Econometric Theory/What is Regression?

Historical Meaning of Regression

The historical meaning of the term regression was coined by statistician Francis Galton. He observed that tall parents tended to have short children and short parents tended to have tall children. It seemed as though the height of people was heading to the average of the population across generations. His friend Karl Pearson collected statistics on the heights of individual family members. He found that sons of short fathers tended to be taller than the average height of those fathers and sons of tall fathers thus turned out to be shorter than their fathers.

Modern Interpretation of Regression

It can be said that regression analysis is used to model relationships between variables and determine the magnitude of those relationships.[1] Regression analysis is really a more accurate description for regression, but regression is fully comprehensible as an abbreviated term and we will use that one henceforth.

Examples

A number of examples where regression can be used is:[2]

• 1. Galton was interested in finding out why average height was stable over generations. We could also say that we are interested in finding out why the average height of sons would be different from the average height of fathers. A hypothetical distribution can be seen in the scatter diagram to the right. In it, you can also see the regression line which shows the average height of sons given the average height of the fathers.

{scatter diagram}

• 2. A monopolist wants to know how demand adjusts for changes in price or output. This allows him to maximise profit. This price responsiveness is called price elasticity.
• 3. The Phillips curve describes the effect of changes in unemployment to the unemployment rate. This could be used to predict a suitable level of inflation that is suitable to the public opinion on unemployment.
• 4. A policy maker may want to see if there is a relationship between expenditure on police and the crime rate in a particular area. It can be useful if we want to know how to tackle crime more efficiently by allocating more money where crime is higher.

Notes

1. Regression analysis
2. Examples 1-3 from Gujarati (2003, p.18-21)

Bibliography

• Gujarati, D.N. (2003). Basic Econometrics, International Edition - 4th ed. McGraw-Hill Higher Education. pp. 16–21. 0-07-112342-3.