Mastering Regression: Understanding Linear Vs. Curvilinear Relationships

Linear relationships and curvilinear associations are often discussed in business research. I discuss the intuition behind linear relationships and the intuition behind curvilinear associations. I think what are some of the differences between linear and curvilinear relationships.

What is a linear relationship in business research? Generally, we think of linear relationships if there is a direct 1:1 mapping between one variable and another. For example, if A increases then B increases, or if A decreases, A increases.

What is a curvilinear relationship in business research? A curvilinear association occurs when variable A has different but consistent values along the values of B. For example, at low values of B, then A is low, at medium values of B, then A is high, and high values of B, then A is low once again.

Why are linear relationships important? Linear relationships do not represent reality very well. Organizations and markets are complex ecosystems. Most variables cause and interact with many other variables.

Most organizational research is in the form of linear relationships because that is how people make sense of the world. We think that if you do one action, than we are going to get one response. Business research also uses linear relationships because the tools we have available to analyze the world mostly use simple linear relationships. For example, ordinary least squares regression is on such tool.

Why are curvilinear associations important? Curvilinear associations are our poor attempt to better represent organizational reality. We will talk in terms of u-shaped relationships and 2x2 matrices to teach MBAs and business students because this is the easiest way to communicate complex ideas.

Where do we go wrong with explaining linear associations and curvilinear relationships? I think a considerable amount of business research fails to first discuss and understand the underlying distributions of the variables. If you do not know the distributions of the variables, than often these relationships can be quite far from reality. We also fail to explain why we expect to get such simple relationships over the choice of many.

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David Maslach is a research professor of entrepreneurship, innovation, and business strategy, I discuss topics, such as behavioral science, strategy, innovation, and entrepreneurship, and apply these to my new peer proofreading and editing platform. Topics include the sharing economy, altruism, investing in technology, starting a business, and bounded rationality. My favorite videos pertain to incentives, goal setting, and learning from failure to drive behaviors such as weight loss, stopping telemarketers, creating novel technologies, and creating new movements.

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