Practice: Predicted Probabilities

If you complete this exercise using the Quarto file used to generate this page, you could be able to change the format: header above to say format: pdf, it will render as a pdf file that includes just the questions and your answers (and not, for example, this text).

In this exercise, you can work with the logit results from the reduced and full model that you fit in the previous problem set on the logit model. Our preference would be that you use the same data and models unless there is some reason not to, in which case go ahead and do something different, but look back at that problem set for the features of the data and model that we wanted you to include.

1. Compute (using software) the predicted probability that \(y=1\) for an observation with a substantively meaningful set of values for the explanatory variables in your model. [1]

2. Compute the predicted change in the probability of your outcome for your key binary explanatory variable changes from 0 to 1. In a sentence, interpret the change you have computed. (You can do the predicted change at the mean, the mean predicted change, or change from a set of values of your choosing for the other explanatory variable, although in your interpretation you want to make clear which.) [2]

3. Using your logit results from the full model, construct a handsome plot showing how the predicted probability of the outcome changes as the explanatory variable changes. In a sentence, describe what this plot shows. [5]

The plot should:

• Have separate lines for the two groups defined by your binary covariate, with different colors and line patterns (e.g., solid vs. dash) for each line.
• Either average over the sample or hold any other covariates constant to some value.
• Label the axes simply but clearly.
  
• The legend of the plot should be clear.
• Have a white background.

4. Compute the average marginal change in the outcome probability for a change in your key continuous explanatory variable. Interpret the result.