Regression and Correlation Introduction

Many real and practical situations demand decisions or inferences about how data from a certain variable can be used to determine the value of another related variable.

For example, a Florida study of the number of powerboat registrations and the number of accidental manatee deaths confirmed that there was a significant positive correlation. As a result, Florida created coastal sanctuaries where powerboats are prohibited so that manatees could thrive.

A study in Sweden found that there was a higher incidence of leukemia among children who lived within 300 meters of a high-tension power line during a 25-year period. This led Sweden’s government to consider regulations that would reduce housing in close proximity to high-tension power lines.

The purpose of correlational research is to find co-relationships between two or more variables with the hope of better understanding the conditions and events we encounter and with the hope of making predictions about the future.
The Least Squares methods is a mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the offsets - the residuals - of the points from the curve.