Linear or Non-Linear Model

Question

I have the following regression equation \begin{align*} y_i = \alpha + \gamma\cdot\beta\cdot x_i+ \varepsilon_i, \end{align*} where $y_i$, $x_i$ and $\varepsilon_i$ are $n\times 1$ vectors, $\varepsilon_i\stackrel{iid}{\sim}\text{N}(0,\sigma^2)$ for all $i=1,\ldots,n$ and $\alpha$, $\beta$ and $\gamma$ are unkown constants.

Is this a linear regression model in the unkown parameters $\alpha$, $\beta$ and $\gamma$ ?

Answer 1

Rename $\beta \cdot \gamma = \delta$ and you have a regression in $\alpha$ and $\delta$ with $\epsilon_i$ denoting the model error.