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In a more general situation, when you have two independent variables that are very highly correlated, you definitely should remove one of them because you run into the multicollinearity conundrum and your regression model’s regression coefficients related to the two highly correlated variables will be unreliable.
What is the problem with collinearity?
Multicollinearity is a problem because it undermines the statistical significance of an independent variable. Other things being equal, the larger the standard error of a regression coefficient, the less likely it is that this coefficient will be statistically significant.
Can a polynomial regression model contain more than one predictor variable?
In general, we can model the expected value of y as an n th degree polynomial. The polynomial regression model may contain one, two, or more than two predictor variables. Each predictor variable may be present in various powers. Further, each predictor variable may be present in various powers.
What is a second order regression with one predictor variable?
We begin by considering a polynomial regression model with one predictor variable raised to the first and second power where This polynomial model is called a second-order with one predictor variable because the single predictor variable is expressed in the model to the first and second powers.
What happens when more predictor variables are added?
When predictor variables are correlated, the precision of the estimated regression coefficients decreases as more predictor variables are added to the model. Here’s the relevant portion of the table:
When to remove a variable from a regression model?
In a more general situation, when you have two independent variables that are very highly correlated, you definitely should remove one of them because you run into the multicollinearity conundrum and your regression model’s regression coefficients related to the two highly correlated variables will be unreliable.