# How to interpret coefficients for a binary DV in an OLS model and constant value meaningfully?

everyone.

I'm a political sciences undergrad student working on a study of the activity of the Upper Chambers in the UK and other former British colonies. I came across a 2008 study by Russell and Sciara called 'The policy impact of defeats in the House of Lords' (https://journals.sagepub.com/doi/full/10.1111/j.1467-856x.2008.00331.x). Government defeats (GDs) are cases in which the government fails to persuade the members of the House of Lords to back its legislative proposal. When facing a GD the government can either accept the defeat by making concessions in favor of the Lords' demands or by re-voting the proposal in a year in the House of Commons and thus overcoming the blockade of the Lords. So the authors of the study made an OLS model (see photo) in which the dependent variable 'outcome of government defeats' is a dummy, where 1 is goverment makes concessions to the Lords' and 0 is government makes no compromise and overrides the peers' veto. The independent variables are reflections of different factors which can influence the acceptance or rejection of a GD (they are explained on pp 576, 578-579). Please explain to me how can I meaningfully interpret the constant and please suggest a sample detailed interpretation for one of the independent variables. As a whole My problem is how to give a meaningful interpretation of the numbers, because the authors' interpretation is too general and strictly fixed to the context of the significance/insignificance of the independent variables. To be honest I never used a OLS model for binary dependent variables and this makes interpretation even more difficult for me. Thank you very much in advance.

• Is there a table of means for the independent variables? At first glance, the constant does not make much sense unless some of the other variables can be negative. This is called a linear probability model in economics. Commented May 25, 2022 at 15:37
• Please don't change your question to the extent that it invalidates existing answers - you can always ask a new question. Commented Jul 3, 2022 at 15:54

$$P(Y = 1 \vert X_1, X_2, \dots, X_k) = \beta_0 + \beta_1 + X_{1i} + \beta_2 X_{2i} + \dots + \beta_k X_{ki}.$$
\begin{align*} P(Y=1\vert X_1, X_2, \dots, X_k) =& \, F(\beta_0 + \beta_1 X_1 + \beta_2 X_2 + \dots + \beta_k X_k) \\ =& \, \frac{1}{1+e^{-(\beta_0 + \beta_1 X_1 + \beta_2 X_2 + \dots + \beta_k X_k)}}. \end{align*}