Multiple Regression Analysis in Business: Uses & Examples

Instructor: Scott Tuning

Scott has been a faculty member in higher education for over 10 years. He holds an MBA in Management, an MA in counseling, and an M.Div. in Academic Biblical Studies.

Regression analysis is a powerful statistical tool that can help remove variables that do not matter and select those that do. This lesson explores the use of a regression analysis to answer research questions in business.

Do We Sell More Socks When It Rains on Thursday?

If you have been a sales professional, or you've listened to a pitch from a sales professional, you already know more about regression analysis than you think. It usually goes something like, ''So in conclusion, businesses that use our software increase their profits by more than 12% on average.'' A statement like this is simultaneously entirely accurate but also may be misleading.

If the software vendor is citing that statistic in a sales pitch, it likely means that they examined the financials of their customers and calculated a simple average. In this sense, the data is correct, but the statement has not yet established that there is actually any relationship at all between the software being pitched and a client's profit increase. This is called a correlation. A correlation is an observation that two things seem to happen with frequency, but it does not speak to whether the variable is actually causing the occurrence. To better illustrate the point, take a look at some exaggerated cases of correlation without a true relationship:

  • The price of milk goes up when a Democrat occupies the White House.
  • When John gets a flu shot, his interest in baseball goes way up.
  • People who are left-handed tend to drive four door sedans.

The goal of a regression analysis is to weed through useless correlations like these, and turn them into actionable data instead. In technical terms, a regression is conducted for the purpose of ''thinning the herd'' of variables in order to find the ones that actually matter. If a regression has been constructed and analyzed correctly, it will establish the presence or absence of a relationship, but it is still not necessarily a cause relationship between variables.

How Do We Know That This Data Actually Means Anything?

Plotting data points in a regression is how statisticians determine whether or not a relationship exists. Graphing the results of a regression is one of the most effective ways of presenting data gathered from a regression analysis. The graph is created by plotting a dependent variable on one axis and an independent variable on the other axis. The data points are placed on the graph and a pattern (or lack thereof) emerges. Let's look at an example to help better explain this process.

A fictional bookstore is seeing sales of adult non-fiction books drop month over month, and the company's directors want to know why. What are some of the variables you think might be relevant?

  • Are some existing customers choosing other booksellers because they have better pricing?
  • Are potential customers unaware that our store exists because marketing efforts are not effective?
  • Does the store lose customers because a competitor offers more discounts and more clearance sales?

Graphing the data is important because the trend line on the graph is essentially the answer to the question. When a regression is plotted and the result shows no pattern (Figure 1), it is unlikely that there is any relationship between the variables at all. In our example, a research question like, ''How does the price of wheat in Europe affect sales numbers in our bookstore?'' is likely to demonstrate no relationship whatsoever.

Figure 1. When there is no pattern when the regression is plotted, there is no significant relationship between A and B.
Figure 1

But what if the question were, ''Is more effective to advertise on TV, radio, or the internet?'' The resulting graph would show a general trend that is much more defined than the chaotic chart that showed no relationship at all (Figure 2).

Figure 2. When a pattern emerges, it can asserted that there is relationship of some kind between A and B.
Figure 2

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