THANK YOU, THANK YOU, THANK YOU! For the past 6 hours, I have read and watched videos on covariance to try and solve this one problem with no success. After watching your video, I worked the problem and immediately got the correct answer. You sir, are my hero!
1:55 bivariate relationships def: relationship between 2 variables 7:40 covariance - how variables 'co-vary', meaning -> how do they change together 8:13 linear relationships 9:13 formal definition covariance - descriptive measure of linear association between 2 variables - positive value indicates direct or increasing linear relationship (if one goes up, other goes up OR if one goes down, other goes down) - negative value indicates inverse relationship (if one goes up, other goes down) - focuses on DIRECTION of relationship, and NOT strength (thats what correlation does) 14:55 covariance formulas - 2 types: sample covariance and population covariance 23:05 review
lol... I picked up on this too...at first i was like...hmm interesting metahphor but hey...it works. Like everything else... Brandon (the stat wiz Foltz) misses very little. i wonder how many of these "perfect' videos were completed the first time?
@@BrandonFoltz I wouldn't say a shot pattern implies violence. Have had a lot of fun growing up skeet shooting. Don't know anyone who has been involved in violence using a shotgun. Statistically I might argue that point ;)
These videos are fantastic! After taking stats courses from multiple professors, I found that my knowledge of stats is jumbled and all over the place. Your videos are easy to understand and explain how all concepts fit together, which is exactly what I needed. Thank you so much for your time and effort into these videos! Also, as someone who gets a bit anxious about stats, the inspirational message at the beginning of the video was so lovely - your passion for teaching shows!
Hi, thanks for your videos, I have a question. If the value of the covariance doesn't matter, then why do we divide by n OR n-1 in the first place? That'll make the value smaller or bigger, but it won't change its sign...
That is very kind of you Mathieu. Sal is an inspiration to so many of us, but I think more so that people like him and me are even more inspired by you; the learners we seek to help. Keep working hard and never stop learning! - B
I have been going through a lot of video's regarding the subject of statistics (for university). Many other authors video's were sometimes confusing, but your video's were thorough, clear and well-build. Thanks for your video's, I hope they contribute financially as you deserve it! Greetings from Belgium.
In sample situations the n-1 is a "correction factor" (easiest way to put it) to account for the fact that we are using a point estimator in the sample. It is one of the hardest things to explain in stats (like degrees of freedom which is related). Not really easy to explain unfortunately...lol :)
These videos are really very wonderful. Even doing a high level, they are helpful for the basic concepts. Would love it if you'd get into more complex topics: clustering, time-series analysis etc
Thank you for these videos, Brandon. I have watched two of them on covariance and found them useful. I like how you emphasis the essential ideas. I notice that the videos don't have sequence numbers. So, for e.g., in the Statistics 101 series it's not clear which video precedes or follows another video. Having sequence numbers would be useful to me.
Sir, I have a question if I may. I understand when you say that covariant is a measure, or indication, of the sign of a relationship (positive or negative) but doesn't speak to the strength of this relationship. But what then is the intuitive way to picture different covariances. If the direction is all that matters, why can't we just have a covariance of -0.1 or +0.1. Those figures would tell us that a relationship is either positive or negative but doesn't the numerical VALUE of covariance represent anything? What's the difference between a covariance of 0.1 and 0.2 if the only thing that matters is the sign (0.1 and 0.2 both being positive.) Thank you for taking the time to read my question and please keep up the stellar work. I hope to one day, by the end of my course, understand statistics well enough to explain it as well as you do.
Hello! Thank you for your comment and for watching. My goal is to explain the basics so that you can take it from there on your own. Glad you are finding them helpful. Keep on learning; never stop! - B
I have seen a lot of instructive videos but you deliver the best I have seen. I have only seen this one till now but I will definitely see more! Thanks!
Thank you for posting your videos. You have been so helpful and speak clearly. The videos are student friendly and easy to follow. I wish that you could have been my college stats instructor back in the day =)
Thank you Neena! You had the ability in you the whole time. And what "back in the day?" LOL :) I am sure you are as sprightly as ever. All the very best, B.
