# regression models for population [duplicate]

I have data on the entirety of a certian population (not a sample). I would like to conduct a multivariate analysis for this data. The data consists of an interval dependent variable and interval and binary explanatory variables.

many colleagues of mine suggested to analyze this with regression model. Given that the analysis subjects are the whole population, what value is there for significance? Is there a better way to conduct a multivariate analysis than a regression model in this case?

thanks.

## marked as duplicate by kjetil b halvorsen, Peter Flom♦ regression StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Aug 31 '17 at 11:24

In a case where you have the entire population and the data is full, and meats parametric assumptions, than yes - you can perform a linear regression. The significance levels of the coefficients will naturally be pointless. A significance level is a measure of the likelihood that the coefficient $\beta_i$ was taken from a population which has a $\beta_i=0$. Since the model has no idea of what part of the population we are using, it does not know that we use the entire population as such, the coefficient in the regression will equal the coefficient in the population and the significance test loses all meaning.
Usually, the coefficient is just an averaged relation between $y$ and $x$ in the sample data, and even when highly significant, does not equal the actual relationship in the population (which can be estimated with confidence intervals). When using the population, even a non significant coefficient is "significant", but more so, represent the actual relationship.