Regression explained for lawyers

Your law firm or law department might want to learn even more from numbers you have collected. One software tool to do so carries out what is called regression. How to understand and benefit from regression will be the topic of a series of posts. The goal will be to use everyday language and a lawyer framework to explain how to use regression responsibly, how to intuitively understand the results of regression, and ways to make it real and nonthreatening to managers of lawyers.

How might managers of lawyers apply regression? A general counsel might investigate whether the size of law firms retained is associated with average effective billing rate. Or she might predict whether more matters assigned to a firm is associated with lower effective billing rates. The managing partner of a law firm might look at several pieces of information about associates and use regression to estimate the likelihood of an associate making partner. Or the head of marketing might learn to what degree the number of participants in a survey influences how many times the report is downloaded. Countless examples exist of the ways regression can illuminate numbers in law firms and law departments.

To start, we need to settle on some terminology. All regression analyses need numbers, which statisticians call data. The example data in this series comes from the 2012 time-frame and consists of the number of private-practice lawyers in each state, the population of each state, the state’s “GDP”, and the number of Fortune 500 companies that have their headquarters in the state. The four numbers for each state are variables.

Here are some more terms you should feel comfortable with from regression. We will create a regression model that predicts the number of lawyers in a state — the number of lawyers is the response variable, from the state’s population, GDP and F500 number, called the predictor variables or the independent variables.

Regression estimates a response variable from predictor variables, which you can rephrase as estimating the dependent variable from the independent variables — in our model the number of lawyers in the state depends to an unknown degree on the number of people living in the state, the state’s economic productivity (its GDP), and how many huge companies call that state its home. You should think of a regression model as a condensed description of a set of numbers by means of an equations. Creating a useful model underlies much of what data analysts do, including many forms of machine learning.

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