Brandon, you are an amazing teacher who explains concepts clearly and concisely. A lot of thought and planning must have gone into making these series of videos to make them easy to comprehend. Thank you very much for making learning so much easier for me! :)
@kritpaco Oh thank you so much for your very nice comment! I do believe in trying to make these concepts as concrete as possible with examples so you can see them in the real world. Hang in there and keep learning! All the best, B.
Hey now! :) Rawr! If you go to my channel homepage and then look in the upper left corner you should see "Playlists." All my videos are organized there. RUclips is terrible about tying a video with its playlist.
i love you man. i keep going through my instructor's lectures a thousand times but i just won't get it until i watch your videos because he fails to describe basic things before he goes into deeper more complex stuff. you are literally saving my life this semester!
Oh you are welcome! But YOU are the awesome one :) Coming on here and making the effort to learn deserves the real praise. Hang in there! All the best, B.
Brandon, I would like to formally thank you for saving my grade!! I have a final exam tomorrow and I am so glad I came across your channel cause I feel so much more confident with the knowledge you have blessed everyone with! You're awesome and sooo helpful, thank you
I never though statistic can be so simple, your delivery of the content is so perfect that i will never forget the Covariance. Thanks a ton to you for preparing such a simple but strong concept.
Thank you for putting your lectures on RUclips. They have made my class life a lot better. Your lectures are clear and concise. Not only that but they far exceed my classroom lectures and materials.
I think it depends on the data you are measuring. If covariance is very small compared to the data values, then it doesn't tell you much about relationship of variables
Dear Mr Foltz, Thank you so much for this awesome video! All other videos made it look way more complicated, then your video came along and everything was as clear as a bell. The only thing that could improve this video is perhaps an explanation of why the formula works the way it does. Why does it return postive when there is increasing relationship and vice versa etc.. Thanks again for the video and if you ever make a digital course (like on udemy or something) I will buy it instantly! Do you plan on creating more complicated stats videos on for example data science and machine learning? That would be awesome!
Good video! What is the reason we are doing (x-x̄)(x-ȳ) and then divided by the observations? I know (x-x̄) means how far is the actual value of x from the x̄ BUT the reason of multiplying (x-x̄)(x-ȳ) and then dividing them with the observations. THANKS!
The sample variance always tends to under estimate the dispersion when compared to population.To compensate for it, its advised to divide the quotient by (n-1) rather than 'n'. Brandon great job with the videos and keep up the good work.You are real inspiration for the rest of us!!
another great video...I actually worked through the table example using an excel spreadsheet...I know almost nothing about excel...however in the few short minutes of watching you input formulas manually in excel like you did in that previous video...I WAS ABLE TO DO THE SAME THING FOR THE TABLE EXAMPLE IN THIS VIDEO... thanks again for sharing beyond the knowledge...but your unique way to really teach this stuff in a universally accessible way.... oh and thanks for helping me conquer and find a new love of excel. Worked around it for years... now can work "within" it. You're the best!!!!!
Hi teacher Brandom. I have a BIG question. How do I graph the Covariance with only one number? I saw the Sxy = 106.93, but I lost how do I draw the blue line? Please, let me know it!!! Thank you
Why does covariance affect the variance of two variables X and Y? My lecturer dropped this equation in with no explanation: var(𝑋 ± 𝑌 ) = var(𝑋) + var(𝑌 ) ± 2 cov(𝑋, 𝑌 )
Great video, Brandon. I just discovered your channel and have subscribed. I just want to point out one very small error. At 17 mins, you said "After we add them all up, we're going to subtract by n - 1." What you meant to say, of course, is "we're going to divide by n - 1." Anyway, I'm looking forward to watching your other videos.
