Regression in a Nutshell

Nigel Da Costa Lewis

Suppose, as the only analyst on duty, you are called into the executive suite by your chief investment officer (CIO). They would like to know whether a pay-fixed/received three-month Libor (London Interbank Offer Rate on Eurodollar deposits) interest rate swap can be used to hedge the trading groups’ variable interest expense associated with a prime-based loan. You have been asked to report back inside 30 minutes with an initial report. Critical to your analysis will be the nature of the relationship between Libor and the prime rate. You could look at the correlation between the two variables, although this may be of limited use because it will only indicate the strength of the linear association. Your real interest lies in using the prime rate to explain three-month Libor. This type of problem is a good candidate for regression analysis.

Regression analysis is a technique that provides quantitative information about the relationship between two or more variables. Consider a sample of N pairs of observations {(y₁, x₁), (y₂, x₂), …, (y_N, x_N)} on two continuous variables, X and Y. Regression analysis uses X to help explain Y. Since X is being used to explain Y, it is known as the