Some useful facts:

For the normal distribution,
95% of observations fall within 1.96 z's of the mean.
99% of observations fall within 2.58 z's of the mean.


For t,

With two degrees of freedom, 95% of observations fall within 4.3 t's of the mean.
With two degrees of freedom, 99% of observations fall within 9.9 t's of the mean.
With four degrees of freedom, 95% of observations fall within 2.8 t's of the mean.
With five degrees of freedom, 95% of observations fall within 2.6 t's of the mean.
With eight degrees of freedom, 95% of observations fall within 2.3 t's of the mean.




With one degree of freedom, 95% of observations fall below 6.63 chi-squares.
With two degrees of freedom, 95% of observations fall below 7.38 chi-squares.
With three degrees of freedom, 95% of observations fall below 9.35 chi-squares.


b=r*(sy/sx)
a=y bar - b*x bar