regressione Archives - paologironi blog

Multicollinearity, Heteroscedasticity, Autocorrelation: Three Difficult-Sounding Concepts Explained Simply (with an Example in R)

In the posts on multiple regression, analysis of variance and time series we came across three terms that seem made on purpose to scare the reader. Multicollinearity, heteroscedasticity, autocorrelation: if we want to convince someone that statistics is a dark and inaccessible subject, these are the magic words to say. 🙂

Surprise: behind the names there are three simple ideas, and above all three very concrete problems. To see them at work, let’s take the model that sooner or later anyone working in digital marketing builds: how many conversions does each euro spent on Google Ads and on Meta bring us? We’ll watch it fall into all three traps, one after the other, and learn how to recognise them and get out.

Correlation and Simple Linear Regression: the Line, Pearson’s r and R²

The hotter it gets, the more ice cream sells: we all suspect as much. But by how much? If tomorrow the thermometer reads 27 degrees, how many ice creams should we get ready? And, moving onto our own ground: if we raise the campaign budget, how many extra conversions can we expect?

Concepts such as the mean or the standard deviation describe one variable at a time. Questions like these, instead, require us to look at two variables together: that is the job of correlation and simple linear regression, two of the most widely used (and most misunderstood) tools in data analysis.