StatQuest: PCA main ideas in only 5 minutes!!!

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  • เผยแพร่เมื่อ 25 มิ.ย. 2024
  • The main ideas behind PCA are actually super simple and that means it's easy to interpret a PCA plot: Samples that are correlated will cluster together apart from samples that are not correlated with them. In this video, I walk through the ideas so that you will have an intuitive sense of how PCA plots are draw. If you'd like more details, check out my full length PCA video here: • Principal Component An...
    For a complete index of all the StatQuest videos, check out:
    statquest.org/video-index/
    If you'd like to support StatQuest, please consider...
    Buying The StatQuest Illustrated Guide to Machine Learning!!!
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    0:00 Awesome song and introduction
    0:27 Motivation for using PCA
    1:23 Correlations among samples
    3:36 PCA converts correlations into a 2-D graph
    4:26 Interpreting PCA plots
    5:08 Other options for dimension reduction
    #statquest #PCA #ML

ความคิดเห็น • 731

  • @statquest
    @statquest  6 ปีที่แล้ว +110

    Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/
    Special thanks to PROTIST for the Russian subtitles!!! :)

    • @falaksingla6242
      @falaksingla6242 2 ปีที่แล้ว +1

      Hi Josh,
      Love your content. Has helped me to learn a lot & grow. You are doing an awesome work. Please continue to do so.
      Wanted to support you but unfortunately your Paypal link seems to be dysfunctional. Please update it.

  • @tuongminhquoc
    @tuongminhquoc 4 ปีที่แล้ว +481

    I appreciated your effort spent on these videos. Sadly, since I am still a student, I have no money to support you just a bit. So, I have spent much of my effort to translate your videos into my language as it is my best language as a thank to you. Hope you would accept my thank.

    • @statquest
      @statquest  4 ปีที่แล้ว +61

      Thank you very much!!!! :)

    • @tuongminhquoc
      @tuongminhquoc 4 ปีที่แล้ว +40

      @StatQuest with Josh Starmer I didn't think you would check this that soon :))) thanks for accepting my contribution!. I'll translate more of your videos whenever I have free time (and wifi haha :D )

    • @statquest
      @statquest  4 ปีที่แล้ว +32

      @@tuongminhquoc I really appreciate it! :)

    • @leonguyen1204
      @leonguyen1204 3 ปีที่แล้ว +8

      No wonder the subtitle was spot on! Great work mate, thanks for that! Also thanks @StatQuest with Josh Starmer, nice video with simple explanation, I'm trying to make sense of it.

    • @ngoctandang9307
      @ngoctandang9307 3 ปีที่แล้ว +3

      Really excited when watching this video in Vietnamese subtitle, thank you!!!

  • @Lastmomenttuitions
    @Lastmomenttuitions 5 ปีที่แล้ว +70

    Very nicely explained thank you so much for Putting this

    • @statquest
      @statquest  5 ปีที่แล้ว +4

      Hooray! I'm glad you like it. :)

  • @rafaelerwin
    @rafaelerwin 5 วันที่ผ่านมา +1

    Without Statquest, I cannot imagine how hard my academic and professional life would be.... Thanks a lot Prof Starmer!

    • @statquest
      @statquest  5 วันที่ผ่านมา

      Thanks!

  • @aborucu
    @aborucu 2 ปีที่แล้ว +20

    This is by far the best on internet, Khan Academy doesnt have this content, all courses on coursera,udemy either wave formulas in the air or dont bother for a simple yet enlightening explanation..This is what practicioners need.Bravo!

    • @statquest
      @statquest  2 ปีที่แล้ว +1

      Thank you! :)

  • @MeetPatel-jx6sn
    @MeetPatel-jx6sn ปีที่แล้ว +13

    If my university would have been teaching 10% like you I would have completed my engineering in just 1year
    Awesome video ♥

  • @guandongkou178
    @guandongkou178 3 ปีที่แล้ว +67

    Thank you Josh for the clearly explained abstract concepts! It is even more informational than a 2-hour lecture in a college.

    • @statquest
      @statquest  3 ปีที่แล้ว +1

      Glad it was helpful!

