Suggest a Transformation in the Variables That Will Linearize the Deterministic

Essay

Suggest a transformation in the variables that will linearize the deterministic part of the population regression functions below. Write the resulting regression function in a form that can be estimated by using OLS.
(a)Y_i = β₀
$X _ { 1 i } ^ { \beta _ { 1 } }$ $x _ { 2 i } ^ { \beta _ { 2 } }$ (b)Y_i = $\frac { X _ { i } } { \beta _ { 0 } + \beta _ { 1 } X _ { i } }$ (c)Y_i = $\frac { e ^ { \beta _ { 0 } + \beta _ { 1 } X _ { 1 } } } { 1 + e ^ { \beta _ { 0 } + \beta _ { 1 } X _ { 1 } } }$ (d)Y_i = β₀
$X _ { 1 i } ^ { \beta _ { 1 } }$ ${ e } ^ { \beta _ { 2 } \beta _ { 2 } X _ { 2 i } }$