Via trial and error where I guess the number of statistical degrees of freedom, I have determined that the single variable linear regression "automatically" performed by Excel provides a p-value for the Y-axis-intercept that is identical to the one that can be calculated by "explicit" Excel functions as follows:
(The p-value is for the null hypothesis that the Y-axis-intercept is zero.)
T.DIST is the function name and it is left tailed, hence the need to flip the sign on the t-statistic. This flip operation is visible as the
0-, or "zero minus".
t is the t-statistic.
n is the number of observations.
TRUE means the function operates in cumulative mode.
The second argument to the function is the statistical degrees of freedom. I guessed that the value would be
n-1 which was wrong and then I guessed it would be
n-2. Why should the statistical degrees of freedom be 2 less than the number of observations?