Problem Set: Linear Probability Model

Practice

If you complete this exercise using the Quarto file used to generate this page, you should 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).

As we consider binary outcomes, you will be interpreting results from a substantively intelligible, empirical, and hopefully interesting example of your choosing regarding a binary outcome.

For the example:

  • Your data should have at least 400 observations and should have at least 80 values for both \(y=1\) and \(y=0\) for your outcome.

  • You will want to have a binary explanatory variable and a continuous explanatory variable that you are comfortable talking about as though they were the key explanatory variables in your model. “Continuous” in this context just means that you are willing to interpret it as an interval-level variable. These variables should have a statistically significant association (at the \(p < .05\) level) with the outcome.

  • You will also want to have at least 1 sensible covariate that you can include in models in addition to these variables.

  1. Clearly, but briefly, motivate the example. That is: Provide a rationale for why you are looking at the relationship between each of your explanatory variables (both binary and continuous) and this outcome. [3]
  1. Fit a linear probability model with your key explanatory variables and whatever covariates. [1]
  1. In a deftly worded sentence, interpret the coefficient for your key binary explanatory variable in the full model. [1]
  1. In a deftly worded sentence, interpret the coefficient for your key continuous explanatory variable in the full model. [1]
  1. How substantively reasonable does the idea of linear probability seem for your example? Explain your reasoning. [3]