  • @fartissimo
    @fartissimo 4 ปีที่แล้ว +10

    I enjoy your videos and you are performing a valuable service. The few things I would mention that would be helpful are that PCA is really a measure of covariance in a sample and that PCA does NOT provide ANY indication of statistical significance. Understanding Covariance is helpful to really understand PCA. Also, PCA is particularly useful when patterns emerge between experimental and non-experimental parameters. If patterns associated with experimental parameters are observed (i.e. treatment conditions) it indicates that there may be changes between samples/populations that are of interest; in cases where there are patterns associated with non-experimental parameters (such as collection date or incubation conditions) it indicates that the date of collection resulted in more variance than experimental parameters. In such a case, it points to a possible flaw in experimental design so that it would be of benefit to re-evaluate sample collection/preparation/incubation etc... in the workflows to minimize the influence on the studied populations.

  • @chintanchawda9725
    @chintanchawda9725 6 ปีที่แล้ว +11

    Every maths prof. must be like, way of explaination is as simple as possible. Thank you.

  • @HoriBar993
    @HoriBar993 5 ปีที่แล้ว +12

    You have a teaching talent.
    Thank you for the all your videos!

  • @kesialeite7913
    @kesialeite7913 4 ปีที่แล้ว +16

    Thanks! Now I finally understand what I am doing in the lab! 🇧🇷

    • @statquest
      @statquest  4 ปีที่แล้ว +4

      Hooray! :)

  • @cynthiacabales22
    @cynthiacabales22 4 ปีที่แล้ว +10

    You are helping me survive my Research Analytics class - HOORAY! :-)

  • @rorals4814
    @rorals4814 6 ปีที่แล้ว +1

    Your voice tone reflects how confident and smart you are... Thanks, plz we need more videos related to machine learning stuff

  • @alondracortezenciso4272
    @alondracortezenciso4272 3 ปีที่แล้ว +3

    You just saved my life, sir! Doing journal club tomorrow and I had no idea how to read a PCA from steady-state metabolomics. Thank you!

    • @statquest
      @statquest  3 ปีที่แล้ว

      Glad I could help!

  • @ZakLiTLearnfortheEnvironment
    @ZakLiTLearnfortheEnvironment 4 ปีที่แล้ว +7

    I wanted to browse a video with the title ''HOW TO THANK STAT QUEST?" the only answer I got is just pray for the channel's success....

    • @statquest
      @statquest  4 ปีที่แล้ว +1

      Thank you! :)

  • @anapeleteirovigil3199
    @anapeleteirovigil3199 25 วันที่ผ่านมา +1

    Came for the explanations and definitely stayed for the openings

    • @statquest
      @statquest  25 วันที่ผ่านมา +1

      bam!

  • @chriscollins5320
    @chriscollins5320 6 ปีที่แล้ว +1

    What a great video that clearly and concisely explains PCA. Great job, keep these up.

  • @nileshhalder7058
    @nileshhalder7058 19 วันที่ผ่านมา +1

    I just cried after watching your video.. I looking to easy concept for one hour .... Thank you

    • @statquest
      @statquest  18 วันที่ผ่านมา

      Glad it helped!

  • @KingstonUponThames
    @KingstonUponThames 4 ปีที่แล้ว +1

    Best explanations of PCA in layman terms. Great work. Thank you!

    • @statquest
      @statquest  4 ปีที่แล้ว +1

      Wow, thanks!

  • @sidekickwatson
    @sidekickwatson 3 ปีที่แล้ว +2

    Thank you for these sequencing, singing, and recipe videos, this channel needs more subscribers.

    • @statquest
      @statquest  3 ปีที่แล้ว

      Thank you very much! :)

  • @jessefp1940
    @jessefp1940 5 ปีที่แล้ว +2

    Extremely helpful thanks, explaining the principal components in the order that you did, you nearly lost me I would consider rearranging the explanation of what pc1 and pc2 are in the video.

    • @statquest
      @statquest  5 ปีที่แล้ว

      Glad you liked this video! If you have time, you should check out the new and improved version (which is longer, but it's worth it, I promise you): th-cam.com/video/FgakZw6K1QQ/w-d-xo.html

  • @ohromujici
    @ohromujici 6 ปีที่แล้ว +1

    Thanks! This was a great overview. I am in big data for a pharma company and we added PCA to one of our data tools. The documentation we received was a little "dry" so thank you for putting this into easy to understand key concepts. This helped a lot. Also, I did my original graduate work in mRNA decay so bonus points for dragging mRNA into this. :) :) :)

  • @nourajamal8166
    @nourajamal8166 2 ปีที่แล้ว +2

    This is one of the most great channels I have ever seen . If u are looking for a good ,easy and quick explanation you are in the right place ;)

    • @statquest
      @statquest  2 ปีที่แล้ว

      Wow, thanks!

