When I run a multiple regression analysis in Excel on 20 independent variables and 1 dependent variable (in two goes), I obtain in the summary a set of p-values. When I select the (six) ones that are less than 0.25 and then rerun the multiple regression analysis, the p values are smaller than they were previously. Shouldn't the p values be the same?? I would have thought that the p-values should be the same as each time an individual regression is run against the dependent variables?

Otherwise could someone please point out my misunderstanding of multiple regression analysis and explain/justify why these p-values are smaller.