# Effect of adding an Independent Variable in Multiple Linear Regression

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?

• 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)