Statistics question: error of slope in linear regression from r

[snellslaw]

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!

 

[HallsofIvy]

What does "the equation y=mx+b with an r² value" mean? In particular, what does "with an r²" mean?

 

[snellslaw]

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