# How to meaningfully interpret coefficients in an OLS model made by other people?

I'm a political sciences undergraduate 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/abs/10.1111/j.1467-856x.2008.00331.x?journalCode=bpia).

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 continious variable (which shows the different outcomes of a government defeat coded with numbers from 1 to 5), where 5 is “goverment makes concessions to the Lords” and 1 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).

The first variable (policy significance) ranges from 2 to 6 where 2 stands for a GD causing small alteration to a minor policy and 6 stands for a GD causing major alteration to a significant policy. The idea of this variable is to test whether a GD is more likely to cause concessions by the government if the proposed amendment is for a non-essential policy.

The second variable (lords bill) is a dummy, where one shows that the Bill defeated in the House of Lords originated from the House of Lords and zero shows that the Bill defeated in the House of Lords originated from the House of Commons. The idea of this variable is to test whether a GD is more likely to cause concessions from the government when the bill is initiated by the House of Lords.

The third variable (majority) is a continuous variable, which shows what was the size of the majority which caused the GD. The idea of this variable is to test whether a GD is more likely to cause concessions from the government if a large majority in the House of Lords initiated this GD.

The fourth variable (no. of labour rebels) is a continuous variable, which shows the number of Labour peers which supported a GD against their own government. The idea of this variable is to test whether a GD is more likely to cause concessions from the government if many Labour peers support a GD in the House of Lords.

The fifth variable (conservative mover) is a dummy, where one shows that the GD was initiated by a conservative peer and zero shows that the GD was initiated by a labour or a crossbench peer. The idea of this variable is to test whether a GD is more likely to cause concessions from the government if it was initiated by a Labour or crossbench peer.

The sixth variable (no. of days before the end of the session) is a continuous variable, which shows the number of days until the end of the parliamentary session (sessions are parliamentary years which are around the length of a calendar year starting from the spring of the calendar year X and ending at the spring of the calendar year Y). The idea of this variable is to test whether a GD is more likely to cause concessions from the government if the parliamentary year is about to end soon.

The seventh variable (legal department) is a dummy, where one indicates that the legal department initiated the bill which was defeated at the House of Lords and 0 shows that another department initiated the bill which was defeated at the House of Lords. The idea of this variable is to test whether a GD is more likely to cause concessions from the government if a bill is initiated by a certain department of the government.

Please explain to me how I can meaningfully interpret the columns of the table. As a whole My problem is how to give a meaningful interpretation of the numbers, because I have no access to the dataset and the coding of the authors. To be honest I was never good at statistics and this makes interpretation even more difficult for me. Thank you very much in advance.

• Haven't read the paper but treating what is essentially a ordered categorical dependent variable as numeric and then treating it as continuous in the regression seems problematic. I think there's lots of answers on CV already about interpreting regression coefficients. However, if your confusion is specifically around how to interpret the coefficients and how they map back to (1: gov, 5: gov, etc.) then this is fair enough. Because the DV was treated as such, the link between the coefficients and the true DV is muddied. E.g. What does a prediction of 1.23 even mean?
– epp
Jul 6 at 8:07