Hello- I am in a doctoral Multivariate Stats course- with very little experience using SPSS software (and I originally took stats 23 years ago! I did well, and videos such as yours are helping me remember. However, I have very intense homework problems in which we must apply our "vast knowledge" of stats and run analyses in SPSS. I do have a few questions about "maximum likelihood estimates" and wonder if you have any videos that will address this specific need? Time is quite valuable to me, and I have watched many videos only to relearn something old without gaining anything that meets my specific needs. Therefore, I ask for your assistance of where to go next. Thank you very much. I have shared your information with my classmates as I know they are struggling as well (we were not adequately prepared for the course we are in now)- bad design by the school (and they will hear about it). :)
This helped me a ton! Thank you for explaining it so clearly and using examples....my instructor is so awful and I felt so lost...helped a lot! (BTW...shotgun target spread is not violent! I shoot trap for fun and its anything but violent :) )
Thanks for the simple explanation. I had a doubt, if the information we gain out of co-variance is just the sign, then why does the formula have a "divided by sample size (n-1) or N". Don't you think that would be unnecessary?
can you explain to me behind the ebit covariance? it's said that A company with a large variable structure is less likely to create a loss if revenues decline. why is that? Read more: Business Risk Ratios - CFA Level 1 | Investopedia www.investopedia.com/exam-guide/cfa-level-1/financial-ratios/business-risk-ratios.asp#ixzz3t9klMDgm Follow us: Investopedia on Facebook
Hi Brandon, I am student at RMIT, Melbourne reading my bachelor of bus in Mktg. Your start up of a video really motivates me as a receiver. I am relatively new and have faith in your produced videos. Can you explain me what are the "other" components that I should have better understanding and practical theory in order to excel myself on a given problem. Tks
Thanks for your video. you are the best and so helpful. I had problems with figuring out these and now I got it 100% after watching your video. I love your explanations. thanks a lot
I have a suggestion. Firstly thank you for a completely comprehensive tutorial. Since you explain things very deeply, for a part of your viewers it might be useful if your video was divided into parts with some titles, what you think of it?
I would like to learn "Understanding Covariance" from this Video lInk. But It seems to be gone. Could you please tell me where I can find the link to access it. Thank you very much
What type of covariance will it be if covariance value is 0.0053? A neutral type or positive type? I am confused since the sign is positive and that the value doesn't matter. In the solved example, for the given data, it is the population & not the sample so why did you take n-1 in the denominator?
Wonderful video and inspiring message. In case, if you have time, can you make a video on how z-value and Mahalobnis distance differ from each other?. Thanks a lot once again.
For all you engineers out there I did up a quick and drity matlab implementation: x = [12 30 15 24 14 18 28 26 19 27]' y = [20 60 27 50 21 30 61 54 32 57]' sample_size = length(x) mean(x) mean(y) scatter(x,y) x_minus_mean = x-mean(x) y_minus_mean = y-mean(y) x_minus_mean.*y_minus_mean % .* is matrix multiplication covariance_numerator = sum(covariance_numerator) % n-1 = 9, since there are 10 samples covariance = covariance_numerator/(sample_size-1)
You are a very good teacher but, you should be more quick and explain more of the logic behind it. You took lmost 7 minutes for calculations which are just easy for everybody to understand since it is just algebra.
If we dont care about the magnitude of the covariance and just care about its sign, then why in the formula we have to divide by n-1 ( or N) . If we just care about the sign then leaving out the denominator shouldn't affect the sign of the covariance, right?
Thank you, you have explained it very well. Usually in class, only the formula is given, and we are asked to solve the problems, but are not told what is its significance, and when to use it.
honestly i wish 70% of my tuition could go to people like you......
Agree!!!!!
THANK YOU, THANK YOU, THANK YOU! For the past 6 hours, I have read and watched videos on covariance to try and solve this one problem with no success. After watching your video, I worked the problem and immediately got the correct answer. You sir, are my hero!
I can't thank you enough Brandon on creating these videos that breaks down complex topics in such easy to understand way. 1 fan up.
The easiest and the best explanation.
1:55 bivariate relationships
def: relationship between 2 variables
7:40 covariance
- how variables 'co-vary', meaning -> how do they change together
8:13 linear relationships
9:13 formal definition covariance
- descriptive measure of linear association between 2 variables
- positive value indicates direct or increasing linear relationship (if one goes up, other goes up OR if one goes down, other goes down)
- negative value indicates inverse relationship (if one goes up, other goes down)
- focuses on DIRECTION of relationship, and NOT strength (thats what correlation does)
14:55 covariance formulas
- 2 types: sample covariance and population covariance
23:05 review
Great video, thank you very much!
