0
$\begingroup$

I have the following regression:

$$\ln(1 + \text{hours}) = \beta_0 + \beta_1 \text{ educ} + \beta_{2-x} \text{ other independent variables} + \varepsilon$$

$\beta_2$ for educ is $0.0642$. How would one interpret this coefficient?

$\endgroup$
1
$\begingroup$

It's fairly straight forward. This is a log-linear model. A one-unit change in $x_i$ is associated with a $100 * \beta_i$ percent change in $y$.

$100\% * 0.0642 = 6.42\% $

We can now interpret it in percentages. For each one unit increase in educ, there is a 6.42% increase in your outcome variable.

ETA in light of whuber's comment:

To be more precise, the relationship between the percent change in $y$ and change in $x$ is:

$100\% * (e^{\beta_i} - 1)$

So,

$100\% * (e^{0.0642} -1) = 6.630564\%$

A whuber states, this is important as the absolute value of $\beta_i$ grows larger than 0.1. The simple $\beta_i * 100$ rule serves as an easy approximation when $|\beta_i| < 0.1$.

$\endgroup$
  • 1
    $\begingroup$ This is only approximately correct. The approximation starts to break down noticeably when $|\beta_i| \gt 0.1$. However, since $y=1+\text{hours}$ in the question, the interpretation ought to concern the original response variable $\text{hours}$ rather than $y$ itself--and now it's no longer such a simple relationship. $\endgroup$ – whuber Oct 27 '16 at 18:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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