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I have the following equation: $\mathrm{ln}(y) = \beta_1 + \beta_2 \mathrm{ln}(x)$.

Assume I have an estimate of $\beta_2$ and its standard error. How do I calculate the confidence interval?

Is it just $\beta_2 \pm t \times se(\beta_2)$ or is there some adjustment that has to be made?

I'm confused because I know when it is a log-linear or linear-log model, there are some changes that need to be made in terms of multiplying or dividing by a 100. Can someone help?

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  • $\begingroup$ Welcome! You should find this post and this post helpful. $\endgroup$
    – Thomas Bilach
    Commented Nov 12, 2020 at 7:56
  • $\begingroup$ Call $\log(y)$ "$Y$" and call $\log(x)$ "$X.$" Now your question reads, "Assume I have an estimate of $\beta_2$ and its SE for the model $Y = \beta_1 + \beta_2 X.$ How do I calculate the confidence interval?" I hope you can now answer this yourself. $\endgroup$
    – whuber ♦
    Commented Nov 12, 2020 at 15:59
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    $\begingroup$ Thank you for your help! It makes more sense! $\endgroup$
    – Chris
    Commented Nov 12, 2020 at 20:51

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