Question

Can someone explain to me how to calculate r^2 in statistics and how it's useful? My notes aren't really helping me understand and I have a test today :(

Answer 1

sounds like a correlation coefficient ....

Answer 2

well I have the definition of it, so I understand it's purpose or what it does, but that's it

Answer 3

yeah, something about an explained variation

Answer 4

the formula looks a bit convoluted, but seems to be a pattern repeated 3 times

Answer 5

\[r=\frac{n~xy-(x)(y)}{\sqrt{n~x^2-(x)^2}~\sqrt{n~y^2-(y)^2}}\]

Answer 6

a simplified notation addresses something called a zscore for a sample value .... but i got no idea what that would be talking about

Answer 7

well I have r^2=(y-y-hat)2 ....

Answer 8

i was given like 2, 3 equations so idk if there's one that's better than the others or if they're all equally correct

Answer 9

i havent delved into the chapters in my book that cover it, but it looks like excel would be very useful for this setup

Answer 10

or a table to organize the stuff

x y xy x^2 y^2
.. .. .. .. ..
sums||

Answer 11

and maybe a spot to remember the n :)

Answer 12

spose for brevity that x={2,4,5} and y = {1,3,3}

x y xy x^2 y^2

2 1 2 4 1
4 3 12 16 9
5 3 15 25 9

sums|| 11 10 29 45 19

and there are 3 rows so n=3

\[r=\frac{3(29)-(5)(3)}{\sqrt{3(45)-11}\sqrt{3(9)-3}}\]
\[r=\frac{72}{\sqrt{124}\sqrt{24}}\]
\[r^2=\frac{72^2}{124*24}\]

Answer 13

thats spose to be (11)(10) not (5)(3) up top

Answer 14

and 3(19) on the right under there not 3(9) .... lol

Answer 15

other than that ..

Answer 16

\[r=\frac{n~\sum(xy)-\sum x \sum y}{\sqrt{n~\sum(x^2)-(\sum x)^2}~\sqrt{n~\sum(y^2)-(\sum y)^2}}\]
\[r=\frac{3(29)-(11)(10)}{\sqrt{3(45)-11}\sqrt{3(19)-10}}\]
oy thats was painful :)