Powerful practical mathematics found in linear regression

A great application of practical mathematics can be found in the statistical technique called Linear Regression. I learned and applied this method while working for 15 years in market research and teaching University Statistics for about 10 years.

Why is this method so useful? It is a forecasting tool that can be extremely valuable to a business. Accurate forecasting is part of the life blood of a successful business. If you do not have a reasonably accurate assessment of the future of your business, it is likely that you are planning too little or too much, resulting in unrealized profit or overspending.

What is linear regression anyway? It is basically a mathematical technique that relates one group of numbers to another in terms of an equation. If these two sets of numbers have a significant relationship, this can lead to a good evaluation for the future.

Let’s say you have a small business related to the construction industry. When overall construction activity increases, it is usually your business, too. There is a statistical way to measure the closeness of this relationship called the Coefficient of Determination, which is also taught in a basic Statistics class. Using the Linear Regression method, you can determine an equation that historically relates overall construction activity to your company’s business results. Then, using a published forecast for future general construction activity (such as from a bank or university), you can estimate your business results.

Companies will even go further in using this method than simple linear regression. They will use what is called multiple regression where they will make predictions using various factors. For example, in the example above, you could predict the company’s sales by considering not only construction activity, but also promotional activity and sales force expansion. The beauty of this method is that it relates one’s business to important factors in the real world, and it does so mathematically.

An additional application of linear regression, y is trend projection. You may not know or have no data on the important factors that influence sales, but you would like to see where the business is heading. With this method, you can find the line that most closely matches the previous results and the forecast based on an extension of this line. You can mathematically measure how close your results have been to this line in the past. Also, you can choose the type of curve that you think best fits the above data. It could be linear or non-linear, such as parabolic.

In short, if you are looking for a very practical application of mathematics, take a look at Linear Regression. For many companies, it helps with the bottom line.