StatQuest: Principal Component Analysis (PCA), Step-by-Step

Principal Component Analysis, is one of the most useful data analysis and machine learning methods out there. It can be used to identify patterns in highly complex datasets and it can tell you what variables in your data are the most important. Lastly, it can tell you how accurate your new understanding of the data actually is.
In this video, I go one step at a time through PCA, and the method used to solve it, Singular Value Decomposition. I take it nice and slowly so that the simplicity of the method is revealed and clearly explained.
If you are interested in doing PCA in R see: • StatQuest: PCA in R
If you are interested in learning more about how to determine the number of principal components, see: • StatQuest: PCA - Pract...
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0:00 Awesome song and introduction
0:30 Conceptual motivation for PCA
3:23 PCA worked out for 2-Dimensional data
5:03 Finding PC1
12:08 Singular vector/value, Eigenvector/value and loading scores defined
12:56 Finding PC2
14:14 Drawing the PCA graph
15:03 Calculating percent variation for each PC and scree plot
16:30 PCA worked out for 3-Dimensional data
#statquest #PCA #ML

[@statquest]

NOTE 1: The StatQuest PCA Study Guide is available! app.gumroad.com/statquest NOTE 2: A lot of people ask about how, in 3-D, the 3rd PC can be perpendicular to both PC1 and PC2. Regardless of the number of dimensions, all principal components are perpendicular to each other. If that sounds insane, consider a 2-d graph, the x and y axes are perpendicular to each other. Now consider a 3-d graph, the x, y and z axes are all perpendicular to each other. Now consider a 4-d graph..... etc. NOTE 3: A lot of people ask about the covariance matrix. There are two ways to do PCA: 1) The old way, which applies eigen-decomposition to the covariance matrix and 2) The new way, which applies singular value decomposition to the raw data. This video describes the new way, which is preferred because, from a computational stand point, it is more stable. NOTE 4: A lot of people ask how fitting this line is different from Linear Regression. In Linear Regression we are trying to maintain a relationship between a value on the x-axis, and the value it would predict on the y-axis. In other words, the x-axis is used to predict values on the y-axis. This is why we use the vertical distance to measure error - because that tells us how far off our prediction is for the true value. In PCA, no such relationship exists, so we minimize the perpendicular distances between the data and the line. NOTE 5: A lot of people wonder why we divide the sums of the squares by n-1 instead of n. To be honest, in this context, you can probably use 'n' or 'n-1'. 'n-1' is traditionally used because it prevents us from underestimating the variance - in other words, it's related to how statistics are calculated. If you want to learn more, see: kzbin.info/www/bejne/rJrOnJytn7aknLc kzbin.info/www/bejne/iau9Z3qmmMuih7s and kzbin.info/www/bejne/qXm1c5psd81-oKs (the last video specifically addresses the 'n' vs 'n-1' thing, but the first two give background that you need to understand first). Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

[@statquest]

@@clydemccoy1768 If you can tell me how to draw a 5-dimensional graph on a 2-dimensional plane (the computer screen), then we have a deal.

[@statquest]

@@clydemccoy1768 There are two ways to do PCA. The original way was to apply eigendecomposition of the covariance matrix. However, that method is not numerically stable, so no one uses it anymore (even though it is still taught as if it is used). The preferred and more modern approach is to use Singular Value Decomposition (SVD), and this is what I cover in this video. At least, I cover the concepts behind how it works. However, I may dive into the math behind singular value decomposition one day. It's a long term goal of mine, but it won't happen for a while.

[@KarthikNagadevara7791]

@@statquest Thank you Josh :)

[@ersincine3248]

2:40 Actually 4-D data can be plotted easily. 4th dimension can be specified by color. Shades of gray would be sufficient. For example a very dark gray (i.e. low "intensity") indicates a small number.

[@kacodemonio]

Could you please clarify me the following: some sources mention that in addition to centering the data (subtraction of the corresponding mean), it must be also standarized, i.e., divided by their corresponding standard deviation. Why is the data not being normalized here?

[@safaabdeljabbar8080]

For someone who is trying to be a data scientist, this channel is the best thing on the internet. You're better than any other teacher that I've ever had. THANK YOU.

[@statquest]

Wow! Thank you very much!

[@cindywang8852]

Can't agree more! This is my second time viewing this PCA video!

[@grahamjoss4643]

@@statquest Safa is right !

[@joshuasheppard7433]

@@statquest I agree entirely, very well explained.

[@ZenithClown]

Exactly, I still sometimes come back to this channel to refresh my memories!

