When regression is not applicable?

Answer 1

There are many cases where you won't get useful results from regression. The two most common kinds of issues are (1) when your data contain major violations of regression assumptions and (2) when you don't have enough data (or of the right kinds).

Core assumptions behind regression include

- That there is in fact a relationship between the outcome variable and the predictor variables.

- That observations are independent.

- That the residuals are normally distributed and independent of the values of variables in the model.

- That each predictor variable is not a linear combination of any others and is not extremely correlated with any others.

- Additional assumptions depend on the nature of your dependent variable; for example whether it is measured on a continuous scale or is categorical yes/no etc. The form of regression you use (linear, logistic, etc.) must match the type of data.

Not having enough data means having very few cases at all or having large amounts of missing values for the variables you want to analyze. If you don't have enough observations, your model either will not be able to run or else the estimates could be so imprecise (with large standard errors) that they aren't useful. A generic rule some people cite is that you need 10-20 cases per variable in the model; there's nothing magic about that number and you might get by just fine with less, but it suggests you could run into trouble if you have much less that that. Missing values can be a big problem as well and in the worst case could skew your results if they are not handled properly.