  • @eemmmaaadd
    @eemmmaaadd 5 ปีที่แล้ว +2

    I always come across your videos when looking for stat information. And always your videos are the best.

    • @statquest
      @statquest  5 ปีที่แล้ว

      Awesome! :) Thank you! :)

  • @quililank
    @quililank 5 ปีที่แล้ว +5

    I've been searching PCA for dummies for so long and I'm glad I found this! I can finally understand what the researchers in this journal I'm reading are trying to say Haha!

    • @statquest
      @statquest  5 ปีที่แล้ว +2

      Hooray!!! I'm so glad I could help. If you want to go a little bit deeper, let me recommend my other PCA video. If you watch that one, you will be a PCA master! th-cam.com/video/FgakZw6K1QQ/w-d-xo.html

    • @naturaldisastertv3298
      @naturaldisastertv3298 3 ปีที่แล้ว

      i was also having the same problem. i watched his 20 min video but I couldn't understand anything.

  • @adelutzaification
    @adelutzaification 6 ปีที่แล้ว

    Great video! I became a bit addicted to the StatQuest videos and my anxiety levels increased for a while, not seeing the usual morning Monday upload. Now I need to figure out what t-SNE plots are... ;)

  • @boundlessbrittany
    @boundlessbrittany 3 ปีที่แล้ว +2

    Holy moly. I finally understand the concept of PCA plots :O THANK YOU SO MUCH

  • @digigoliath
    @digigoliath 3 ปีที่แล้ว +10

    Wow, this sheds a lot of light on dimension reduction. Very clearly explained & illustrated. TQVM!!!

    • @statquest
      @statquest  3 ปีที่แล้ว +2

      Thanks! :)

  • @luonhanquocvu8411
    @luonhanquocvu8411 2 ปีที่แล้ว +1

    As I learn PCA in a machine learning course, I knew that you have a good video explanation on this topic!! thanks!

    • @statquest
      @statquest  2 ปีที่แล้ว

      Glad it was helpful!

  • @sanathgunawardena832
    @sanathgunawardena832 หลายเดือนก่อน +1

    You're a lifesaver, Josh!
    Thanks!

    • @statquest
      @statquest  หลายเดือนก่อน

      Thanks!

  • @verdasney
    @verdasney 3 ปีที่แล้ว +1

    It is more understandable that my 1.5 h lecture and a good start of PCA class.
    Thank you for the video. Very well created.

    • @statquest
      @statquest  3 ปีที่แล้ว

      Glad it was helpful!

  • @timlofton6595
    @timlofton6595 ปีที่แล้ว +2

    Good stuff Josh. Going to the lengthier version to further blast this through my thick skull. 😃 Appreciate your efforts with this!

  • @findingnemo4637
    @findingnemo4637 6 ปีที่แล้ว +48

    100s of lines in 5 min.. great work sir.

    • @zes7215
      @zes7215 5 ปีที่แล้ว +1

      wrg

  • @Nicblocks
    @Nicblocks 10 หลายเดือนก่อน +2

    I had to wrap my head around PCA plots as part of a presentation and just could not understand it. This was really well done and I'll be taking this knowledge in with me. Thank you!

    • @statquest
      @statquest  10 หลายเดือนก่อน

      Hooray! :)

  • @marjanyaghoubi5729
    @marjanyaghoubi5729 5 ปีที่แล้ว

    Hi sir, your explanation is very clear and vivid, I truly appreciate for it. Please do a video on Laplacian matrix and its application in dimension reduction.

  • @liranzaidman1610
    @liranzaidman1610 4 ปีที่แล้ว +2

    2:03 People should stop here and listen very carefully because this is a really important concept, and I mean - Really important!
    When analyzing data and the parameters effecting the outcome of something - this must be the way to think.
    Great work

  • @amitrokade1140
    @amitrokade1140 6 ปีที่แล้ว

    Finally understood it!
    Thank You for a great video

  • @juanno3581
    @juanno3581 4 ปีที่แล้ว +1

    Thanks for the explanation!! It makes sense to use it with dendrograms for plant breeding!!

