Question

Consider a binary response variable y and an explanatory variable x. The following table contains the parameter estimates of the linear probability model (LPM) and the logit model, with the associated p-values shown in parentheses. LPM Logit -0.66 -7.00 (0.06) (0.06) 0.04 0.16 (0.08) (0.06) Variable Constant

If u get answer is -3.80 and -1.72or positive 3.80 and 1.72 the answer will be wrong

Answer 1

In the logit model, the predicted value is given by,

$\widehat{y}=\frac{1}{1+e^{-(\beta_0+\beta_1x)}}$

Here, $\beta_0=-7.00,\beta_1=0.16$

For x=20,

$\widehat{y}=\frac{1}{1+e^{-(-7+0.16*20)}}$    $=\frac{1}{1+e^{-(-3.80)}}$ = 0.02

And For x=33,

$\widehat{y}=\frac{1}{1+e^{-(\beta_0+\beta_1x)}}$ = $\frac{1}{1+e^{-(-7+0.16*33)}}$ = $\frac{1}{1+e^{-(-1.72)}}$ = 0.15.