Statistics 101: The Covariance Matrix

[@DucHoang-xp1cs]

List of people who have faith in me: My dad My mom Brandon Thank you for your priceless contribution!

[@reeceanderson911]

Protect this man at all costs!

[@yanniksimpson]

I really needed that short motivational part in the beginning. Thank you!

[@wisemandenny8]

I watched this video to study for my stats 2 final... I was so happy to hear some very kind words of encouragement at the beginning. Teachers like you who care about their students (or in your case, just all students in general) are a treasure for this world. Thanks for being part of that amazing group of people who make the world a better place through caring education.

[@gutlesswarrior]

I'm only one minute into the video and I already have to thank you for this. So many people get down on themselves for not understanding a concept without realizing just how far they've come. Thank you for being so positive! We need more people like you.

[@DKZomb0]

I did not see that wholesome intro coming... But it was really welcome :)

[@fadikf]

Finally someone who is fluent in both stats and English ! Please keep making videos

[@jessi9375]

I really like that you give some positive words in the beginning. You have no idea how much that actually helps boost my confidence! :)

[@sahb8091]

Your pep talks, and I don't use that word to trivialise your intentions, are very encouraging. They have the quality of being uplifting by not being condescending. My ambition is to be a qualified teacher in the next 2-3 years and I really, really hope I can learn to express things as clearly, and positively, as you do sir.

[@evanstoid]

did you end up becoming a teacher?

[@xXMushiriXx]

This is the best intro ever.., Just what I needed to hear, at the right time and in the right place.

[@Puzzle488]

Hi, As a worker in the field, who has been out of statistical analysis for about 15 years, I found you videos (and I've watched over 20 of them) very clear, concise, and helpful. Your videos are much clearer than most of my statistics books. Thank-you very much for the time and effort to make these videos and making the statistical analysis so clear.

[@BrandonFoltz]

@resal81 Hello! Thank you for watching and for your question. Covariance, correlation, and regression are all based on a matching concept for each variable. For example in this video, the returns are "paired" by month. If we were doing a height/weight analysis for people, the height/weight pair would be for the same person. The pair order does not matter so long as they remain a pair. Hope that helps! All the best, B.

[@devaratikar5397]

You explain the things so simply and by taking practical examples that the concept becomes crystal clear

[@earlcarter1750]

Thank you so much for your encouraging words and for making this confusing subject easier. No one takes the time to explain like you do.. you are truly a teacher. Thanks again

[@paulallen579]

I just want to tell you that you're a very kind man and that your videos are of the highest quality in terms of content.

[@sahb8091]

Thank you for actually caring about teaching and education. It makes all the difference and I've forwarded and shared these videos with my classfellows.

[@BrandonFoltz]

Oh thank you so much Mohammad! I appreciate you taking the time to learn along with me. All the best, B.

[@daviddrake60]

How long has it been since I heard such encouragement! "Saruman believes it is only great power that can hold evil in check, but that is not what I have found. I found it is the small everyday deeds of ordinary folk that keep the darkness at bay… small acts of kindness and love."

[@petercourt]

The intro was as wholesome as it was welcome! Brilliantly explained and very clear - thank you very much!

[@thelonelyone2713]

This is really a great video, the best statistic teaching channel I've came across so far. Looking forward to watch your next videos

[@supriyabisht5637]

I am learning it for Factor Analysis and was overwhelmed by the jargon before I saw your covariance and covariance matrix. Thank you!

[@nkosikhonagumede5755]

This video saved me so much of time. I couldn't find any text that explains this with such detail. Thank you!!

[@kaushikhatti7443]

Hi, The one thing that impressed me most is the quotes that you have used in every video of yours! Needless to say, I am understanding Stats better from watching your videos. Thanks so much.

[@BrandonFoltz]

Kaushik Hatti Thanks so much! Very glad you feel they help your learning. Keep on learning!

[@zairoxs]

I am working on a self-balancing robot that implements a Kalman Filter. It uses covariance as part of the calculation, and I spent about 5 days trying to learn it to no avail. I completely get it now. I just wish I had found your videos sooner. Thank you!

[@nhanNguyen-wo8fy]

Oh! I'm engineering student too! And Kalman Filter lead me here too!

[@vicadegboye684]

Me too!!

[@miloinindo]

More thorough than I needed but was very good.

[@ssshukla26]

KZbin is my classroom and Brandon is my machine learning mentor.

[@yandelyano]

Man, I liked and subscribed since the start of the video. It comes from the heart, thank you.

[@StephenReidN]

For the problem at 13:30 - In Excel 2016 you can choose to calculate variance for population (function: Var.P) or sample (function: Var.S)

[@justanotherpoet125]

Thanks a lot 🙏... I just started hearing about all these in my Data mining class and most of my peers seem to know about these and I started freaking out. Your videos are very descriptive and crystal clear. 🙂

[@outrebeauty]

Mr. Foltz thank you very much for your encouragement and excellent educational video. I wish you the very best.