Great video! Thanks
great explanation
Best statistical tutorial. Thanks for your efforts in educating us.
Can i get the ppt s used in the lecture for reference.
"I don't like to use violent metaphors like that" LOL
Well, I don't hahaha Sometimes it just comes to mind. 🙃
lol... I picked up on this too...at first i was like...hmm interesting metahphor but hey...it works. Like everything else... Brandon (the stat wiz Foltz) misses very little. i wonder how many of these "perfect' videos were completed the first time?
@@BrandonFoltz I wouldn't say a shot pattern implies violence. Have had a lot of fun growing up skeet shooting. Don't know anyone who has been involved in violence using a shotgun. Statistically I might argue that point ;)
@@taylorschneider6967 Agreed, shotgun pattern is not inherently violent, so the association with violence is his own projection.
These videos are fantastic! After taking stats courses from multiple professors, I found that my knowledge of stats is jumbled and all over the place. Your videos are easy to understand and explain how all concepts fit together, which is exactly what I needed. Thank you so much for your time and effort into these videos! Also, as someone who gets a bit anxious about stats, the inspirational message at the beginning of the video was so lovely - your passion for teaching shows!
Feel totally the same
"You may just have a temporary tough patch." You are so encouraging! Thank you!
Hi, thanks for your videos, I have a question. If the value of the covariance doesn't matter, then why do we divide by n OR n-1 in the first place? That'll make the value smaller or bigger, but it won't change its sign...
Well, short answer is that covariance value is required for other calculations like correlation
I really like your videos, you teach very well. You are very comparable to Salman Khan from Khan Academy. We need teachers like you on RUclips!
That is very kind of you Mathieu. Sal is an inspiration to so many of us, but I think more so that people like him and me are even more inspired by you; the learners we seek to help. Keep working hard and never stop learning! - B
+Brandon Foltz that was a really kind statement :)
+Brandon Foltz Yeah i agree with you Brandon. Mathieus compliment was well written, but not a A+ compliment, so a -B grading is justified.
I have been going through a lot of video's regarding the subject of statistics (for university).
Many other authors video's were sometimes confusing, but your video's were thorough, clear and well-build.
Thanks for your video's, I hope they contribute financially as you deserve it!
Greetings from Belgium.
Thanks a lot for your awesome presentation.Just that at 17:00 it should be "divide" and not "subtract"
Well... you do need to (n-1) but then you divide the sum of the products by (n-1). But yeah he forgot to say divide.
In sample situations the n-1 is a "correction factor" (easiest way to put it) to account for the fact that we are using a point estimator in the sample. It is one of the hardest things to explain in stats (like degrees of freedom which is related). Not really easy to explain unfortunately...lol :)
Thank you Sir, I finally understood the concept of Covariance
you teach so well!
Through your teaching, I can easily understand the concept of covariance.
Deeply appreciate.
Honestly, best explanation of covariance I ever heard
These videos are really very wonderful. Even doing a high level, they are helpful for the basic concepts. Would love it if you'd get into more complex topics: clustering, time-series analysis etc
Thank you for these videos, Brandon. I have watched two of them on covariance and found them useful. I like how you emphasis the essential ideas.
I notice that the videos don't have sequence numbers. So, for e.g., in the Statistics 101 series it's not clear which video precedes or follows another video. Having sequence numbers would be useful to me.
Very, very clear, structured and visual demonstration of Covariance.
> "Fire all the tutors and professors, we've found THE GUY !!" - Me, 2020
Sir, I have a question if I may. I understand when you say that covariant is a measure, or indication, of the sign of a relationship (positive or negative) but doesn't speak to the strength of this relationship.
But what then is the intuitive way to picture different covariances. If the direction is all that matters, why can't we just have a covariance of -0.1 or +0.1. Those figures would tell us that a relationship is either positive or negative but doesn't the numerical VALUE of covariance represent anything? What's the difference between a covariance of 0.1 and 0.2 if the only thing that matters is the sign (0.1 and 0.2 both being positive.)
