Consider a Poisson regression model for a count response (y) with a single continuous covariate (x, E(y mid x)=exp left(alpha_{0}+alpha_{1} x ight)). If (x) is

Consider a Poisson regression model for a count response \(y\) with a single continuous covariate \(x, E(y \mid x)=\exp \left(\alpha_{0}+\alpha_{1} x\right)\). If \(x\) is measured on another scale

 \(x^{\prime}\) such that \(x^{\prime}=k x\), and the model expressed in terms of \(x^{\prime}\) is (E\left(y\midx^{\prime}\right)=\exp\left(\alpha_{0}^{\prime}+\alpha_{1}^{\prime}x^{\prime}\right)\), show that \(\alpha_{0}^{\prime}=\alpha_{0}\) and \(\alpha_{1}^{\prime}=\alpha_{1} / k\).