<p>Can I differentiate a quadratic regression model formula with the form</p>
<p><span class="math-container">$$Y_i=\beta_0+\beta_1 X_{1i} +\beta_2 X_{1i}^2+\epsilon_i$$</span></p>
<p>(added to this formula would be other control variables e.g dummy variables) to obtain the correlation between X and Y holding everything else constant? Also, if I were to add a female dummy variable, how would the correlation of X and Y differ between men and women? Or would the correlation be the same?</p>

CC BY-SA 4.0
2020-08-10T17:52:37.593Z
By "correlation" did you mean the *linear* association between two variables as measured by the [Pearson correlation coefficient](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient), or some *non-linear* dependence?
Herr K.
CC BY-SA 4.0
2020-08-10T18:50:17.353Z
See this thread, it has a well-written answer with examples https://stats.stackexchange.com/questions/52585/what-happens-when-i-include-a-squared-variable-in-my-regression
london
<econometrics><regression>
How do I obtain a correlation between two variables?
Esther Blaese
# How do I obtain a correlation between two variables?

(Asked by: username_0 on 2020-08-10)

Can I differentiate a quadratic regression model formula with the form

$$Y\_i=\beta\_0+\beta\_1 X\_{1i} +\beta\_2 X\_{1i}^2+\epsilon\_i$$

(added to this formula would be other control variables e.g dummy variables) to obtain the correlation between X and Y holding everything else constant? Also, if I were to add a female dummy variable, how would the correlation of X and Y differ between men and women? Or would the correlation be the same?

**Tags:** econometrics, regression
> **Comments:**
> **username_1**: By "correlation" did you mean the *linear* association between two variables as measured by the [Pearson correlation coefficient](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient), or some *non-linear* dependence?  
> **username_2**: See this thread, it has a well-written answer with examples https://stats.stackexchange.com/questions/52585/what-happens-when-i-include-a-squared-variable-in-my-regression  

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