Predicting Binary Dependent variable with predictor variables (both categorical and numerical)

Question

I have all the information I need from my logistic regression and know which variables are significant and by how much, but is there any way for me to write an equation that will give me the probability of a "yes" result based on new independent variable entries? I'm sure I could figure out individual cases by hand maybe, but does anyone have any methods for using logistic regression results in a formula (excel maybe?) to predict the DV based on IVs?

I am using SPSS (sorry, not a true R statistician) and there doesn't seem to be a way to use the results of my regression to predict the DV of new samples I gather.

If anyone can point me in the right direction, I would appreciate it as I am fairly new to the stats game. Thanks!

Answer 1

You could easily do this 'by hand' using excel if you were not concerned about the uncertainty in your predictions (e.g., obtaining a 95% confidence interval for the estimated probability).

First calculate the estimated log odds of the outcome by substituting the new values for the variables into your regression formula (note that the betas are the estimated regression coefficients from your model):

$log odds_i = \beta_0 + \beta_1 X_i + \beta_2 Z_i ....$

Then, perform the inverse logit transformation on the estimated log odds to get into the probability scale:

$Pr(Y_i = 1) = e^{log odds_i} / (1 + e^{log odds_i})$

In excel, it looks like you can use the LOGIT command here instead of manually coding the above formula (set Return_type = 2).

If you also want to estimate uncertainty in your predicted values (with a confidence interval/standard error), this is trivial in R but I'm not sure exactly how to do this in SPSS or Excel.