Regression Analysis


Regression analysis is a statistical method that attempts to find relationships within a data set.


When using a scatter diagram for the data.

When working with paired numerical data.

When looking at how changing an independent variable will affect the dependent variable.

When predicting future performance using past results.

How do I use this tool?

1. Linear regression can be done by hand or with the use of computer programs. A linear regression analysis generates a graph with a best-fit regression line through the data. A series of statistics will also be supplied, and typically includes the following:
a. Slope of the line, with the equation of the form y = mx + b, where the slope of the line is m.
b. Intercept of the line, which is equal to b in the line’s equation. The intercept is the value of y where the line crosses the y-axis.
c. Coefficient of determination, r². This number, which is between 0 and 1, is a measure of how well the data fits the line. A result of r² = 1, indicates the line is a perfect fit, but as r² gets decreases, the fit becomes increasingly poor, resulting in less accurate predictions based on the line.
d. Confidence interval is often 95 percent. This is a range of values around one or more of the previous statistics. You can be 95 percent certain that the true value of a given statistic is within the provided range.

Expertise Required
This tool is an advanced tool and requires formal training or education.
Recommended Supplies/Materials
Paired numerical data
Statistical software

Allows one to determine relative influence of (independent) variables on an outcome (dependent variable).


Training in linear regression techniques is needed.

Where can I go to learn more?

Tague N. The tools. In: O'Mara P, editor. The quality toolbox. 2nd ed. Milwaukee, WI: ASQ Quality Press; 2005. p. 93-521.

George M, Rowlands D, Price M, et al. Identifying and verifying causes. The lean six sigma pocket toolbook. New York: McGraw - Hill; 2005. p. 141-96.