  • @wesleysbr
    @wesleysbr 5 ปีที่แล้ว +2

    Best regards from brazil, you are the best! thank you

  • @ghatshilagogol
    @ghatshilagogol 20 ชั่วโมงที่ผ่านมา +1

    awesome pca for dim reduction with vertical+horizontal+depth all in one 3-d rotates

    • @statquest
      @statquest  17 ชั่วโมงที่ผ่านมา

      :)

  • @robb8763
    @robb8763 ปีที่แล้ว +7

    so well structured, so on point - like all of the videos. very rare quality of a teacher: the comibnation of deep understanding AND the ability to narrow it down... almost like reducing dimensions to make things simpler to understand ;) what a great work!

  • @UKFishCam
    @UKFishCam ปีที่แล้ว +2

    Thank you so much for making this video! I've got my final year project due soon and Id lost the plot before this video!

  • @fredkiffer6753
    @fredkiffer6753 3 ปีที่แล้ว +1

    Thank you for existing!

  • @jorgepinto2241
    @jorgepinto2241 4 ปีที่แล้ว

    Excelent work! I love your video, It is so well explained. Thanks a lot!

  • @winniewu8581
    @winniewu8581 4 ปีที่แล้ว +1

    Thanks again. Good as always. Thanks for the weight and height example!

    • @statquest
      @statquest  4 ปีที่แล้ว

      Thank you! :)

  • @thatbackbenchdude
    @thatbackbenchdude 5 ปีที่แล้ว +17

    StatQuest is the best

    • @statquest
      @statquest  5 ปีที่แล้ว +1

      Hooray!!! :)

  • @edsonwinnerify
    @edsonwinnerify ปีที่แล้ว +1

    Thanks Josh, I can always get something new from your videos.

  • @putriestimandasari4173
    @putriestimandasari4173 5 ปีที่แล้ว +2

    I looovee your voice and your explanation... Great job, Sir.. Thank you !!!

    • @statquest
      @statquest  5 ปีที่แล้ว

      Hooray! I’m glad you like the video!! :)

  • @andersonbessa9044
    @andersonbessa9044 3 ปีที่แล้ว +2

    Great explanation as always! Thanks a lot for your effort!

    • @statquest
      @statquest  3 ปีที่แล้ว

      Glad you liked it!

  • @jeremmoses8562
    @jeremmoses8562 2 ปีที่แล้ว +1

    You tech Harvard type of kind of stuff in elementary school way in all your videos, how do you that man! It's amazing, Thank you so much

  • @tomoleusz
    @tomoleusz ปีที่แล้ว +2

    I was dumb before watching this video. Now I am still dumb but at least I understand PCA.

  • @fereidoon82
    @fereidoon82 5 ปีที่แล้ว

    well done, short and clean, thank u

  • @nadhirahbaharin.
    @nadhirahbaharin. 6 ปีที่แล้ว

    you need more subscribers!!! Thank you so much your videos are life saver

    • @nadhirahbaharin.
      @nadhirahbaharin. 6 ปีที่แล้ว

      I didn't skip the ad to support you (it's the least I can do haha. )

  • @AbHiShEkdAS1505
    @AbHiShEkdAS1505 4 ปีที่แล้ว +8

    I have taken ML this semester and to be very honest I am understanding all the concepts from your videos. I would be really grateful if you could upload a playlist on Neural network and Deep Learning.

    • @statquest
      @statquest  4 ปีที่แล้ว +3

      Awesome! Neural Networks should come out in the next few months.

    • @LorwaiTan
      @LorwaiTan 4 ปีที่แล้ว +1

      @@statquest Thank you for so clearly explaining these concepts. Looking forward to your Neural Networks videos! Will share your videos with my colleagues.

  • @vimalakirtilotus4611
    @vimalakirtilotus4611 2 ปีที่แล้ว

    You have saved me from the sea of formulas. Thank you!

  • @edupazz
    @edupazz 2 ปีที่แล้ว +1

    Great!! Your Calm and crystal pronunciation makes the concept very clear to understand. Thanks

    • @statquest
      @statquest  2 ปีที่แล้ว +1

      Thank you!

  • @menghongpor2667
    @menghongpor2667 4 ปีที่แล้ว +1

    Thank you for all the videos. It is super easy to understand.

