dubai_life_ Год назад

    Thsnk you much. Please more statistics.

  • @KristalBox
    @KristalBox 2 года назад

    Damm next level teaching

  • @sauravmishra2010
    @sauravmishra2010 7 месяцев назад

    It’s truly intuitive … is there a way I can connect with you?

  • @jmb9040
    @jmb9040 9 месяцев назад

    eloquently explained

  • @jacobapplebaum3326
    @jacobapplebaum3326 2 месяца назад

    Do you use manim?

  • @Gar136
    @Gar136 Год назад

    Very helpful thank you!

  • @pavlonatalenko1828
    @pavlonatalenko1828 2 года назад

    Brilliant animations, thanks

  • @yts9363
    @yts9363 Год назад

    well explained

  • @erinmeyers-t9w
    @erinmeyers-t9w Год назад

    very good video!

  • @Symon_Musician
    @Symon_Musician 4 дня назад

    Thanks!

  • @S.G.2
    @S.G.2 6 месяцев назад

    tyvm

  • @michaelcoleman7762
    @michaelcoleman7762 2 года назад

    great video!

  • @thienphan1541
    @thienphan1541 Год назад

    This video is well explained than my teacher

  • @krzysztofbiay462
    @krzysztofbiay462 3 месяца назад

    Brilliant!

  • @ayaelayyan8826
    @ayaelayyan8826 Год назад

    amazing video

  • @raghavbhatia5548
    @raghavbhatia5548 8 месяцев назад

    amazing and satisfying

  • @TheBlueFluidBreathe
    @TheBlueFluidBreathe 4 месяца назад

    Beautiful

  • @MeargNgusseSahle
    @MeargNgusseSahle 5 месяцев назад

    thankyou

  • @govamurali2309
    @govamurali2309 3 года назад

    Please do degrees of freedom

  • @EthericImpulse
    @EthericImpulse 11 месяцев назад

    That is beautiful 😢

  • @enzeru97
    @enzeru97 Год назад

    Perfect!

  • @felicemorgigi1764
    @felicemorgigi1764 2 года назад +2

    I recognise a lot of 3Blue1Brown's animation and audio style here ^^ nevertheless, thanks for the helpful video

  • @prajakta4359
    @prajakta4359 3 года назад

    Best explanation..👍..sir, please make videos on regression line.....🙏

  • @malikjavadov366
    @malikjavadov366 11 месяцев назад

    this is the best thin ever!

  • @FariaManalRahman
    @FariaManalRahman Год назад

    thanks!!!

  • @louisemm6339
    @louisemm6339 4 месяца назад

    Amazing

  • @DineshGhimire-f2c
    @DineshGhimire-f2c 11 месяцев назад

    Nice animation

  • @EffigyOfficial
    @EffigyOfficial 2 месяца назад

    holy shit that was incredible

  • @sathiyanarayanan7245
    @sathiyanarayanan7245 Год назад

    Thank you..

  • @abuhelal2073
    @abuhelal2073 8 месяцев назад

    super video

  • @TheoriesofEverything
    @TheoriesofEverything 3 года назад

    Limpid. Great job.

  • @lliw4934
    @lliw4934 2 года назад

    Lovely animations, 3B1B style c:

  • @MiroslawZoladz
    @MiroslawZoladz 4 месяца назад +1

    Eventually somebody did it ! :)

  • @AI_Sports_Zone
    @AI_Sports_Zone Год назад

    wow