[@rayskum1]

Dr. Starmer - I really really wish I had you as my stats teacher during my student days. I can't put in words how much I appreciate your videos and how to go about explaining core concepts. Thank you very much!

[@statquest]

Wow, thank you very much!!! I really appreciate your support! It means a lot to me that you care enough to contribute.

[@futurefriendly77]

6 years into my phd and I finally understand how a PCA plot actually works. Thank you!

[@statquest]

BAM! :)

[@anjalikrishna203]

Same!!!!!!

[@adipurnomo5683]

What research topic / thesis did you do sir @Dee T?

[@stallman3738]

Where did you study? :|

[@wumichael487]

little bam

[@aizazkhan5439]

I can say without a shadow of doubt that you are one of the world's best teachers. Mr. Starmer I can never thank you enough.

[@statquest]

Hooray! Thank you very much!!! :)

[@kushnigam2000]

I am a data scientist and have performed PCA using advanced statistical softwares . I have even taken company sponsored expensive MVA courses. THIS is the best explanation of PCA I have seen and cleared my fundamental doubts and missing links. THANK YOU.

[@statquest]

Hooray! I'm glad the video was helpful. :)

[@AD-dy1hi]

Can you please help me with the names of best software for PCA analysis!?

[@SHARMAKUMAR-zl6ku]

Hi kush i request you to guide me to become a data scientist like you

[@stephaniechen5536]

uni student day 14 of self-quarantine: the first thing to do in the morning is to watch StatQuest. Thank you Josh. Your videos help me surviving thru my uni in the time of covid19

[@statquest]

Awesome!!!! I'm so glad to hear my videos are helpful and good luck with your courses.

[@ap4558]

This is the most helpful video on PCA I have ever seen. I'm a neuro PhD student and I was struggling to understand this concept for a year. This video is a life saver!

[@statquest]

Thanks!

[@kidkaitou1412]

I have forgotten how much I love maths. You are such a good teacher.❤❤. Instead of wasting time on shorts or tiktok, I am gonna watch this, learn something and improve my life instead. Thanks.

[@statquest]

bam!

[@manisharyal4239]

This is honestly the best explanation on PCA. connects lot of loose strings of ideas. thanks !!

[@statquest]

I'm so glad to hear that you like this video! :)

[@sahej97]

Then you haven't watched any other PCA videos

[@DragonDaron]

I agree 👍

[@AnanyaPandeyIndia]

@@sahej97 Not everyone is a born genius like you some others need detailed explanation. You know Albert Einstein said if you cannot explain to a 6 year old you have not understood it yourself.

[@fisherh9111]

Josh is brilliant.

[@edchavez9960]

I'm studying for a final and this is way better explained than the entire semester.

[@statquest]

Awesome! Good luck on your final. :)

[@user-xn4yu5rn9q]

Hi, what class is this you are preparing? Just curious

[@ireliatt2190]

@@user-xn4yu5rn9qFor me it's Multivariate Data Analysis. Honestly, I got totally lost when just reading the lecture notes.

[@edchavez9960]

@@user-xn4yu5rn9q Exploratory Data Analysis quite similar to @irelia tt

[@edchavez9960]

@@ireliatt2190 ha! mine was Exploratory Data Analysis, which included Supervised/Unsupervised learning and multivariate data analysis

[@arianetalosig575]

I love how you explained "linear combination is just basically this... no big deal" when my lecturer makes it such a BIG DEAL! Thank you!!!

[@statquest]

Hooray! I'm glad the video was helpful. :)

[@josiahnielsen9972]

I'm in my first semester of grad school for stats.. and you are single-handedly going to save me! I already knew of all of the concepts of eigenvalues/eigenvectors, loadings, etc. but you summarized the 60 pages of theorems/proofs my prof had us read, and helped my intuition immensely. Please never stop making videos!

[@statquest]

Thank you very much and good luck with graduate school. :)

[@ajinkyaghadge3106]

Your work, with 3Blue1Brown, and other online material like Dr.Gilbert Strang, has given me a whole new perspective about Maths, learning and machine learning.

[@statquest]

Awesome! Those guys are my heros!

[@princeebenezeradjei3008]

I honestly think you deserve a noble prize or something. You're amazing. Like, just amazing!

[@statquest]

Thank you! :)

[@rebecagarcia1071]

I had to pause and let you know, that this is gold! The way you simply describe terrifying names, it just makes it look so easy. Thank you so much

[@statquest]

Glad you liked it!

