If I have a multiple regression model with a dummy variable that consists of 3 entries A, B, and C there are two questions
First: After I remove one dummy variable column so that my model is Linearly independent and avoids multicollinearity say I dropped the A column and the B and C remains and fit my model if I see one of my dummy variables is statically insignificance can I drop it only or I should drop all dummy variables (A, B, and C)?
Second: When I drop a column (it will be my baseline) and fit my model and after that, I create another model but choose a different column as baseline the P-value changes for the coefficients, and the insignificance coefficient in the first model may be significant in the second one so the question is how can I choose the best model that can provide the best interpretation and prediction of Y and which model represents the right P-value?
Photos show different p-values for the second question model 1
Photos show different p-values for the second question model 2
Photos show different p-values for the second question model 3
