Question

Consider the following population regression model to explain monthly beerconsumption \text { beer }_{i}=\beta_{0}+\beta_{1} \text { inc }_{i}+\beta_{2} \text { price }_{i}+\beta_{3} \text { educ }_{i}+\beta_{4} \text { female }_{i}+u_{i} E(u \mid \text { inc, price, educ, female })=0 ; \operatorname{Var}(u \mid \text { inc, price, educ, female })=\sigma^{2} \text { inc }^{2} \frac{b e e r_{i}}{i n c_{i}}=\frac{\beta_{0}}{i n c_{i}}+\beta_{1}+\beta_{2} \frac{p r i c e_{i}}{i n c_{i}}+\beta_{3} \frac{e d u c_{i}}{i n c_{i}}+\beta_{4} \frac{f e m a l e_{i}}{i n c_{i}}+\frac{u_{i}}{i n c_{i}}_{i} \text { O } \frac{\text { beer }_{i}}{\sqrt{\text { inc }}_{i}}=\frac{\beta_{0}}{\sqrt{\text { inc }_{i}}}+\beta_{1} \frac{1}{\sqrt{\text { inc }_{i}}}+\beta_{2} \frac{\text { price }_{i}}{\sqrt{\text { inc }_{i}}}+\beta_{3} \frac{e d u c_{i}}{\sqrt{\text { inc }_{i}}}+\beta_{4} \frac{\text { female }_{i}}{\sqrt{\text { inc }_{i}}} \text { O } \frac{\text { beer }_{i}}{\text { inc }_{i}^{2}}=\frac{\beta_{0}}{\text { inc }_{i}^{2}}+\beta_{1} \frac{1}{\text { inc }_{i}}+\beta_{2} \frac{\text { price }_{i}}{\text { inc }_{i}^{2}}+\beta_{3} \frac{e d u c_{i}}{\text { inc }_{i}^{2}}+\beta_{4} \frac{\text { female }_{i}}{\text { inc }_{i}^{2}}+\frac{u_{i}}{\text { inc }_{i}^{2}} \begin{array}{l} \text { Oeer }_{i}=\frac{\beta_{0}}{\sigma \times i n c_{i}}=\beta_{1}+\beta_{2} \frac{\text { price }_{i}}{\sigma \times \text { inc }_{i}}+\beta_{3} \frac{e d u c_{i}}{\sigma \times \text { inc }_{i}}+\beta_{4} \frac{\text { female }_{i}}{\sigma \times \text { inc }_{i}} \\ +\frac{u_{i}}{\sigma \times i n c_{i}} \end{array}

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