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I am new in machine learning and learning linear regression concept. Please help with answers to below queries. I want to understand effect on existing independent variable(X1) if I add a new independent variable(X2) in my model. This new variable is highly correlated with dependent variable(Y)

  • Will it have any effect on beta coefficient of X1?
  • Will relationship between X1 and Y become insignificant?
  • Can adjusted R-square value decrease?
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  • Yes, the addition of the independent variable ($X_2$) will have an impact on the beta coefficient of $X_1$.
  • Maybe, it depends on the relationship between $X_1$ and $Y$, and whether you are using any regularization or not.
  • If the independent variable $X_2$ is more correlated than $X_1$, then the value of $r^2$ should be higher (but I am not sure on this)
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