Regression Analysis With Excel

Regression Analysis With Excel

Regression Analysis With Excel

In statistics, we see for the first time how certain mathematical equations are formulated. One way to derive relationships between two or more quantities is called regression analysis. The applications are numerous and apply to the biological, physical, and social sciences. Essentially, what this method does is allow us to make predictions based on data outside the observable range. Such predicting is known as extrapolation.

Functions and Models

A key part of mathematics involves patterns, relationships, rules, and models. The reaches of this subject extend well beyond what the casual observer might first contemplate. Yet most people fail to understand that the ability to make very accurate predictions is what gives mathematics its validity. When the deflection of light as predicted by Einstein's General Theory of Relativity was confirmed during a solar eclipse in 1919, the world proclaimed the greatness of mathematics, and indeed physics. As my advanced calculus professor would often say, "Calculus works very well in the real world." For this reason, calculus---as well as many other branches of mathematics---has credibility within the universe.

In mathematics, functions are the rules or models that govern. Functions are the tools that allow us to make predictions about what we see around us. Linear functions are some of the simplest of mathematical models, yet they figure in many applications. Linear regression is a method which creates a linear equation from a series of observed data points. Once we have such a line, we can extend it in both directions to make predictions about values outside the observed range. This what extrapolation is all about.