When we fit a regression model with indicator variables and if we change the indicator variables then the regression coefficient changes. It make interpretation problem??
Sorry to hear this. It sounds like over fitting, a statistical nightmare in which the model (the regression coefficients, etc.) uniquely fit the "training model". The interpretation cannot be generalized to anything else. Best find a way to start from scratch, maybe with more data (and avoidance of adjustments or whatever). Good hunting.
I can code color as light green, medium green, or dark green.
Alternatively I can code color as very light green, light green, medium green, dark green, or very dark green.
I can also code green as two binary variables: light green versus medium green, and another variable as medium green versus dark green.
The regression coefficients change depending on how I model the system. This is what should happen. You now have to figure out which model is right for your application. There is no one right answer.
If you have enough data I would say that recoding a continuous variable into a discrete variable is a bad idea -- though it is often done anyway.