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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?

Thomas Bilach
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Chris
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  • Welcome! You should find this [post](https://stats.stackexchange.com/questions/388706/confidence-interval-of-a-log-linear-regression) and this [post](https://stats.stackexchange.com/questions/93230/beta-confidence-intervals-in-transformed-linear-regression) helpful. – Thomas Bilach Nov 12 '20 at 07:56
  • 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. – whuber Nov 12 '20 at 15:59
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    Thank you for your help! It makes more sense! – Chris Nov 12 '20 at 20:51

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