I think I am making this more difficult than it is but in a simple linear regression what is the difference the T-Stat calculated r * sqrt (n-2) / sqrt (1-r^2) and the T-Stat calculated Estimated Coefficient - 0 / Std Error? I have calculated and compared now for several problems and they usually produce a slightly different answer each time? What am I missing here? Thanks

Isnâ€™t the T-stat (r * sqrt (n-2) / sqrt (1-r^2)) for testing the significance of the correlation coefficient while the other t-stat is for the individual coefficients of the regression?

The first equation is only for the T-stat to test if the correlation is significant. The second equation is for the T-stat to test if anything else is significant. I guess correlation plays by another set of rules.