5
$\begingroup$

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 $\hat{\beta}_2=0.024$?

$\endgroup$

2 Answers 2

7
$\begingroup$

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 $y$.

$\endgroup$
0
5
$\begingroup$

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.

$\endgroup$
4
  • 2
    $\begingroup$ 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
  • 1
    $\begingroup$ @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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.