Regression model bias [closed]

I know in the case of regression analysis, when we are studying the relationship between the dependent and independent variable, we are also checking for bias. If the error term is correlated with the dependent variable, we can remove it from our model.

How about in the case of a bias that exists for a range of values but doesn't exist for the rest of values? How do I correct for that in regression analysis?

Example regression: $$Y=α_0+α_1X$$

There is a bias in model for X values that range from 0 to 5, but no bias for X values greater than 5.

closed as unclear what you're asking by Martijn Weterings, kjetil b halvorsen, Michael Chernick, Ferdi, Peter Flom♦Jan 12 at 13:02

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• How would you describe the different 'ranges of values'? What model did you perform? (I am guessing that you did some linear model with different means for a categorical variable but no different slopes/interaction for that same categorical variable, where the categorical variable is defining your different ranges?) – Martijn Weterings Jan 10 at 20:15
• @MartijnWeterings I've added more detail to the problem, hopefully it answers your question – hsayya Jan 10 at 20:48
• It seems like your linear relation is not correct. Could you add a plot? Do you have an idea about a source of bias? Can you imagine why the model would not be a good fit in the entire range? – Martijn Weterings Jan 10 at 23:56
• What do you mean by " If the error term is correlated with the dependent variable, we can remove it from our model. " What can you remove? – Peter Flom Jan 12 at 13:02