  • @ArtsIntentive
    @ArtsIntentive 2 ปีที่แล้ว +1

    WOW. YOUR EXPLANATIONS, MY GOOD MAN, WERE CLEAR.

    • @statquest
      @statquest  2 ปีที่แล้ว

      Thank you! :)

  • @Diegoblismartmedpengar
    @Diegoblismartmedpengar 3 ปีที่แล้ว +1

    oh man!! thank you, I needed this so bad

  • @mc9272
    @mc9272 3 ปีที่แล้ว +2

    StatQuest is really the best! that you so much to prevent my brain to explode!!!

  • @SuperLameStuff
    @SuperLameStuff 4 ปีที่แล้ว +1

    Thank you for your clarity!

  • @kevinwidgo
    @kevinwidgo ปีที่แล้ว +1

    WTF HOW IT CAN BE THIS SIMPLE OMG! THANKS.

  • @rezaheydari3661
    @rezaheydari3661 6 ปีที่แล้ว +1

    thanks Josh your videos are amazing!!!

    • @statquest
      @statquest  6 ปีที่แล้ว

      Hooray! If you have time, check out the new PCA video that I made. It's longer, but it goes way deeper and it's just as easy to understand: th-cam.com/video/FgakZw6K1QQ/w-d-xo.html

  • @laure189
    @laure189 6 ปีที่แล้ว +1

    Fantastic video, thank you!

  • @daphnes1001
    @daphnes1001 6 ปีที่แล้ว

    Thank you so much!

  • @96unicorns
    @96unicorns 2 ปีที่แล้ว +1

    This was such a great explanation and so entertaining!

    • @statquest
      @statquest  2 ปีที่แล้ว

      Glad you enjoyed it!

  • @MeditaBrasil
    @MeditaBrasil 2 ปีที่แล้ว +1

    So well explained it!!! AMAZING!!! Thank you very much for making this video!!!

    • @statquest
      @statquest  2 ปีที่แล้ว

      Glad you enjoyed it!

  • @noneoftheabove1589
    @noneoftheabove1589 5 หลายเดือนก่อน +1

    I love your humor! What a lovely way to present and explain. ahem.. what could be daunting to some lol (such as myself!) Grateful for the work and the passion! Keep up the good work!
    A new subscriber!

    • @statquest
      @statquest  5 หลายเดือนก่อน

      Thanks so much!

  • @alaa9613
    @alaa9613 7 หลายเดือนก่อน +1

    this saved my life thank you i hope you're doing well sir

    • @statquest
      @statquest  6 หลายเดือนก่อน

      Thanks!

  • @giraldeaufagaerone4213
    @giraldeaufagaerone4213 4 ปีที่แล้ว +1

    thanks for these videos it helps me understand better compared to classes

  • @newlifestartsnow4444
    @newlifestartsnow4444 5 ปีที่แล้ว

    Thanks for the video. What do the sizes and colours of the circles represent in the 3D scatter plot which appears around 2'47"? Are these just an aid for giving the plot depth?

  • @arkadipbasu828
    @arkadipbasu828 2 ปีที่แล้ว +1

    Clearly explained Josh. Thank you

  • @naturaldisastertv3298
    @naturaldisastertv3298 3 ปีที่แล้ว +1

    i watched your 20 min video too. But this was easier to understand. Thank you so much.

  • @nompumelelongubane7579
    @nompumelelongubane7579 4 หลายเดือนก่อน +1

    simple enough for my understanding. thanks a lot.

    • @statquest
      @statquest  4 หลายเดือนก่อน

      Glad it helped!

  • @Jenna-iu2lx
    @Jenna-iu2lx ปีที่แล้ว +1

    StatQuest is definitely the best 📊

  • @domenicodifraia7338
    @domenicodifraia7338 6 ปีที่แล้ว

    Your're great man!

  • @adelutzaification
    @adelutzaification 6 ปีที่แล้ว

    Thank you. Good to know.

  • @MrKB_SSJ2
    @MrKB_SSJ2 2 ปีที่แล้ว +1

    This was so smoothly explained. Thank you soooooooooooooooo much!!!!!

  • @carlosalfonso5829
    @carlosalfonso5829 6 ปีที่แล้ว +1

    Excelent video thank you very much!

