What are the uses and limitations of regression analysis in statistics? What are some things you should keep in mind when reporting the results of regression analysis?

Regression analysis is a powerful research tool as it allows researchers to isolate variables of interest. However, regression analysis can be dangerous if its results are misinterpreted or misreported.

Here are a few pointers to keep in mind when interpreting regression analysis results.

## Regression Analysis Pitfalls

Since we use regression analysis to study some of society’s most pressing problems, Wheelan explains that using regression appropriately can be a matter of life and death. Therefore, Wheelan emphasizes the importance of keeping the limitations of regression analysis in mind. To that end, he gives the following reminders for obtaining and interpreting reliable regression analysis results.

Reminder 1: Even when our regression analysis shows that our independent variable is a strong predictor of our dependent variable, we still can’t report that one has caused the other. For example, there may be a highly significant regression coefficient and large R2 for the relationship between white-tailed deer populations and rates of Lyme disease. But this doesn’t mean that the deer are causing the Lyme disease (as we know, the ticks that feed on the deer are).

Reminder 2: We should be careful not to invert our independent and dependent variables. For example, if you wanted to study the link between money and happiness, you would have to be very thoughtful about which variable you selected as the independent variable. If money is your independent variable, you would be studying whether rich people tend to be happier than less-rich people. In contrast, if you select happiness as your independent variable, you would be studying whether happy people tend to be richer than less-happy people. While the two questions may sound similar, these are quite different studies from a research perspective.

Reminder 3: Our results will be misleading if they omit a critical independent variable. For instance, say we published a hypothetical paper highlighting a large and significant regression coefficient for the amount of time people spent at the beach and rates of skin cancer. Our results imply that just being at the beach might somehow give a person cancer when in reality it would be the sunburns in unprotected beachgoers that lead to cancer.

Reminder 4: We shouldn’t extrapolate our regression analysis results to a population for whom our study was never intended. For instance, say we ran a regression analysis that showed a large and significant negative relationship between the number of miles that healthy 1- to 5-year-old dogs walked each day and behavioral problems. We shouldn’t use these results to make a blanket statement that all dogs will behave better when they are walked as far as possible, as this would likely be bad advice for many senior dogs and dogs with certain health conditions.

The Limitations of Regression Analysis in Stats

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Darya’s love for reading started with fantasy novels (The LOTR trilogy is still her all-time-favorite). Growing up, however, she found herself transitioning to non-fiction, psychological, and self-help books. She has a degree in Psychology and a deep passion for the subject. She likes reading research-informed books that distill the workings of the human brain/mind/consciousness and thinking of ways to apply the insights to her own life. Some of her favorites include Thinking, Fast and Slow, How We Decide, and The Wisdom of the Enneagram.