Test Statistic for Correlation Coefficient

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verse214

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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…
 
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.
 
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