Thank you for taking the time to read my question and please keep up the stellar work. I hope to one day, by the end of my course, understand statistics well enough to explain it as well as you do.
Hello! Thank you for your comment and for watching. My goal is to explain the basics so that you can take it from there on your own. Glad you are finding them helpful. Keep on learning; never stop! - B
Thanks Gus! I get several comments a day from people who like the intro/outro bits, and one can always fast forward. :D
@ 17:00 did you mean divide instead of subtract?
I have seen a lot of instructive videos but you deliver the best I have seen. I have only seen this one till now but I will definitely see more! Thanks!
Thank so much! I appreciate you watching and learning. Glad you found them helpful. Keep on learning!
Thank you for posting your videos. You have been so helpful and speak clearly. The videos are student friendly and easy to follow. I wish that you could have been my college stats instructor back in the day =)
Thank you Neena! You had the ability in you the whole time. And what "back in the day?" LOL :) I am sure you are as sprightly as ever. All the very best, B.
Me too Neena, me too, my stats professor is a zombie and can barely explain things, loll...thank goodness for Brandon!
Thanks so much for this video. It was part of assigned viewing for a Business Analytics program I'm taking, and was very helpful.
Brandon, you are an amazing teacher who explains concepts clearly and concisely. A lot of thought and planning must have gone into making these series of videos to make them easy to comprehend.
Thank you very much for making learning so much easier for me! :)
@kritpaco Oh thank you so much for your very nice comment! I do believe in trying to make these concepts as concrete as possible with examples so you can see them in the real world. Hang in there and keep learning! All the best, B.
10x better than those $200 textbook, thumb up!
Hey now! :) Rawr! If you go to my channel homepage and then look in the upper left corner you should see "Playlists." All my videos are organized there. RUclips is terrible about tying a video with its playlist.
i love you man. i keep going through my instructor's lectures a thousand times but i just won't get it until i watch your videos because he fails to describe basic things before he goes into deeper more complex stuff. you are literally saving my life this semester!
@ragsanoor My one moment of lucidity! :) Thank for the kind comment and I wish you all the best, B.
Oh you are welcome! But YOU are the awesome one :) Coming on here and making the effort to learn deserves the real praise. Hang in there! All the best, B.
Brandon, I would like to formally thank you for saving my grade!! I have a final exam tomorrow and I am so glad I came across your channel cause I feel so much more confident with the knowledge you have blessed everyone with! You're awesome and sooo helpful, thank you
Thank you! :) Good old PCA...haha...I will get to that...eventually! All the very best, B.
Thank you for this! You make learning a wonderful experience!
Thanks. This tutorial was very very helpful. Keep more coming
I never though statistic can be so simple, your delivery of the content is so perfect that i will never forget the Covariance. Thanks a ton to you for preparing such a simple but strong concept.
Thank you for putting your lectures on RUclips. They have made my class life a lot better. Your lectures are clear and concise. Not only that but they far exceed my classroom lectures and materials.
What does "near zero" mean? Is 2.1 near zero? Is 0.5 near zero? Is -15.8 near zero?
I think it depends on the data you are measuring. If covariance is very small compared to the data values, then it doesn't tell you much about relationship of variables
Dear Mr Foltz,
Thank you so much for this awesome video! All other videos made it look way more complicated, then your video came along and everything was as clear as a bell. The only thing that could improve this video is perhaps an explanation of why the formula works the way it does. Why does it return postive when there is increasing relationship and vice versa etc..
Thanks again for the video and if you ever make a digital course (like on udemy or something) I will buy it instantly! Do you plan on creating more complicated stats videos on for example data science and machine learning? That would be awesome!
Thank you, Brandon!
You have a way to make your students understand each statistical concept very well.
Well done! Great Job!!
Brandon, thank you so much. I am in a class and you explain it so much better than our instructor. You are the man sir.
