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For my master's thesis I am examining a mediated relationship. I need to write out the equation model, but do not know exactly how to do this. In my case I have four independent variables, one mediated variable and one dependent variable. How do I add the mediated variable to the equation? Until now I got this:

Exploitative innovation $= \alpha + \beta_1\ $Inspirational motivation $+\ \beta_2\ $ Individual consideration $ +\ \beta_3\ $ Intellectual stimulation $+\ \beta_4\ $ Idealized influence $+\ \beta_5$ Knowledge exchange and combination capabilities $+\ \epsilon, \epsilon \sim$ iin (0, $\sigma$).

$\beta_5$ is my mediated variable. Can I just add this or do I have to multiply something?

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Not an expert on this, but the Statistical Mediation Wikipedia Page uses three regressions. In them, you would use an interaction (multiplication).

You might also look into Structural Equation Modeling (SEM), which I believe can directly model mediation. R, Stata, and other packages can do SEMs, though it seems to be a bit of an art to me.

Also be clear if you're looking for mediation or moderation (or moderated mediation).

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