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

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The Answer is The equation cannot be estimated using linear methods or transformations that
allow linearization.However, nonlinear least squares estimation is possible as
described in section 11.3 of the textbook. $The equation cannot be estimated using linear methods or transformations that allow linearization.However, nonlinear least squares estimation is possible as described in section 11.3 of the textbook. Some students may point out that \widehat { \beta } _ { 0 } will give an estimate of the satiation level (perhaps 10 TVs per household), and that the point of inflection is at 20 X = \frac { 1 } { \beta _ { 2 } } \ln \beta _ { 1 } .$ Some students may point out that

\widehat { \beta } _ { 0 }

will give an estimate of the satiation level (perhaps 10 TVs per household), and that the point of inflection is at 20

X = \frac { 1 } { \beta _ { 2 } } \ln \beta _ { 1 } .

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

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The Population Logit Model of the Binary Dependent Variable Y Pr⁡(Y=1∣X1)=11+e−(β0+β1X1)\operatorname { Pr } \left( Y = 1 \mid X _ { 1 } \right) = \frac { 1 } { 1 + e ^ { - \left( \beta _ { 0 } + \beta _ { 1 } X _ { 1 } \right) } }Pr(Y=1∣X1​)=1+e−(β0​+β1​X1​)1​

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

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Verified