What is The Correlation Coefficient & The Coefficient of Determination?

Hi! My name is Kody Amour, and I make free math videos on CZcams. My goal is to provide free open-access online college math lecture series on CZcams using free open-access resources. I rely on generous donations and ad revenue - a special thanks to everyone who helped this channel grow.
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Credit to all of the authors of all of the resources below that greatly helped influence this video. My newer videos are much more original than these videos.
Free open-access online math textbooks:
aimath.org/textbooks/approved...
My favorite number theory textbooks:
Number Theory: In Context and Interactive by Dr. Karl-Dieter Crisman: math.gordon.edu/ntic/
Elementary Number Theory:
Primes, Congruences, and Secrets by Dr. William Stein: wstein.org/ent/
A Computational Introduction to Number Theory and Algebra by Dr. Victor Shoup: shoup.net/ntb/
My favorite programming language:
SageMath (which in my view is categorically more productive than Python, R, Mathematica, Matlab, Maple, Magma, etc - if you're using any of these and they aren't working out, consider switching to Sage): www.sagemath.org/
A free in-depth tutorial for SageMath: doc.sagemath.org/html/en/tuto...
Learn LaTeX in 30 minutes: www.overleaf.com/learn/latex/...
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My favorite math/science CZcams channels that I absolutely love (in no particular order):
Zach Star: / @zachstar
Numberphile: / @numberphile
3Blue1Brown: / @3blue1brown
MIT OpenCourseWare: / @mitocw
Khan Academy: / @khanacademy
PBS Infinite Series: / @pbsinfiniteseries
Lex Fridman: / lexfridman

[@mitchell9169]

fantastic video, great audio quality too and concisely explained. Thank you sir

[@larasmith4467]

Thank you so much, this explained it so well!

[@thecupdidit]

Dude this is amazing. Honestly man. Been trying to find something that explains this to me for the past 40mins and hit your video. Now I can get on with the work again LOL THANK YOU. KEEP MAKING VIDEOS!!!

[@tiffanyder2377]

thanks for this. i'm taking a machine learning course and this really helped refresh my brain!

[@ftaslimi]

Nicely done! Thank u.

[@hasnaaelshennawy]

BIG THANKS!

[@MisterBinx]

I think if r=0 it means no LINEAR relationship. There could be a relationship but not linear.

[@noneuvyobisness2042]

thx easily explained

[@boobalarasuvelu9804]

Well explained what is r and r2.

[@SajidhMarikkar]

Thanks. This is good theory. Can you give us some examples? i.e. what an r score of two sets of data mean and what an r squared of the same data sets mean? That would be really helpful. Thanks.

[@ramkii18]

Can you please let me know link of next video where you calculate r of a linear equation

[@nadeeyapa1597]

Thank you so much

[@classiccatastrophe1518]

Thank you good sir

[@alexmarvin3093]

I was watching to understand the difference between r and r-squared.
"so lets talk about the difference between r and r-squared.."
- gives definition of r-squared - says it's a weird explanation but here's how he approaches it in real life (practically) -- the idea is I never use the correlation coefficient (r).. never, ever..
still a good video, i just have to look elsewhere for "r"
thumbs up!
I think my question is, where does (r) come into play, other than with helping to understand the +/- relationship with the slope?
thanks

[@hollygoodson6025]

Helpful ty

[@razvanefros411]

If you add a lot of independent variables to train the linear regression model,and you end up with a really high coefficient of determination, you risk getting a model that has weird spikes and outliers. Our university prof recommended aiming for a model in the range of 70%-80%

[@thabangmoloi3772]

Thank u.

[@geetown3485]

Dude thanks !

[@joshuapepito8581]

If my r2 is 0.95, then does that mean that the predicted y of the regression line has a +-5% error?
Should it be used as a factor of safety?

[@dailyStewie504]

It means that your dependent variables (Y) are explained by 5% of other factors and not the independ varibles (X).

[@chathuhasi]

Thanks !! Well explained

[@xyz-ip9hr]

thx

[@user-xr8vw6zc3g]

Hi, R and r are not the same thing. r deals with x and y, while R deals with multiple x variables and y.

[@annmaria1374]

If R =0.712 what's that correlation

[@yilu1384]

for nonlinear , R^2is not equal to r^2.

[@ashi4951]

Sir you are beautiful. Ok thank you. I've got my paper in 3 hours from now. Pray. Ok bye.