<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>

CC BY-SA 4.0
2020-08-28T08:44:11.633Z
2020-08-28T08:44:11.633Z
Karan Dhingra
<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>

<machine-learning><linear-regression>
Effect of adding an Independent Variable in Multiple Linear Regression
Snehal Gupta
# 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


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## 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)


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