[@ker0666]

I am french and I can grasp your very good explanation. That's perfect: to improve both my english ans my stat knowledge.

[@erick2051]

It just took me to to watch the plot at 7:57 to understand most of the topic. Amazing representation! many thanks

[@lwolstanholme]

best intro to a tutorial video ever thanks

[@BrandonFoltz]

@outrebeauty Thank you so much for your kind words. I am glad you find them beneficial. All the best in your work and studies! - B

[@sev3477]

Thank you so much for this incredible video ! it was so helpful ! I've never heard such clear an explanation (and the intro was exactly what I needed), so thank you again !

[@araeneangela]

Thank you Brandon, I was struggling with this concept in my finance class, but now it is much more clear as you have provided a 'window'

[@robbiemallett]

Hi Brandon, I needed to quickly refresh my knowledge on this for a piece of research and you did a great job explaining! Thanks.

[@desnamjp]

I literally FAILED multivariate statistics and these videos are making everything clear in preparation for my doctoral COMPS exam! Bradon, simply saying thank you will not suffice. The English language needs another word for your sacrifice and expertise!

[@ohalpin]

This is great thanks...jesus you taught me ten times more in the last 45 min than my uni teacher did in the last 9 (and painful) hours!

[@brandonb9416]

The intro really cheered me up!

[@kingj030]

Thanks, the intro is what I need right now!

[@nilosmitabanerjee2492]

Hey Brandon! Big fan of all your videos and content for years! Your explanations have been a backbone to my stats learning that I started using during my undergraduate degree and continue to do it till this very day when I am now doing my PhD! Can I request you to make a video on multiple linear modelling. Thanks, Love Akira

[@Melissameii]

Thank you for the pep talk in the beginning!!!

[@kvandep]

Thank you so much, incredibly useful! Grad student just getting in depth with stats, these videos are incredibly helpful!

[@Achrononmaster]

Constructive comment: you do not need to repeat the upfront message. It's nice, but only needs repeating once or twice. If somene persists and follows the later videos in your series then just tell them to refer to the first intro video for this motivaitonal stuff. Don't underestimate your followers for their ability to be self-motivated. They wouldn't be learning via KZbin if they were not already somewhat motivated. Having said this... you do a better job than I can in teaching via online vids. So keep up the great work Brandon.

[@achillesarmstrong9639]

I spent a whole day to figure out what is covariance matrix , the text book was explained badly. Your video make me understand it within 20 minute.

[@xiw5075]

It's cute to hear the encouragement at the beginning of a stats video.

[@darladarlading]

I wish all teachers and professors taught as well as you. We'd all be so much smarter than we are.

[@swetasrini]

This is a great explanation! Thank you Brandon!

[@vicadegboye684]

All I can say is Wow!! Ok. Let me add these: I'm currently taking a class on controls and state estimation, where I'm learning about Kalman and Particle filters. The covariance matrix part was not clear to me until now! Thank you!

[@sajikuttan5956]

This is really a good one. You have explained like a primary school teacher which is what beginners want. To have more clarity, you may show the data set that was used, also before going for the computations. In fact, covariance matrix is obtained by finding the variances between each variable and then grouping it as a matrix. What is the significance of this matrix as compared to looking/analyzing individual covariances? Suppose the variables are height, weight, wealth and education of 20 people, how do we explain the physical meaning of the covariance matrix obtained from this data?

[@shariulhashmi6343]

Amazing work man. Not new to stats, but I really wish I had started with these lectures. Thanks a lot and keep up with the good work.

[@ayanaoden5727]

Awesome video! This really helped make this concept clear. I wish my textbooks had such concise explanations.

[@thisxvi3txgotxrice]

The words of encouragement at the beginning were so helpful! Thank you~~

[@Grkgermn333]

Thank you for this video, Brandon. I'm taking an online class on robotics, and the instructor just skipped over explaining covariance matrices (whilst teaching something called Kalman Filters). This video helped a lot!

[@lekhaemerald]

Hi! Can you please let me know a to which online robotics class are you taking? I want to take up one too!

[@yael123gut]

Great!! Very well explained, my applauses

[@Thiyagadhayalan]

at last i understood what covariance matrix is, thanks Brandon!

[@lakeside_serenity167]

crisp and clear explanation sir! love u!

[@yutassmilehealsme6572]

Thanks for the motivation in the beginning.. I have to take mandatory stats and I’m not very good at it

[@henrikmanukyan3152]

for the problem of 13:30 you can calculate also the variance and covariance of samples as well now. Check out the functions of covariance.s and var.s.

[@albertyao4457]

u are so great and ur teaching is amazing please keep going on !!! from Taiwan !!

[@prabhapanth6762]

Thank you for a clear and easily understood lesson on covariance. request you to teach factor analysis and principal component analysis as well, we will all greatly benefit from such a lesson. Thanks.

