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

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Covariance, Variance and the Slope of the Regression Line
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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!
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Опубликовано:

24 авг 2024

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Комментарии : 67

@MaxAgapoff 7 лет назад

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

@user-ti1rx5ui2e 2 года назад

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

@zingg7203 8 лет назад

I hope my instructor tells this instead of spreading cancer.

@leechmaster21 6 лет назад

And I hope you dump that loser boyfriend of yours.

@mandelbro777 4 года назад

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 :)

@tadaasam2036 6 лет назад

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

@jfht318 5 лет назад

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.

@user-xi9sx7wn5v 5 лет назад

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!

@AsgharKhan-fd1ul 12 лет назад

KHAN IS KING!

@Skulltroxx 3 года назад

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

@royzou4471 8 лет назад

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

@shreyaschaturvedi1933 5 лет назад

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

@ketansharma6955 Год назад

This video was gorgeous !

@Sutto3721 11 лет назад

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 13 лет назад

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

@ygbr2997 2 года назад

happy new year

@L2.Lagrange Год назад

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

@svsujeet 12 лет назад

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

@SimplyAndy 3 года назад

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

@james9254 7 лет назад

Best Teacher Ever:)

@ericmorris5914 Год назад

Amazing!!! thanks for the insight

@MohamedElsheikh22 11 лет назад

You are the best !

@riderblack6401 6 лет назад

so gooD!

@vinaykumardaivajna5260 Год назад

12 Years wow still going On wow wow wow

@rizwanshahid8242 7 лет назад

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

@dashzevegp7685 6 лет назад

Thank you.

@sofieskarupkristensen893 5 лет назад

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

@animeonperseest 5 лет назад

It's Chris Brown

@yvonnet8613 8 лет назад

wow that just made soo much sense. thanks

@tranngoc5692 2 года назад

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

@PrincessGillianWang 12 лет назад

thank you 100000000+. you are amazing!!

@MyJackzhang 9 лет назад

Thank you!

@youngcw3177 7 лет назад

It helps a lot!!!!thank you!

@aveekdas6343 7 лет назад

very nicely explained.

@sreekumarmenonk7678 3 года назад

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

@dobraOsoba 12 лет назад

pretty colors

@ad2181 13 лет назад

Keep up the good work, you make my day.

@jsymons1985 13 лет назад

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

@pedrogaspa 9 лет назад

excellent!

@JI77469 6 лет назад

"...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...

@binashbobby8891 6 лет назад

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

@stevecharmer4296 4 года назад

You forgot a closing parentheses after expected value Y

@LastManRising 3 года назад

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

@anas99anas 2 года назад

I love you

@Tyokok 3 года назад

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!

@deejaaay7600 2 года назад

Really complicated to follow...

@beedoog0717 10 лет назад

already knew it

@djaiseman 12 лет назад

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

@rruizanimations1 6 лет назад

yes it seams

@Zurh1994 11 лет назад

Contradicting name ;)

@HL-iw1du 5 лет назад

@Josephus_vanDenElzen 8 лет назад

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

@theodorjohnson2984 7 лет назад

Siebe van den Elzen Around 18-19

@gurminderbharani1260 8 лет назад

Thank you

@devanpatel39 7 лет назад

nVariance=Sxx

@piersanna8866 4 года назад

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

@ddennis911 12 лет назад

how many times did he say expected value ? :D

@EOCmodernRS 6 лет назад

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

@jim8289 5 лет назад

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

@birdstheword5 6 лет назад

@mathman2170 3 года назад

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

@wielkiemico7740 3 года назад

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?