# Population / Sample question

Today we started arguing at work, and couldn't come to conclusion. Let's say that we have a population of 1000 observations about various people. 50 of these people went bankrupt (1 - bankrupt, 0 - did not went bankrupt). Can we take sample of 100 people (50 bankrupt, 50 not bankrupt) and use them to make a model of bankruptcy (using linear regression or MDA)? Or must we take a random sample of 100 people, which should include around 5 people that went bankrupt?

Do we have to keep the same proportions as in population in modelling sample, to use the model on population ?

What problems would occur with 50-50 sample ?

Thanks!

• Basically: in 50-50 sample your model will see data where 50% people go bankrupt, so it will (correctly given data!) assume that the chance of getting bankrupt is 50%. I guess this is not what you want your model to conclude... See e.g. stats.stackexchange.com/questions/306122/… and stats.stackexchange.com/questions/283170/… for the other side of the coin.
– Tim
Nov 8, 2017 at 14:08
• @Tim, Your conclusion will be true only for some models. If you have two artificially created clusters where one has 1000 data samples and the other one has 100. Assuming that they are linearly separable (+noise), training model using 50 samples from each clusters shouldn't produce model that make 50%-50% prediction. Nov 8, 2017 at 14:25
• @itdxer true, but the question asks about potential risks and mentions regression, so this is one of the potential risks.
– Tim
Nov 8, 2017 at 17:37