Answers.Body: <ul>
  <li>Yes, the addition of the independent variable (<span class="math-container">$X_2$</span>) will have an impact on the beta coefficient of <span class="math-container">$X_1$</span>.</li>
  <li>Maybe, it depends on the relationship between <span class="math-container">$X_1$</span> and <span class="math-container">$Y$</span>, and whether you are using any regularization or not.</li>
  <li>If the independent variable <span class="math-container">$X_2$</span> is more correlated than <span class="math-container">$X_1$</span>, then the value of <span class="math-container">$r^2$</span> should be higher (but I am not sure on this)</li>
  </ul>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-08-28T08:44:11.633Z
Answers.LastActivityDate: 2020-08-28T08:44:11.633Z
Answers.UserDisplayName: Karan Dhingra
Body: <p>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)</p>
  <ul>
  <li>Will it have any effect on beta coefficient of X1?</li>
  <li>Will relationship between X1 and Y become insignificant?</li>
  <li>Can adjusted R-square value decrease?</li>
  </ul>
  
Tags: <machine-learning><linear-regression>
Title: Effect of adding an Independent Variable in Multiple Linear Regression
UserDisplayName: Snehal Gupta
ThreadText: # Effect of adding an Independent Variable in Multiple Linear Regression
  
  (Asked by: username_0 on 2020-08-28)
  
  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?
  
  **Tags:** machine-learning, linear-regression
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2020-08-28. Score: 0 | Accepted answer
  
  * 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)
  
  
  ---
  
  