Statistics question: error of slope in linear regression from r

snellslaw
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A text says that if you calculate the linear regression of data points and you get the equation y=mx+b with an r2 value, the error in the slope is given by:
δm/m=2(1-r)

No explanation was given. Could someone please explain this formula? Thanks!
 
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What does "the equation y=mx+b with an r2 value" mean? In particular, what does "with an r2" mean?
 
Hi HallsofIvy!

like say you insert some data points and then use your calculator to calculate the linear regression. the calculator spits out
y=0.0283x+0.0012, r2=0.998

so the r2 is the coefficient of determination
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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