Variables supposed to be kept show low significance Here is an interview question.
In a model, if we believe some variables should be kept. However, those variables are not significant according to the model output. What are some possible reasons?
 A: The list could be endless.  After vowing to stop at 20, I came up with the list below.  Many are from examples on this site; others are from my experience.  None are theoretical or speculative: I have seen them all.  They are in a very rough order from those worth checking first, on down.  There is some overlap, but each category is distinctive enough to be worth mentioning separately.


*

*Residual variability is high.

*Sample size is insufficiently low.

*The model is of the wrong form entirely.

*Collinearity.

*Mistakes in model fitting.

*The belief is mistaken.

*Small effect size.

*High measurement variability in the explanatory variables.

*Measurement error (in response or explanatory variables).

*Failure to sample as intended.

*Erroneous interpretation of the output.

*Too many variables were included.

*Violations of implicit model assumptions, such as


*

*Non-independent responses

*Nonidentically distributed residuals

*Residuals distributed differently than assumed


*Overly coarse binning, discretization, or measurement of the variables.

*Absence of crucial variables.

*Missing data or poor data imputation.

*Errors in recording, transcribing, or processing data.

*Errors in applying software.

*Software bugs.

*Pure bad luck. 
A: I assume the question is about significance of individual variables in a regression model.
P-values for one variable are got from contrasting a model with that variable against a model without that variable. There are two usual reasons for a high p-value:


*

*The variable is not related to the response.

*The variable is related to the response but it's highly colinear with other variables. That is, the variable doesn't add more information to that of another predictor.


In first case, you could assess if it's worth keeping the variable. In the second, you may want to remove some variable and test for significance again.
