The Population Logit Model of the Binary Dependent Variable Y $\frac { 1 } { 1 + e ^ { - \left( \beta _ { 0 } + \beta _ { 1 } X _ { 1 } \right) } }$

question 48

Essay

The population logit model of the binary dependent variable Y with a single regressor is
Pr(Y=1 | X₁)= $\frac { 1 } { 1 + e ^ { - \left( \beta _ { 0 } + \beta _ { 1 } X _ { 1 } \right) } }$ Logistic functions also play a role in econometrics when the dependent variable is not a binary variable. For example, the demand for televisions sets per household may be a function of income, but there is a saturation or satiation level per household, so that a linear specification may not be appropriate. Given the regression model
Y_i = $\frac { \beta _ { 0 } } { 1 + \beta _ { 1 } e ^ { - \beta _ { 2 } X _ { i } } }$ + u_i,
sketch the regression line. How would you go about estimating the coefficients?

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