Test Statistic for Correlation Coefficient

How did they derive the T-score test statistic for the correlation coefficient: t=sqrt(n-2)/sqrt(1-r^2) Is this just a given??

hi, you’re missing the correlation coefficient in the numerator. my best answer is just memorize it…

is it r squart root (n-2)/square root (1-r^2) do you attack the 2?

???

tigas Wrote: ------------------------------------------------------- > ??? attack the 2 dude.

sorry “dude”…no native english so probably missing your point…

my question is if they derived it from somewhere or is it just a given?

it is a given. no derivation necessary. also you seem to have the formula down wrong. it is r * sqrt(n-2) --------------- sqrt(1-r^2) you are missing the r * in the numerator.

yeah - sorry forgot to type it Thanks all - sorry i thought they derived it from the T- test stat and a correlation coefficient

verse214 Wrote: ------------------------------------------------------- > yeah - sorry forgot to type it > > Thanks all - > > sorry i thought they derived it from the T- test > stat and a correlation coefficient Refer to econometrics by Gujrati

i tried to go take the route of understanding how the derivation of these formulae work. Save yourself the time- NOT WORTH GETTING INTO. Just memorize the formula.

it’s just a formula that you gotta know: r x (square root of n-2) / the square root of (1-r^2)

one trick : t-stat of correlation coeff should be the same as t-stat of independent variable … which is usually given.

If you combine the formulas for r^2 and the f.stat, take k=1, you can get the formula for the f stat in terms of r and n. then t= sqrt f.

Or,just remember the formula! Although you may be similar to me, deriving the formula, or at least going through it once really helps me remember it, and I think increases the chance of making a good guess if I forget the formula in the exam.

can post a scan of the derivation if you like, can we attach PDF,s ?

If you combine the formulas for r^2 and the f.stat, take k=1, you can get the formula for the f stat in terms of r and n. then t= sqrt f.

Or,just remember the formula! Although you may be similar to me, deriving the formula, or at least going through it once really helps me remember it, and I think increases the chance of making a good guess if I forget the formula in the exam.

can post a scan of the derivation if you like, can we attach PDF,s ?

Basically your breaking down the components. Tstat = slope/standard error.

Slope = r

R = cov(x,y)/ std1 std2. If that looks familiar it’s because you use it to find beta for the stock and the market. The beta of a stock is just the slope of the stock when compare to the market.

Standar error =root (mse)

Mse = sse/n-2

You can break sse into 1 - r^2.

Sorry I m missing something… SST fits somewhere in the equations but it cancels out at the ends.

https://onlinecourses.science.psu.edu/stat414/node/254

(check out the derivation here)