Good video! What is the reason we are doing (x-x̄)(x-ȳ) and then divided by the observations? I know (x-x̄) means how far is the actual value of x from the x̄ BUT the reason of multiplying (x-x̄)(x-ȳ) and then dividing them with the observations. THANKS!
My whole appreciation for your effort... really grateful.
Didáctico y bien explicado, cuando se conoce el tema es fácil de explicarlo. Es un buen video. Gracias.
Thank you very much Scott! All the best, B.
The sample variance always tends to under estimate the dispersion when compared to population.To compensate for it, its advised to divide the quotient by (n-1) rather than 'n'.
Brandon great job with the videos and keep up the good work.You are real inspiration for the rest of us!!
another great video...I actually worked through the table example using an excel spreadsheet...I know almost nothing about excel...however in the few short minutes of watching you input formulas manually in excel like you did in that previous video...I WAS ABLE TO DO THE SAME THING FOR THE TABLE EXAMPLE IN THIS VIDEO... thanks again for sharing beyond the knowledge...but your unique way to really teach this stuff in a universally accessible way.... oh and thanks for helping me conquer and find a new love of excel. Worked around it for years... now can work "within" it. You're the best!!!!!
thank you, Xièxiè, gracias, dankeschön,shukran, Sha'abi Ndo (Mixtec).
Thanks. That was a swell of a simplified explanation on covariance. Keep the spirit.
Deeply touched by this video. :)
Great explanation! Finally I fully understand covariance.
Thank you. :)
Hi teacher Brandom. I have a BIG question. How do I graph the Covariance with only one number? I saw the Sxy = 106.93, but I lost how do I draw the blue line? Please, let me know it!!! Thank you
Why does covariance affect the variance of two variables X and Y? My lecturer dropped this equation in with no explanation:
var(𝑋 ± 𝑌 ) = var(𝑋) + var(𝑌 ) ± 2 cov(𝑋, 𝑌 )
Thank you so much! It was very useful for RAP preparation! Waiting for new exciting videos from you!
simple understanding methodology of teaching complex subject statistics hats off to your teaching style...
Great video, Brandon. I just discovered your channel and have subscribed. I just want to point out one very small error. At 17 mins, you said "After we add them all up, we're going to subtract by n - 1." What you meant to say, of course, is "we're going to divide by n - 1." Anyway, I'm looking forward to watching your other videos.
This was incredibly helpful. Thank you!
Hello- I am in a doctoral Multivariate Stats course- with very little experience using SPSS software (and I originally took stats 23 years ago! I did well, and videos such as yours are helping me remember.
However, I have very intense homework problems in which we must apply our "vast knowledge" of stats and run analyses in SPSS. I do have a few questions about "maximum likelihood estimates" and wonder if you have any videos that will address this specific need? Time is quite valuable to me, and I have watched many videos only to relearn something old without gaining anything that meets my specific needs. Therefore, I ask for your assistance of where to go next.
Thank you very much. I have shared your information with my classmates as I know they are struggling as well (we were not adequately prepared for the course we are in now)- bad design by the school (and they will hear about it). :)
Very good and straitforward explanation, liked it very much, very helpfull. Thank you! :)
This helped me a ton! Thank you for explaining it so clearly and using examples....my instructor is so awful and I felt so lost...helped a lot! (BTW...shotgun target spread is not violent! I shoot trap for fun and its anything but violent :) )
Thanks for the simple explanation. I had a doubt, if the information we gain out of co-variance is just the sign, then why does the formula have a "divided by sample size (n-1) or N". Don't you think that would be unnecessary?
can you explain to me behind the ebit covariance? it's said that A company with a large variable structure is less likely to create a loss if revenues decline. why is that?
Read more: Business Risk Ratios - CFA Level 1 | Investopedia www.investopedia.com/exam-guide/cfa-level-1/financial-ratios/business-risk-ratios.asp#ixzz3t9klMDgm
Follow us: Investopedia on Facebook
Great lesson! Question: when you use sigma for covariance, shouldn't it be sigma squared? because sigma would be standard deviation?
