Quick Question
Suppose the coefficients of a logistic regression model with two independent variables are as follows:
\( \beta_{()} = -1.5 , \enspace \beta_1 = 3 , \enspace \beta_2 = -0.5 \)
And we have an observation with the following values for the independent variables:
\( x_1 = 1 , \enspace x_2 = 5 \)
What is the value of the Logit for this observation? Recall that the Logit is log(Odds).
Explanation
The Logit is just log(Odds), and looks like the linear regression equation. So the Logit is -1.5 + 3*1 - 0.5*5 = -1.
What is the value of the Odds for this observation? Note that you can compute e^x, for some number x, in your R console by typing exp(x). The function exp() computes the exponential of its argument.
Explanation
Using the value of the Logit from the previous question, we have that Odds = e^(-1) = 0.3678794.
What is the value of P(y = 1) for this observation?
Explanation
Using the Logistic Response Function, we can compute that P(y = 1) = 1/(1 + e^(-Logit)) = 1/(1 + e^(1)) = 0.2689414.