I am discussing this issue with a colleague. They argue.
"
However, when building a regression model, the p-values are used to determine whether or not a given predictor variable has a significant impact on the outcome that is being measured. In this context, the p-values show whether or not there is any mathematically calculated reason to keep each predictor variable in the final regression model.
Building regression model is not the same subject as ‘drawing inference from sample mean versus populationmean’. "
If you want to be really strict on your colleague:
1) "significant impact" is a nonsensical statement as "significance" is an arbitrary dichotomization of the outcome for a particular statistical significance calculation and is
not a property of the relationship or thing under study (i.e. a "significant relationship" doesn't exist, because "significance" is not a property of any phenomenon which either exists or doesn't or takes on some value or doesnt, but a calculated p-value may be grouped into one of two groups on the basis of the chosen p-value for that calculation).
2) p-values are more accurately described, but still imprecisely, as a continuous, summary statistic of how different the observed data are from the expectations of a particular assumption (null hypothesis); not really a "mathematical reason" to keep variables until you apply some subjective criterion to the p-value to make a decision (and the p-value need not be part of the decision at all)
3) Building a regression model really takes two general purposes: prediction or inference (you could loosely say description if you want, but generally those two former categories) and I think the prediction and inference objectives can often overlap and blur, but are frequently different
4) if colleague did say "drawing inference from sample mean versus population mean" this doesn't really make sense because inferences are always drawn from the sample values otherwise it's not a matter of inference.
5) if you want good predictions from the model this can be very different from if you want to examine relationships and make inferences
Interested to hear what people can offer as criticisms on the accuracy of my points (even if some are picky).