Linear Regression and Correlation

Summary :

This chapter grounds linear regression and correlation in economic model-building, using the theory of consumer choice and the demand curve as an example of how assumptions lead to a testable relationship between variables. It covers the correlation coefficient, testing its significance, linear equations, and the regression equation itself.

Models, theories, and testable relationships

The chapter opens by connecting regression to the broader idea of a model, a theorized cause-and-effect relationship, illustrated with the economic model of consumer choice, where assumptions about preferences and utility maximization generate the prediction embodied in the demand curve, an example of how a theory produces a relationship that can then be tested statistically.

The correlation coefficient and its significance

The correlation coefficient r measures the strength and direction of a linear relationship between two numeric variables, and the chapter covers how to calculate and interpret it, followed by a hypothesis test for whether the observed correlation is statistically significant or could plausibly have arisen from an uncorrelated population.

Linear equations and the regression equation

Building on the algebra of a linear equation, the chapter develops the regression equation as the statistical technique for finding the line of best fit through a set of paired data, letting an analyst predict one variable, such as pay for a repair job, from another, such as an initial fee plus an hourly rate.