I fitted a continuous dependent variable against two explanatory variables. However, one of the explanatory variables is expressed as a percentage. Consider the regression model: $y = 0.05 + 0.032x_1 + 0.024x_2,$ where $x_2$ is expressed as a percentage. How can one interpret $\hat{\beta}_2=0.024$?


2 Answers 2


The interpretation is not very different from the normal regression interpretation: a 1 unit (in this case 1 percentage point) increase in $x_2$ is associated with a 0.024 unit increase in $y$.


This is easy to get wrong. A $1$ percentage point ($1\%p$) increase in $X_2$ is associated with a $0.024$ unit increase in $Y$. That is, if two observations have equal values of $X_1$ while their $X_2$ values differ by $1\%p$, the estimated expected difference in their $Y$ values is $0.024$.

Note the subtle difference between percent and percentage points: values $50\%$ and $51\%$ differ by $1\%p$, yet at the same time the latter is $2\%$ larger than the former $(\frac{51\%-50\%}{50\%}=0.02=2\%)$. Here is a related thread.

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    $\begingroup$ I don't see that your statement says something different. One percentage point (1%) is the natural unit when the variable is expressed as a percentage. Percentage point $\endgroup$
    – dipetkov
    Commented Aug 29, 2022 at 11:55
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    $\begingroup$ @dipetkov, after mkt's edit, the answers say the same thing. When I posted my answer, they were saying different things. Regarding how natural something is, I think it varies from person to person. I have encountered plenty of cases where people were mistaken due to missing the subtle difference between $\%$ and $\%p$. $\endgroup$ Commented Aug 29, 2022 at 12:08
  • $\begingroup$ Thank you all for your answers and comments. All are very useful to me! $\endgroup$
    – iGada
    Commented Aug 29, 2022 at 12:27
  • $\begingroup$ @Gada, you are welcome! $\endgroup$ Commented Aug 29, 2022 at 12:58

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