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I have been asked to check over a paper. The paper is using log linear regression. In the following log linear equation, $x$ is the dependent variable, $y$ is a continuous covariate, $z$ is a categorical variable taking value of 0 or 1 for yes/no. $A$ and $B$ are regression coefficients and $C$ is the intercept. The equation is:

$\log(x) = A \times \log(y) + Bz + C$

$\log$ here is natural logarithm.

Solving this equation for x, the writer got

$x = y^A \times e^Bz \times e^C$

For some reason, I feel that's not correct. Can someone please tell me if this is correct? If not, what would be the correct derivation of equation 2 from equation 1?

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    $\begingroup$ the middle term should be $e^{Bz}$ $\endgroup$
    – Glen_b
    Sep 11, 2013 at 13:25

1 Answer 1

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Have you tried solving the equation in terms of $x$?

\begin{align*} \log(x)&=A\log(y)+Bz+C\\ \end{align*} so take the exponential of both sides to get

\begin{align*} x&=e^{A\log y+Bz+C}\\ &\\ &=e^{A\log y}e^{Bz}e^{C}\\ &\\ &=e^{\log y^A}e^{Bz}e^{C}\\ &\\ &=y^Ae^{Bz}e^{C} \end{align*}

and so this should be the solution.

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