[@endouyuu269]

I lost it at "Little BAM!!!"

[@statquest]

:)

[@cate9541]

Same😂

[@maximmazurov1102]

As a current high-ranked uni student may say this channel is a lifesaver for people who cannot understand something without guided decomposition of relatively more complex algorithm than OLS. Thank you Josh.

[@statquest]

Thanks!

[@FranFerioli]

"Mathematicians call this recipe a linear combination". I would have called it a Gene tonic!

[@statquest]

This might be the best comment ever. BAM! :)

[@longnguyenhoang764]

As a non-English speaker, I just like, I have no words, I don't no how to tell you how much I appreciate the way you put almost your "lyrics" or whatever you said on the videos that help me a lot. Many thanks to you, Josh!

[@statquest]

Thank you! :)

[@user-vb1no5lq1e]

I am a cloud architect taking an MIT ADSP course. If I see things are overwhelming there, I come and watch Statquest. What I like the best about Statquest is how you explain terminology alerts in simple layman's terms. Your channel is something I am more than happy to support. Indeed this is a great service.

[@statquest]

Thank you very much!

[@ArcenisRojas]

This is simply amazing! Josh, you communicated this idea so incredibly clearly and simply. As a practitioner in the stats/data science world I'm so impressed by how you were able to describe PCA so intuitively and without using the word "orthogonal." I've done the math behind PCA and I actually feel like I have a better understanding of it by watching your video. Thanks for demystifying stats for us all.

[@statquest]

Thank you so much! I'm glad you picked up on my omission of the word "orthogonal". :)

[@takethegaussian7548]

I have seen no book explaining this topic better than you. Your skills and efforts are invaluable!

[@statquest]

Wow, thank you!

[@kiaruna]

I have a cognitive science exam in one hour, your explanation saved me lots of time, so I wanted to thank you so very much before going.

[@statquest]

Thanks and good luck with your exam! Let me know how it goes. :)

[@blueicer101]

Wow, my lecturer just dropped eigenvectors in as an abstract matrix equivalent. Without these graphs and explanations I don't think I'd understand that an eigenvector is a ratio vector that enables you to reduce two correlating values into 1 set of a values and a vector, ultimately losing some information but only losing the most effective variables to lose. Thanks statquest.

[@statquest]

bam!

[@srishtis6896]

This man is helping me get through my diploma in Business Analytics. I have no background of stats or programming whatsoever. Could you imagine how intimidating the situation is for me. man thank you!

[@statquest]

Hooray! Good luck with your degree. :)

[@wilsonlwtan3975]

Clearest explanation of PCA to date! better than all university lecturers who usually just regurgitate jargons that students dont appreciate!

[@statquest]

Thanks! :)

[@emmanuel3929]

Explained it so much better than a 2 hour lecture. The concept makes more sense now.

[@statquest]

Thanks!

[@Oliver-2103]

Buddy you are an awesome guy. I wish one day I could give you a big hug of appreciation, but my honest thank you much has to be sufficient. I'd bet that there are people out there that would not be alive today without you. With your amount of views, there is probably at least one person who succeeded an important test that he would not have without you which may ended in a bad life. You're doing pure good with those videos.

[@statquest]

Thank you very much! :)

[@subbuktek]

Thanks dude. You are a godsend

[@AhmedIsam]

@19:41 should be triple bam

[@pyarepiyush]

BAM!!!!

[@AndreDiasRJ]

Double BAM!

[@hemanthkumarb9444]

Bam is not sufficient!

[@noli-timere-crede-tantum]

*with sad voice* "Little bam..." Awesome video. Thanks!

[@cyclone975]

Little bam got me too 🤣

[@AC-wk6hh]

Please never stop making videos. This is the only explanation of PCA I've seen that makes intuitive sense.

[@statquest]

Thank you!

[@FabianoRodriguesPereira-je8su]

It is unbelievable how Dr. Starmer makes such complex concepts so easily understandable!!! Thanks a lot!

[@statquest]

Glad it was helpful!

[@kyoosikkim749]

I just took some other online course for hours only to struggle... this video helped me understand the concept, which that course couldn't! Even in way shorter time! And even with the minimum animation! Always grateful

[@statquest]

Thank you very much!!! I'm glad to hear that the video was so effective, even though it's not very fancy. :)

[@dummmkopfff]

I've been watching quite a lot of your videos for the past few days to study for my finals and I'm so glad your videos exist! I'd be very desperate without them. Thank you so much for the amazing work! You have a natural talent of expressing complicated ideas so simply!

