Linear Regression

QRB Concepts - Linear Regression

Concept: Conduct a linear regression analysis.

Reading Reference: Ch. 13 of Lind, Marchal, & Wathen and pp. 452-458 of Sevilla & Somers

Example of Application

Linear regression allows us to help quantify the relationship between two variables to show the effect that the independent variable has on the dependent variable. By using this relationship we can say how much of the variation in the dependent variable is explained by the independent variable and also predict the value of the dependent variable for a given independent variable.

The regression output will be in the form of

Y = aX + b where

Y = dependent variable

a = slope

X = independent variable

b = constant or intercept

Regression analyses can help find the strength and magnitude of the link between variables in many fields, not just finance. It is used in research, engineering, and forecasting as well as many other fields where quantitative analysis is required. The use of regression analysis not only helps you find the best relationship, but a relationship that is easily supported and can be replicated by others. Here is an example of how regression analysis is used.

The output for the cost of labor for a printed circuit board line (PCB) yielded the CER.

Y = .05X + 3 where Y is total cost and X is the number of components placed on the board. What this represents is a cost of $3 in fixed labor to load the board and start the machine, and a cost of $0.05 for each component that is place on the board. A board with 100 components would have a predicted cost $0.05 * 100 + $3 = $8.

If the R^2 was .9 then the quantity of components would explain 90% of the cost variation in labor costs in assembling a PCB.

How the Math Connects to the Concept

Using regression analysis in finance, we can define cost estimating relationships (CERs) that can be used to define a model for a cost driver. A regression analysis returns three important numbers:

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