The irony of the random variable (r.v.) is that although it takes on an “unpredictable” value every time, it’s not exactly random if we understand the shape of its distribution. This is why descriptive statistics matters a lot—they define the boundaries of the set of values an r.v. can take, otherwise known as, again, the […]

One assumption we discussed for linear regression is the independence of error terms. In that setting, we were typically dealing with cross-sectional data, where we assumed that observations don’t influence each other. Time series data is a little special. Over time, observations are rarely ever independent. If we observe that today’s stock price is high, […]

One of the most important assumptions for statistical models to work is the notion of consistency. This means that statisticians often drool with excitement when they find out that their data has approximately stable statistical properties, because they can finally unlock the cabinet of unused dusty models. In time series analysis (and several other disciplines), […]

We’ve briefly talked about how pp-values should be interpreted. It’s crucial to understand that a pp-value of 0.01 doesn’t mean that there is a 1% chance of some null hypothesis being true. Instead, it implies a 1% chance of observing data as extreme or more extreme than the current data under the condition that the […]

The normal distribution is one of statistics’ most precious models of reality. It’s analytically tractable, computationally simple, and provides a universal language for uncertainty. As such, it definitely deserves an in-depth exploration of its characteristics, properties, and significance. And then, we’ll explode in, Game of Thrones style, to ruin the perfect rainbow world of normality […]

There was a time when I used to apply linear regression to some data and if the resulting metrics (R2R^2, RMSE, MAE, etc.) were unsatisfactory, I simply concluded that the regression wasn’t a good fit and I should probably instead look at other models like gradient boosting or neural networks. If you don’t think this […]