Correlation & Linear Regression

[ecoli]

For example, I know that r^2 of linear regression is, in certain cases, related to the correlation coefficient (goodness of fit) but is there are precise mathematical definition? Perhaps with a geometric interpretation?

 

Any and all references would be helpful.

[ecoli]

shameless bump

[John Cuthber]

Not really my field but...

If you have two variables for example height and weight and you measure lots of people and calculate the correlation coefficient and find that, for example, it's 0.8 the you can find R^2 easily enough: 0.64 .

That tells you that 64% of the variation in weight is "due to" the variation in height. The rest of the variability must be due to other factors.

[ecoli]

Not really my field but...

If you have two variables for example height and weight and you measure lots of people and calculate the correlation coefficient and find that, for example, it's 0.8 the you can find R^2 easily enough: 0.64 .

That tells you that 64% of the variation in weight is "due to" the variation in height. The rest of the variability must be due to other factors.

 

Couldn't you just as easily state the reverse? Since you haven't controlled for weight or height.

[EquisDeXD]

I don't exactly understand linear regression and "linearizing a graph". It seems like anti-science, my sci-professor for a class made me linearize every graph because "we don't have enough information to determine that it's a parabola (or inverse square or w/e)" even though all the points PERFECTLY fit on a parabolic function. THAT'S WHY YOU DO MORE TESTING!!! Why on EARTH wouldn't you throw out other possibilities for equations just because you like linear graphs more and then not even test to make sure? That seems to go against what science itself is!!! Without extensive knowledge, people think that you can just add speeds of objects to get the relative speed of either object to the other object which is completely wrong because there's another equation that makes more sense if you consider that nothing goes past the speed of light which I think is some kind of hyperbola or inverse equation which shows that the relative speed levels off as either object approaches the speed of light.

Edited October 3, 2012 by EquisDeXD

[Psiddle]

Applied Mathematics is always an alien stuff for me And to be very honest half of said information does not even get closer to me.

[John Cuthber]

If you think the data is a parabola then you plot the log of it .

If it comes out with a slope of 2 (as determined by calculating the best line through the data) then you have shown that it is a parabola.

 

You needed a better professor.

[John Cuthber]

If you think the data is a parabola then you plot the log of it .

If it comes out with a slope of 2 (as determined by calculating the best line through the data) then you have shown that it is a parabola.

 

You needed a better professor.

 

If you think the data is a parabola then you plot the log of it .

If it comes out with a slope of 2 (as determined by calculating the best line through the data) then you have shown that it is a parabola.

 

You needed a better professor.

 

If you think the data is a parabola then you plot the log of it .

If it comes out with a slope of 2 (as determined by calculating the best line through the data) then you have shown that it is a parabola.

 

You needed a better professor.

 

If you think the data is a parabola then you plot the log of it .

If it comes out with a slope of 2 (as determined by calculating the best line through the data) then you have shown that it is a parabola.

 

You needed a better professor.

 

Has the site got a stutter?

[mathteacher025]

Hello! I can help with graphic.

You can check geometric interpretation of r^2 right here:

http://www.numberempire.com/graphingcalculator.php?functions=r%5E2&xmin=-3.648755&xmax=4.163745&ymin=-3.772169&ymax=7.946581&var=r

I used Graphing Calculator.

Good luck!