For a binary outcome variable, lets say true or false OR yes or no - i have around 31 independent variables.

I tried using PCA to see if they can be reduced basis collinearity. but none was.

What is the advisable approach, should we enter one variable at a time and see if it is significant and remove the one which may be insignificant or reduce the power of the model once these insignificant variables were added.

What do the other researchers, data scientists, analyst follow.

Ideally adding one variable at a time would be great but this could be really time consuming.

Please suggest.

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