I am trying to interpret one of the p-values in a one variable linear regression. Some of the answers I've seen for similar questions were not worded as thoroughly as I would have liked. My interpretation is deliberately verbose because it will aid my understanding if faults are found within it.
From Microsoft Excel the linear regression formula from 90 samples of (x,y) pairs is
y = 0.514x + 0.00087
and the p-value of the first coefficient is 4e-16 (scientific notation) and for the second it is 0.0027.
Would it be correct to say that the interpretation of the p-value of the 0.00087 term is:
Under the assumption that the true value of the y-intercept is zero and the first coefficient is 0.514, random sampling of the same number of (x,y) pairs, specifically 90, would result in a least squares best fit line with a y-intercept at least as extreme as 0.00087, with a probability of 0.0027.
If not, then what would be the correct interpretation?
Not so importantly, but just to be complete, I am also inquiring if it would be more accurate and complete to put the relevant phrase as
"at least as extreme as 0.00087 in the same direction, that is, positive".
Edit: The Excel funcion is
Tools > Data Analysis > Regression in Office 2003 with service pack 2. Excel regression p-values on coefficients are 2 sided.
Edit: Regarding differentiation from this question here: The most up voted answer there discusses the p-value of a hypothesis, which seems ill defined or at least not specific. I am not interested in that. I am interested in the p-value of a coefficient that is not the coefficient of an independent variable. I am being very specific.