[@statquest]

Good luck with your finals and let me know how they go. :)

[@buihung3704]

The true definition of genius: teach other a very complex concept in a very simple way.

[@statquest]

Thanks!

[@kahlimang]

Dude, you did not just explain eigenvectors! I have spent years bumping into this term, googling it, not really getting it, and moving on. That is the first explanation that ever made sense, and its not even what I came here for. Thank you so much.

[@statquest]

bam! :)

[@BoZhaoengineering]

one of best interpretation of PCA. It is like turning several math techniques into one idea.

[@statquest]

Thank you! :)

[@Ananda110201]

This is the easiest way I understand PCA. I've been working with PCA algorithms for 2 years and two of my university professors provide lesson on PCA but couldn't make it clear. But, watching this 20 minutes video I understand in depth. Such a good lesson. Thank you so much!! ☺️ 😊

[@statquest]

Awesome!!! I'm glad the video was helpful. :)

[@kushagrachaturvedy2821]

You are a real godsend. Teaching such advanced concepts in such a simple manner and that too in just 20 mins is exceptional

[@statquest]

Thank you very much! :)

[@himanshu8006]

This is such a complex topic and with the visualization you made it so simple, you really are magical in explaining the concepts, a million thanks for this Josh

[@statquest]

Thank you!

[@beshr1993]

I took a whole seminar on this thing complete with a mini project and I didn't understand a single thing. Then comes along this little video and makes it all crystal clear in just 20 min! Hats off to you sir.

[@statquest]

Hooray! :)

[@evebogomil2777]

Have a test on my Data Science course tomorrow, I was so lost with how to visualise what we are doing in every step and this video helped me so much!

[@statquest]

Best of luck on the exam. Let me know how it goes. :)

[@onbeatz90]

you are straight up saving my phd thesis proposal, I wrote I'm gonna be using PCA but didn't understood it properly until now thank you

[@statquest]

Good luck!

[@bec_Divyansh]

The way you explain these supposed complex topics with ease and in a very interactive way is just out of the world! Best content out there ❤❤

[@statquest]

Thank you very much!

[@JohnEusebioToronto]

This is without question the best explanation for PCA I have ever seen. Much clearer than my PhD multivariate statistics course. Thanks so much!

[@statquest]

Awesome! :)

[@kachappillyjean]

This is what a good teacher can do to you ! Now I can explain PCA even when I am woken up from sleep ! Thank you Josh ! You have amazing talent at teaching !

[@statquest]

Thank you very much! :)

[@darkfafi]

I am a programmer, and apply mathematics within my code for 10 years already. But I know none of the terminology because I am self thought. So, I always feel like a fool watching videos on mathematics because they mix in terminology and go too fast over basic knowledge or terms I do not have. While ultimately I know a lot of the logics which come with it. Leaving me clueless, even with things I already mastered in practice. This video really helped me connect the already linked logics I have, with the knowledge of terms and mathematical notation I don't have. Thank you so much for making this.. It helps a lot being able to connect what I know out of experience with the fundamentals of the knowledge itself and helps me grow within my field of expertise.

[@statquest]

Thanks! I'm glad the video is helpful. :)

[@tranminhhieu9492]

I've been looking for a clear explaination for eigenvector when i accidentally found it in a PCA video by StatQuest. You sir is a savior.

[@statquest]

Bam! :)

[@BBBBBBAAAl]

simply amazing. I just hope u never stop teaching us those 'complex' topics in such friendly and clear way.

[@statquest]

That's the plan!

[@alecvan7143]

Thank you very much! Opening my textbook, I was frightened by the Zs, phi, and "principal component directions" everywhere but as always your videos enable me to see the logic and fearlessly read the jargon :P

[@statquest]

Awesome! :)

[@user-zg9qx6yz4s]

Very impressive! I searched a lot of websites and you are the only one that make the conceptions clear. Your graphs and explanations are vivid and easy to understand.

[@statquest]

Thank you very much! :)

[@pouetpouet704]

Great job. I've rewatched this countless times today until it became as easy to explain to others as it was to understand ! You're truly a gifted teacher ! Keep up the great work ! Cheers from France !

[@statquest]

Merci!

[@bechumathew8819]

All i can say after watching the video is "Double BAM"😂

[@toploz_jr5597]

i have for the first time in my life visualized eigenvalues and eigenvectors. THANKS MY SAVIOR

[@statquest]

Hooray!

[@nabeelhasan6593]

Simply this is the best explanation of PCA on entire KZbin platform, After this you don't need to get anywhere

[@statquest]

Bam!

