For a simple regression (one independent variable), statistics programs
produce two estimates, a (the "constant term")
and b (the "linear coefficient"),
for the parameters α
Each estimate has an associated t-value (along with its
degrees-of-freedom, df) and
the test that the corresponding parameter is zero.
How to report this information:
For each regression test you do, at least t, df,
for the linear coefficient β should be reported.
A succinct notation is:
t(df) = t-value, p = p-value
When β is significantly different from zero
(p < 0.05), report
b (and be sure to include its units).
If α is "meaningful" (i.e. we are concerned with the exact location
of the regression line, not just with its slope, β),
report its t, df,
and p values (along with a, if significant).
As with the
comparison-of-means t-test, when it comes to
the number of digits to report, we are primarily concerned with whether p
than or less than 0.05. Therefore, one need only report one digit behind
the decimal for a t-value, and report two digits behind the decimal for a p-value
(one could go to three if the p-value is near 0.05, such as 0.045 or 0.055).