Covariance and the regression line | Regression | Probability and Statistics | Khan Academy

Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacademy.org/math/stat...
Covariance, Variance and the Slope of the Regression Line
Watch the next lesson: www.khanacademy.org/math/prob...
Missed the previous lesson?
www.khanacademy.org/math/prob...
Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Probability and Statistics channel:
/ @khanacademyprobabilit...
Subscribe to KhanAcademy: kzbin.info_...

[@MaxAgapoff]

Sal is awesome! Einstein was right: *If one understands something properly, one can explain it simply*

[@tadaasam2036]

dayum , its like pulp fiction. everything meets up in the end and story makes sense

[@user-ti1rx5ui2e]

المقطع نزل وعمري ٨ 🥺والحين ١٩ واحتجته لقيته بعد هذي السنين

[@shreyaschaturvedi1933]

best explanation of covariance, hands down! Thank you, Sal

[@svsujeet]

Awesome job...Great work...Inspirational. My mind is cooking right now on lots of new ideas based on your education delivery technique here.

[@Skulltroxx]

thanks a lot for doing the entire derivation thing, I couldn't understand two formulas for covariance while I wasn't able to derive one from another

[@user-xi9sx7wn5v]

I just wanted to have a look into a video on regression but ended up with three days of watching dozens videos on statistics. Let me go, Khan!

[@zingg7203]

I hope my instructor tells this instead of spreading cancer.

[@leechmaster21]

And I hope you dump that loser boyfriend of yours.

[@mandelbro777]

Amen .... statistics teachers need to be taught statistics using simpler methods such as this, especially the understandability for beginners of the EXPECTED notation method. So much easier than smashing students with symbols they don't understand and then muttering about how formula A translates to formula B because of "adfjhasdfljhasbdclahbflwhef". Students all migrate directly to the bar after class, for some reason :)

[@L2.Lagrange]

Great video. Defiintely will be checking out many other of your statistics vids

[@SimplyAndy]

Wow. Beautifully sequenced and explained so well in a short vid..

[@youngcw3177]

It helps a lot!!!!thank you!

[@yvonnet8613]

wow that just made soo much sense. thanks

[@ad2181]

Keep up the good work, you make my day.

[@ericmorris5914]

Amazing!!! thanks for the insight

[@MyJackzhang]

Thank you!

[@riderblack6401]

so gooD!

[@AsgharKhan-fd1ul]

KHAN IS KING!

[@ketansharma6955]

This video was gorgeous !

[@pedrogaspa]

excellent!

[@Tyokok]

Thanks for the great video Khan! One question, so does multiple regression has the same thing? say i have b0, b1, b2 (b0 is the intercept), then do we still have b1, and b2 with the same formula? Cov(y, x1)/ var(x1), and Cov(y, x2)/var(x2)? Thank you!

[@PrincessGillianWang]

thank you 100000000+. you are amazing!!

[@jfht318]

I dont even know why Universities exist. Sal is providing an amazing service for free while universities provide a joke of a service for a lot of money. Sal should therefore put universities out of business but these cancerous institutions just do not disappear . This guy is what you call a teacher not some joke of a stuck up professor. No homework, no BS modules, no time wasting with commuting, just pure learning the way you want it at peace in your home; how it should be.

[@aveekdas6343]

very nicely explained.

[@MohamedElsheikh22]

You are the best !

[@james9254]

Best Teacher Ever:)

[@royzou4471]

You are a Life saving god of maths!! Please do more proofs !

[@dashzevegp7685]

Thank you.

[@Sutto3721]

Yes, it is the mean but it should be differed from the mean of a sample. The expected value is the mean of a population, of what to expect as the mean of the population.

[@ad2181]

Sal, The covariance is related to the correlation function of two variables and also convolution.

[@rizwanshahid8242]

can you please do a video on sample co variance and why we use n-1 in the formula for sample covariance and not n-2

[@jsymons1985]

I like this video but it could use a concrete example. Also, a covariance matrix would be a good topic

[@ygbr2997]

happy new year

[@tranngoc5692]

Character In the video It's great, I like it a lot $$

[@JI77469]

"...then it would make sense that they have a negative covariance: when one goes up the other goes down, when one goes down, the other goes up." Why is something like this always said in favor of "...when one goes above its mean, the other goes below it's mean, when one goes below it's mean, the other goes above it's mean." Why does it matter if one goes up/one goes down if it's not relative to the mean? Or is this what is really meant when one says colloquially "if one goes up the other goes down"? Just trying to clarify since I'm teaching covariance soon...

[@LastManRising]

can anyone tellme wheree can i get these slides khan sir teaches from in this statistics playlist? @Khan Academy

[@dobraOsoba]

pretty colors

[@vinaykumardaivajna5260]

12 Years wow still going On wow wow wow

[@sreekumarmenonk7678]

I pressed Del button twice between @3:12 and @3:29 before it hit its not my screen :p

[@beedoog0717]

already knew it

[@binashbobby8891]

beginning part of video helped, but getting to the middle confused me.

[@gurminderbharani1260]

Thank you

[@sofieskarupkristensen893]

Who is speaking on this? This guy is my favourite!

[@animeonperseest]

It's Chris Brown

[@djaiseman]

What is expected value??? Is that the mean?

[@rruizanimations1]

yes it seams

[@stevecharmer4296]

You forgot a closing parentheses after expected value Y

[@ddennis911]

how many times did he say expected value ? :D

[@Josephus_vanDenElzen]

Wondering, how old are students in Us when they are taught about covariance?

[@theodorjohnson2984]

Siebe van den Elzen Around 18-19

[@anas99anas]

I love you

[@piersanna8866]

whats the meaning of x times two and the other x, where is the y... explain ffs

[@deejaaay7600]

Really complicated to follow...

[@Zurh1994]

Contradicting name ;)

[@HL-iw1du]

?

[@EOCmodernRS]

I don't get the difference between x^2bar and (xbar)^2

[@jim8289]

Hi, its been a while since you posted but I'll try my best to answer in case anyone else has the same question. (x^2)bar is simply squaring all the x values and dividing it by the number of points. It is finding the mean of x values, however you square the x values. E.g. (2,3), (1,2) - it would be (2^2+1^2) / 2 = 5/2. (xbar)^2 is finding x-bar and literally squaring that amount. Using the prev. example - (2+1)/2 = 3/2. However this is squared so answer is (3/2)^2 = 9/4

[@devanpatel39]

nVariance=Sxx

[@birdstheword5]

E

[@mathman2170]

keeping the colors is such a waste of effort. otherwise nice.

[@bangthatdrumb]

facebook is a fad

[@calinoiz]

If facebook can worth 70billion dollar, how much would youtube worth? google got the best deal of century

[@martinelenkov2113]

Who has time for that? 15 mins drawing with different colours.....

[@wielkiemico7740]

It does not explain anything. You take the covariance definition out of nothing, do some simple algebra and state that this is a numerator in the formula for the slope. The question is: why does this formula look like so? And why covariance is defined this way?

[@NikitaSharma-bs4gg]

Really grateful 🥲...always awesome