[@DeVirMagician]

You are probably the best teacher of maths in the world. I salute you.

[@statquest]

Thank you very much! :)

[@kittikajorns1811]

Tear really flows from my eyes after I watched this video. I learned several hours from my professor but almost did not understand. But you could teach me in under 30 minutes.

[@statquest]

Wow! Thank you! :)

[@franciszhang1809]

This is the best PCA video ever, finally understand how PCs come out, Josh u r genius

[@statquest]

Wow, thanks!

[@AnkitYadav-sc2sm]

You really made me feel the mathematics in PCA....... earlier I can solve the math in PCA but now I know what's the purpose of each step in finding PCA components. I'm a B.tech student of final year. Thank you ❤️

[@statquest]

BAM! :)

[@tomjanson4004]

Wow, we should all just start studying solely with yt. There simply is no better way to understand complex stuff than with a nice video like thise one. Thx

[@statquest]

Thank you! :)

[@raisaoliveira7]

No words to tell how this video helped me! Thanks a lot, Josh! Your way to explain is extremely simple and makes anything easy for us.

[@statquest]

Thank you very much! :)

[@abhijithmnair]

Hi Josh , I should say this that you make even the more complicated logic so simple for us to understand . For people like us who are in learning phase , that means a lot . Thank you very much .

[@statquest]

Thank you! :)

[@debasisdas2076]

Hi Josh, You are the gold standard that all teachers from all spheres should aspire to be.

[@statquest]

bam! :)

[@jdkworld97]

My professor starts with formulas etc. straight away. You start with the bigger picture and a geometric understanding. It makes it much more intuitive and easy to remember! Afterwards I link your geometric interpretation to the professor's formulas and then my understanding is complete! :) Whenever I teach other people, I will always remember to start with the big (yet correct!) picture before diving deeper because of you. It works way better than starting with the details

[@jdkworld97]

maybe Josh should start a business teaching people how to teach!

[@statquest]

Thank you very much!!! I'm glad my video is helpful.

[@sheanaynay8]

Wow man thank you! Just had a moment of clarity, teachers like you are rare!

[@statquest]

Hooray!!! I'm glad the video was helpful. :)

[@royalpkr1390]

Just incredible!! The best explanation of PCA ever!!! And I'm not even a native speaker of English while I can still understand you better than all the other PCA material written in my mother tongue!

[@statquest]

Awesome!!! Thank you very much. :)

[@leventcangultekin3006]

This video is by far the best explanation of PCA

[@statquest]

Thank you! :)

[@scheket]

I don’t know what is better: the song befor each lesson or my understanding of the theme after the lesson?) everything is the best!)

[@statquest]

double bam! :)

[@lucasparisi7394]

you took 10 minutes to blow my mind with your amazing explanation. Thanks!

[@LaylaMiki]

This video is really awesome !!! I wish I have a teacher like you ! Yours explanations are so clear ! Thank you very much for sharing your knowledge !!!

[@vivekcraman5489]

The quality of the content you provide is top-notch and is incomparable with some of the paid courses I've taken before. Thanks a lot for the effort you put into making these amazing videos. :)

[@statquest]

Much appreciated!

[@mohitdeshpande6210]

JUST WOW!! Never I had thought that Stats could be this efficiently & easily understandable!! I feel immensely lucky that the content of this quality is freely available on the internet!! Thanx a lotttt for this magnificent effort from the whole team of StatQuest😇

[@statquest]

Glad it helped!

[@silentassassin4929]

How ur calculating the parts that u said like 4 parts of gene 1 and 1 part of gene 2 please respond cannot understand

[@llDietryingll]

You're literally teaching ML better than uni, cheers mate

[@statquest]

Thank you! :)

[@fade-touched]

You have no idea how grateful I am!!! Your channel is the best!

[@statquest]

Thank you so much!!! I'm glad you like the channel. :)

[@Marcos61783]

Congratulations! This is the best explanation of PCA without overcomplicating things with matrixes. In my opinion, everyone who explain PCA should start from an explanation like this... Thank you for the amazing video!

[@statquest]

Wow, thanks!

[@aremon7491]

Really you make me clear after several months about PCA. Lots of love from Bangladesh.

[@statquest]

Thank you!

[@gunjeet40]

just amazing, how you clearly put across so complex concepts with ease..!

[@statquest]

Thanks! :)

[@MauricioPosser]

The best PCA explanation ever! Plus a linear algebra bonus!!! Thanks a lot!