    • @statquest
      @statquest  6 ปีที่แล้ว

      Hooray! I'm glad you like it. :)

  • @trela47.
    @trela47. 2 ปีที่แล้ว +1

    Just want to let you know, the 'Awesome song' just won you a subscriber.

  • @MM-qq6xp
    @MM-qq6xp 5 ปีที่แล้ว

    Excellent demonstration

  • @QuynhMata
    @QuynhMata 8 หลายเดือนก่อน +1

    Phew, thank you so much! This was very helpful.

    • @statquest
      @statquest  8 หลายเดือนก่อน

      Glad it helped!

  • @lizhongchen4376
    @lizhongchen4376 2 ปีที่แล้ว +2

    StatQuest is indeed the best.

  • @lakep7798
    @lakep7798 2 ปีที่แล้ว +1

    Wow--this was SO very helpful, even if corny at times, lol. Thank you so much!

    • @statquest
      @statquest  2 ปีที่แล้ว

      Thanks so much! :)

  • @sridharmaloth87
    @sridharmaloth87 5 ปีที่แล้ว

    Thanks for keeping this video

  • @nftk5413
    @nftk5413 4 ปีที่แล้ว +1

    i love your way of explaining things tnx alot ...these videos are really helpful

    • @statquest
      @statquest  4 ปีที่แล้ว

      Glad you like them!

  • @Muuip
    @Muuip 2 ปีที่แล้ว +1

    Great concise presentation!
    Much appreciated!👍

  • @iftrejom
    @iftrejom 2 ปีที่แล้ว +2

    The way you easily and calmly explain such complex topics is outstanding. Thank you very much.

  • @user-pw7hc6fd3h
    @user-pw7hc6fd3h 4 ปีที่แล้ว +2

    Such a beautiful work
    Great video indeed
    thanks !!

    • @statquest
      @statquest  4 ปีที่แล้ว

      Thank you! :)

  • @xialinsang6403
    @xialinsang6403 4 ปีที่แล้ว +1

    I really really enjoy your videos!!! Thank you so much !!!!

    • @statquest
      @statquest  4 ปีที่แล้ว

      Thank you! :)

  • @eveqian
    @eveqian 5 ปีที่แล้ว +1

    really good video!! thanks for the super comprehensive explanation! (I'm also a University of North Carolina graduate. Tar Heels!)

  • @gabrielbolivar16
    @gabrielbolivar16 6 ปีที่แล้ว +1

    Hi! Your videos have helped me to understand multivariate analysis! Do you have some video about PCR or PLS? I would really appreciate them. Have a good day!

  • @steveellison8686
    @steveellison8686 2 ปีที่แล้ว +1

    Dude, you are my hero. Thanks!

  • @majfbi
    @majfbi 5 ปีที่แล้ว

    Thanks for the priceless videos, Can you make a video on FPCA, please?

  • @SPeeDKiLL45
    @SPeeDKiLL45 2 ปีที่แล้ว +1

    Im so thankful for your videos bro !

    • @statquest
      @statquest  2 ปีที่แล้ว

      Glad you like them!

  • @DrATIF-ij9hy
    @DrATIF-ij9hy 2 ปีที่แล้ว +1

    Thank you for the Arabic subtitling, as I have always recommended your channel to my students; best wishes.

  • @ZNMelowLeloNeka
    @ZNMelowLeloNeka 3 หลายเดือนก่อน +1

    You just earned yourself a subscriber!!!!!

    • @statquest
      @statquest  3 หลายเดือนก่อน

      bam!

  • @not1AM
    @not1AM 3 หลายเดือนก่อน +1

    thanks man.. your videos are both very informative and fun.. really appreciated ❤❤❤❤❤❤

    • @statquest
      @statquest  3 หลายเดือนก่อน

      Glad you like them!

  • @ameliadiazdepascual9127
    @ameliadiazdepascual9127 4 ปีที่แล้ว +1

    Congratulation. it is an excellent example of PCA.

  • @adielbarrera9848
    @adielbarrera9848 3 ปีที่แล้ว

    This is saving my mind. I am an archaeologist trying to understand statistics and really reading abount ir has been nothing but torture XD

    • @spag5296
      @spag5296 3 ปีที่แล้ว

      Wow can I ask, do you study statistics out of pure interest?

    • @statquest
      @statquest  3 ปีที่แล้ว

      Good luck with your studies!