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 of and applied this method while working for 15 years in market research and teaching college 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 don’t have a reasonably accurate assessment of the future for your business, you are likely to under-plan or over-plan, leading to unrealized gain or overspending.
What is Linear Regression anyway? Basically it’s a mathematical technique that relates one group of numbers with another in terms of an equation. If these two sets of numbers have a meaningful relationship, this can lead to a good assessment for the future.
Lets say you have a small business related to the construction industry. When overall construction activity is up, so tends to be your business. There is a statistical way to measure the closeness of this relationship called the Coefficient of Determination, also taught in a basic Statistics class. Through the method of Linear Regression, you can determine an equation that relates general construction activity with your company’s business results historically. Then by using a published forecast for future general construction activity (such as from a bank or college), 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 do predictions using several factors. For example, in the prior example, you could predict the business’ sales considering not only construction activity but promotional activity and sales force expansion. The beauty of this method is it relates one’s business to important real world factors and does it mathematically.
One additional application of Linear Regression, and that is trend projection. You may not know or have data for important factors influencing sales but would like to just see where business is heading. Using this method, you can find the line that most perfectly fits past results and forecast based upon an extension of this line. You can mathematically measure how close results have been to this line in the past. Also, you can choose the type of curve you believe best fits past data. It could be linear or nonlinear, such as parabolic.
In summary, if you are looking for a very practical application of Mathematics, take a look at Linear Regression. For many businesses it helps with the bottom line.