[@statquest]

Thanks! :)

[@SeDa441]

Man this is the best video explaining PCA for biology. I've been struggling so much to understand it over the last 1 year. Finally, I get it haha. I am a MSc bioinformatics student

[@statquest]

Glad it helped!

[@SeDa441]

@@statquest Haha I have a committee meeting tomorrow. It was much needed

[@statquest]

@@SeDa441 Good luck!

[@SeDa441]

@@statquest thanks! I literally explained PCA to my committee the same exact way you did in this video. And they loved it and understood everything.

[@statquest]

@@SeDa441 That is awesome! Congratulations!

[@ilyabykov2437]

this is the most mind-bending thing I've ever attempted to learn so far.

[@statquest]

I hope the video was helpful! :)

[@tuskofgothos2637]

Excellent video! Seriously, you are the compass of biologists trying to navigate through the sea of biostatistics!

[@statquest]

Thank you! :)

[@charlespendragon1742]

You saved my future!!! Oh my god, this is amazing! You are a talent who can transfer complex to simple.

[@statquest]

Awesome! :)

[@SathyaSankar]

Explained very well, Starmer! I'm about to attend a Data Science Interview on 14th of this month. Your videos have been extremely useful for me to revise all concepts. I went through many comments under this video and it is amazing to see that you are taking time to reply to each and every comment! Even as a small youtuber, I'm not able to do that! Hats off man! I see that a few people are doing super thanks. 30% of that will go to KZbin. I will definitely come back and support statquest when I get a job soon. But not in the form of Super Thanks!

[@statquest]

Thank you and good luck with your interview! BAM! :)

[@ahmedboughammoura5990]

The ability to just explain complexe idea is just amazing! Thank you !

[@statquest]

Thanks!

[@leandrovegadure9930]

Man, this work of yours is pure gold. can't thank you enough

[@statquest]

Thanks! :)

[@gesuchter]

Glad I found your channel this month! Looking forward in inhaling all of your content :D It's a very great addition to the very emotionless lectures of my prof..

[@statquest]

Awesome, thank you! And thank you for your support!!!

[@amywilderson85]

When I search for PCA on youtube and I saw that Statquest has a video for it, I was sure that I will learn PCA without any pain. Thank you!!

[@statquest]

Bam!

[@erfanmoosavi9428]

I want to start learning machine learning and your videos are the best for me. Thank you so much!

[@statquest]

Happy to hear that!

[@mamado226]

This video can not be recommended enough! BAM!! the best PCA explanation in youtube BAM!!

[@statquest]

Thank you! :)

[@muhammadzulfikararief5966]

This hidden gem channel is so great, yet I found it 1 year after my graduation :/

[@statquest]

better late than never? :)

[@muhammadzulfikararief5966]

@@statquest true, thank you for sharing your knowledge! :D

[@shanthinagasubramanian2866]

This youtube channel has created a lot of interest in me for Machine learning concepts. I totally appreciate the efforts by Josh Starmer. Thanks Josh for the excellent explanations. By the far, the best tutorial videos on data science in the internet.. Free of cost !!!

[@statquest]

Thank you very much!!! :)

[@hermanadriaensen]

StatQuest you are my lord and saviour. If I could I'd start a religion about this channel. I'm an AI major and this has been so helpful thank you so much

[@statquest]

Thanks! :)

[@Ga18bo03]

I love the exitement of the "BAM!" moments, thanks really helpful

[@Pmarmagne]

I'm probably going to have to watch this video a couple more times to fully understand everything but this is really cool and very digestible. I was still able to understand the main concept from the first watch. Thank you Josh!

[@statquest]

Awesome, thank you!

[@daily-news-update-with-john]

You boil all of this down into very understandable bite-sized steps. Amazing job! thanks for your work in explaining this.

[@statquest]

Thank you!

[@nikhilgoparapu1001]

Hello Josh, I wanted to thank you. You are one of those great teachers who makes learning fun and easy. I’d prefer watching your videos again over a good movie. Thank you so much for all of your videos.

[@statquest]

Wow! Thank you! :)

[@ZLK2000]

One of the best explanations I’ve seen hands down. Thank you

[@statquest]

Thanks! :)

[@bilourkhan3345]

genius you are in the presentation of your knowledge...

[@statquest]

Thank you!

[@luisernestobuenosalasar5738]

Congrats on the excellent tutorial, it helped a lot! I just want to highlight what is said in 8:30: distances can not be negative and the reason to take the squared distances must be only mathematical convenience to obtain the fitted line.