Hi Brandon, I am student at RMIT, Melbourne reading my bachelor of bus in Mktg. Your start up of a video really motivates me as a receiver. I am relatively new and have faith in your produced videos. Can you explain me what are the "other" components that I should have better understanding and practical theory in order to excel myself on a given problem. Tks
I really wish I had discovered your videos along time ago. It would have saved me a lot of confusion and frustration. Thank you!!!
Wow, you made it 🪄understandable🪄😮
Thank you
Thanks for your video. you are the best and so helpful. I had problems with figuring out these and now I got it 100% after watching your video. I love your explanations. thanks a lot
this video makes me understand completely about Covariance.So many thanks
I have a suggestion. Firstly thank you for a completely comprehensive tutorial. Since you explain things very deeply, for a part of your viewers it might be useful if your video was divided into parts with some titles, what you think of it?
I would like to learn "Understanding Covariance" from this Video lInk. But It seems to be gone. Could you please tell me where I can find the link to access it. Thank you very much
If I don`t mistake last average number in sample exercise should be 96.24 not 962.4
What type of covariance will it be if covariance value is 0.0053? A neutral type or positive type? I am confused since the sign is positive and that the value doesn't matter.
In the solved example, for the given data, it is the population & not the sample so why did you take n-1 in the denominator?
Awesome! Glad you find them helpful!
Why do you devide by N or n-1, if only the sign matters. It's not gonna change the sign, so it doesn't matter, so why do it? And why n-1 specifically?
You are awesome teacher.... How I wish all teachers teaches like you. Keep it up Brandon Foltz. Hope to see video from you about Quality tools.
Wonderful video and inspiring message. In case, if you have time, can you make a video on how z-value and Mahalobnis distance differ from each other?. Thanks a lot once again.
For all you engineers out there I did up a quick and drity matlab implementation:
x = [12 30 15 24 14 18 28 26 19 27]'
y = [20 60 27 50 21 30 61 54 32 57]'
sample_size = length(x)
mean(x)
mean(y)
scatter(x,y)
x_minus_mean = x-mean(x)
y_minus_mean = y-mean(y)
x_minus_mean.*y_minus_mean % .* is matrix multiplication
covariance_numerator = sum(covariance_numerator)
% n-1 = 9, since there are 10 samples
covariance = covariance_numerator/(sample_size-1)
YOU ARE WONDERFUL! MY Professor gets paid for the work you do with us :-)
Just watched it for a refresher. Lovely video, very well done! And so encouraging thank you good sir!
What about non-linear relationship like y = x^2 where x>0? Covariance can measure their relationship?
You are a very encouraging teacher, sir. I really appreciate your videos. Quick question: why is the denominator n-1 instead of just n?
Best ever videos. Thanks for sharing your knowledge and your efforts for making such detailed videos and simple ones to learn the basics.
I have been binge watching your videos for past 2 days and I have completed 3 playlists.
Hi Brandon
I really liked your video. You are a fantastic teacher. Thank you for helping me to better understand covariances.
Oh Brandon sometimes the flow of your playlists and video numbers are not clear.otherwise excellent
i love how you teach and how you start with encouraging words. u make the course so easy
thank u for your video I'm studying basic statistics to pass a DSST exam. Your video was great and very easy to follow. Keep it up!!!
Your videos continue to simplify things and help me understand things my university lecturer, nice guy that he is, does not explain well. Thank you!
You are a very good teacher but, you should be more quick and explain more of the logic behind it. You took lmost 7 minutes for calculations which are just easy for everybody to understand since it is just algebra.
If we dont care about the magnitude of the covariance and just care about its sign, then why in the formula we have to divide by n-1 ( or N) . If we just care about the sign then leaving out the denominator shouldn't affect the sign of the covariance, right?
Thank so much!!!
Brandon I gave a thumbs up and subscribed in the first minute itself. You are awesome. Thanks for a great video!!
Thank you for all these helpful videos. As a former tutor you are doing wonderful job.
Amazing video - Didn't get covariance until I saw this video.
Thank you so much for these videos, they are trully awesome!! Greetings from Honduras.
Thank you, you have explained it very well. Usually in class, only the formula is given, and we are asked to solve the problems, but are not told what is its significance, and when to use it.