Ebook: Interpreting Linear Regression

Master the Art of Interpreting Linear Regression Coefficients

Clearly understanding regression coefficients is perhaps the most useful and important knowledge you can have as a data analyst. When you don’t understand your results, it’s hard to make compelling conclusions about your research.

But understanding the results of your analysis is about more than reaching the right conclusions. When you intuitively understand what each coefficient communicates, you can conciously choose the predictors that succictly answer your research questions.

In 10 years of statistical consulting, misunderstanding linear regression results is the single biggest source of questions and mistakes I’ve seen.

Sometimes it makes the analysis take longer and be more frustrating.

But not always. Sometimes it really affects your research. I have personally seen all of the following happen:

• Real, interesting, compelling results that were completely missed when the researcher didn’t include a categorical, polynomial, or interaction term.
• Articles rejected on statistical grounds, even though the statistics were correct! The authors just didn’t explain the results of the model accurately.
• Panic, and unnecessary stress, when results change in the presence of different kinds of predictors.
• Regression models with predictors that don’t answer the intended research questions.
• Arbitrary practices like median splits in order to squeeze data into the statistical method the analyst understands.

Often it’s one of these outcomes that compels researchers to seek out statistical help.

It all comes down to the same result–you can’t do accurate and compelling data analysis if you don’t understand what the different types of predictors will tell you.

The good news is that anyone with a basic background in regression or ANOVA can attain this level of intuitive understanding.

The meaning of regression coefficients is largely determined by the form of the predictor variable. How they are interpreted is fundamentally the same in all kinds of regression models–logistic regression, multilevel models, analysis of covariance, survival models, poisson regression–all of them.

But because these other models include logarithms, odds, extra sources of variance, and other mathematical complications, the coefficients in all these other models are harder to understand–they’re less intuitive.

You don’t want to be struggling with understanding the meaning and consequences of concepts like centering, intercepts, polynomials, and interaction terms at the same time you’re trying to understand hazard functions, odds ratios, or covariance matrices. You’ll drive yourself crazy.

But, if you can master how to interpret the different types of coefficients in the context of a straightforward model like linear regression, it’s only one step further to apply them to more complicated models.

In linear regression, understanding how to interpret coefficients is generally staightforward. It didn’t make all that much sense in your statistics classes because the focus there is on giving you background knowledge, not working with real data.

This ebook will give you a solid understanding of many types of regression coefficients in the context of real output.

You will learn:

• How correlations among predictors affect the meaning of their coefficients
• When to use Standardized Coefficients and what they mean
• How and when to center predictors to improve interpretability of coefficients and when centering affects the meanings of other coefficients in the model.
• How to interpret all your coefficients when your model contains polynomial terms, including quadratic and cubic terms
• The differences between dummy and effect coding, the advantages of each, and why Regression and ANOVA are really the same thing
• How to dummy code binary and multi-category predictors
• How to use and how to finally understand interactions for categorical predictors
• The only way to interpret interactions for two continuous predictors
• How to make sense of interactions with categorical and continuous predictors
• How including interaction or polynomial terms changes the meaningof other coefficientsHow the meaning of all these coefficients changes when they’re included together in the same model–centering, dummy coding, interactions, polynomials.

Who is it for?

• You will get the most out of this ebook if you have had at least two statistics classes—an intro class, and a class that contains multiple regression or Analysis of Variance (ANOVA). This ebook does not cover the theory or derivation of regression modeling. It touches on creating results, but the real focus is on understanding the output.
• That said, if you’ve had one statistics class, but need to use regression and are confused, this ebook will give you a firm understanding of what linear regression is for, what it means, and how to work with different kinds of predictor variables.
• You should be familiar with using a statistical software program.  I use SPSS in the examples and discuss some issues in the context of SPSS. That said, this ebook is not about the software, and it will be helpful to you as long as you use some statistical software.

If you would like to learn the ins and outs of linear regression coefficients, I invite you to real understanding.

This 179-page ebook contains everything I teach in my 4.5 hour workshop. If you are someone you prefers to read than to watch or if you want a resource that is easy to look things up in, this is for you.