## Six Sigma Toolkit: What is Linear Regression

The equation *y=a+xb *may remind you of elementary grade school, high school algebra, or college calculus. However, one thing is certain, everyone recognizes this equation. Simply put, it calculates the equation of a line of a graph. Basic information, such as the slope of the line and the y-axis intercept help calcualte the final equation. In the end, you have the linear regression. In industry, linear regression is becoming a widely-used method for business process improvement. More specifically, Six Sigma professionals are discovering the benefits of using such a method. In today’s article, we will discuss the definition of linear regression, how it’s used in Six Sigma, and why you should use it as a professional.

**What is it?**

By definition, This is a mathematical formula you can use to calculate the relationship between multiple variables. Typically, two variables are plotted against each other and their trends are made visible. However, linear regression can become more detailed than simple line equations. First, this formula can be used to calculate the difference between two different data points on a chart. Equations, like best fit line, standard error of estimate, and coefficient of correlation are all complimentary tools you can use. With these equations, you will quickly visualize your business processes and relations to one another.

**How to Use Linear Regression in Six Sigma**

Because Six Sigma supports itself on statistical data, linear regression is a great tool for business process improvement. Whether understanding the correlation between two variables or making predictions about future processes, linear regression is ideal for professionals. For linear regression, there are a few complimentary equations that can benefit any Six Sigma project management and analysis.

First, when graphically plotting the linear relationship between two variables, you can calculate the Standard Error of Estimate. This equation calculates how far specific data points are from the linear regression and thus visualizes trends, outliers, or other relevant data. Likewise, if you need to calculate the percentage of variation in your linear regression model, you can use the Coefficient of Correlation. This equation calculates the accuracy of your linear regression and how precise your correlation is. The closer 1.0, the better!** **

**Why You Should Use Linear Regression**

Simply put, linear regression measures the relationship between two independent variables. For Six Sigma professionals, this is usually variables in a business process. As a project manager, senior advisor, or a part-time team member, your job is to find ways to improve the tasks at hand. In Six Sigma, a focus on increasing efficiency while reducing error take priority. Using the statistical data provided by linear regression models, you can easily spot correlations between variables in your production, manufacturing, and logistical processes. For example, when conducting root cause analysis, linear regression is a simple tool employers use to locate the cause of errors. While not every tool will be beneficial to your specific Six Sigma project, linear regression is a easy to use, readily available one to have on hand!