[@joannwang6486]

Thanks sir! Clear explanation and make a complicated math to easy understand

[@DirectionEverywhere]

Helped me to finally understand it, and I have an exam in stat soon!! THANKS!!

[@cherylpatton4749]

You mention that covariance values only tell us positive or negative relationship unless it is "at or around zero". Can you give an approximate number range of just how close to zero the number must be to tell us that there is probably no relationship?

[@flowdsch9865]

Very well explained, exactly what I have been looking for! Thanks

[@neilhack10]

Much thanks, the figure at 9.21 helps a lot !

[@romanvasiura6705]

Thank you for this amazing lesson!

[@martinamarina6688]

THANK YOU!!!! it is so great to be able to hear something and understand it. :)

[@zckfu]

Very excellent video teaching here. I do not expect learning statistics can be so easy especially the conceptual aspects. Very nice work. For me, if higher level topics could be covered, I will be much appreciating such as logistic regression, count model, odd ratios, chi-square, ...

[@celinikal]

I was given an assignment to interpret statistical output and couldn't figure out the variance-covariance table. Thank you for this video.

[@marianievesvarela5378]

hi Brandon, as always you make everything very easy, thanks and congratulations

[@alancook79]

Goes over some very basic concepts which are often blown past in class. It's good to slow down and get the fundamentals explained again.

[@tausal1]

Thank you for a such a clear explanation sir!

[@Max-my6rk]

Why r u so awesome! Best statistic teacher!!!!

[@BrandonFoltz]

Awe thank you so much! I've had many great teachers over the years so I just try to do what they do. Thanks so much for watching and keep on learning!

[@BrandonFoltz]

You are very welcome! Pay it forward. :)

[@kevinharrison2719]

Great video! Very helpful.

[@youngjin8300]

clear, well-explained video! I appreciate it

[@npt0112]

Thanks a lot Brandon.

[@tassoskat8623]

Great videos I'm glad I found you

[@KrishnadevM]

Thank you for a very nice explanation!

[@Michelle-mv1gg]

Thank you for making this topic clear for me ....

[@sachinthakkar4131]

Thanks for these videos - top quality

[@maxpercer7119]

Do you have the original raw data for x1,x2,x3,x4 for the matrix covariance example. Excellent video!

[@dmoaddle]

Thanks for this video. I have one question. How the variance, which is the square power of standard deviation, equals to covariance which is calculated by another formula?

[@annereeser9279]

Thank you so much. You make things so clear.

[@cunghoctienganh]

Thank you very much indeed.

[@cunghoctienganh]

I am struggling to get to know Structural equation modeling. I starts to read book and watch KZbin video for understanding it, however there are many unfamiliar terms for me. Do you have any advices for me to understand SEM easily? i am not familiar with statistics before except for the regression (i learn this from you when i did my research using regression). However, things are getting tough now, i have to get to know SEM for my research. I am struggling indeed. I know it is very time costing to make a video as i am myself a youtube creator as well, so i am very appreciated if you could give me any hint for this? I can get a lot of sources for SEM, but you are the best who can simplify everything.

[@marinabaskakova2333]

Thank you, you’re saving my life! 🤩

[@resal81]

Great video. Really. One question though; for calculating covariance of two variables x1 (20 items) and x2 (20 items), do you get different covariances if you change the order of items in each variable?

[@lkjadslkfjlaksj]

Thanks for this! I really like your teaching style :)

[@zdl3014]

sir this video really help me a lot, but i have one question, why the sum of all the elements of the covariance matrix rather then the sum of all elemens on the diagonal is the variance of the sum of the random variables involved? thank you

[@ALI_B]

Hello, great job. Don't you stop doing these amazing videos. I have a question : what is your method for analyzing correlation between qualitative and quantitative variables ?

[@sum1sw]

Brandon, do you have or know of a video (or a website) that shows the details of how to calculate the "Parameter Correlation Matrix"? Just to be clear, let's say I regressed 50 x, y points (using orthogonal distance regression), and I have four adjustable parameters (a1, a2, a3, a4). How do I arrive at the parameter correlation matrix?

[@agustinblacker1324]

your videos really rock! Hoping to see time series, and neuronal network! I; ll share them to my mates!

[@speakers159]

WOW, such a positive support

[@mhamd2020]

Dear Mr. Barandon, This is an absolutely awesome incredible beneficial tutorial. Please keep going, and if there is a way for donation we all welling to.. thank you so much ..

[@joelagbo3862]

You are a blessing !!!

[@FilmNerd2010]

Thank you! So helpful!

[@chenwei7]

Thank you very much, so happy with the statistics!

[@oduduafangide6380]

please do you have a video on interpeting statistics on reserch papers. i dont understand it

[@petrhorak931]

Love the motivation part. I feel really special now. :D

[@LumiHeartbeats]

Hi Brandon, thanks a lot for the video, it's very helpful. But just to avoid confusion, isn't in Excel, now we have both co-variance function using population co-variance as well as the sample co-variance as: COVARIANCE.S(). Dose this formula give us the correct result?