Forward selection has drawbacks, including the fact that each addition
of a new variable may render one or more of the already included
variables non-significant.
An alternate approach which avoids this is *backward selection*.
Under this approach, one starts with fitting a model with all the
variables of interest (following the initial screen). Then
the least significant variable is dropped, so long as it is not
significant at our chosen critical level. We continue by
successively re-fitting reduced models and applying the same rule until
all remaining variables are statistically significant.
Applying this to the same data as before:

. sw reg wtpct12 ventdays blish gest bw bl conv, pr(.10) begin with full model p = 0.9705 >= 0.1000 removing bl p = 0.3065 >= 0.1000 removing conv Source | SS df MS Number of obs = 150 -------------+------------------------------ F( 4, 145) = 8.65 Model | 21074.0503 4 5268.51257 Prob > F = 0.0000 Residual | 88363.3897 145 609.402688 R-squared = 0.1926 -------------+------------------------------ Adj R-squared = 0.1703 Total | 109437.44 149 734.479463 Root MSE = 24.686 ------------------------------------------------------------------------------ wtpct12 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- ventdays | -.2031126 .0946998 -2.14 0.034 -.390283 -.0159423 blish | -.2658678 .1301217 -2.04 0.043 -.5230482 -.0086874 gest | -3.601116 1.10194 -3.27 0.001 -5.779057 -1.423175 bw | .0247148 .0054799 4.51 0.000 .0138839 .0355456 _cons | 113.7379 29.14385 3.90 0.000 56.13626 171.3396 ------------------------------------------------------------------------------

Though we have started from the "other end", in this case we wind up with the same model. There is no guarantee that this will always happen. Backward selection has it's own drawbacks, as well. Sometimes variables are dropped that would be significant when added to the final reduced models. This suggests that some compromise between forward and backward selection methods should be considered.