R Tutorial: Introduction to Statistical Modeling in R

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Hi. Welcome to statistical modeling. I'm Danny Kaplan, the author of this course. I'll be the instructor in these DataCamp video segments and I'll be behind the scenes in the interactive exercises that follow each video.

Statistical modeling is one of the most important aspects of dealing with data. A statistical model is a kind of summary of data. That summary can be a way to encapsulate patterns in data: some of those models are part of what's called "machine learning." The summary can be a way to translate from existing observations into conclusions, for instance classifying a sales prospect as strong or weak, or a wine as excellent or poor. Very often, models are used to untangle the many influences that can shape an outcome, quantifying how each influence contributes. And models are an essential part of the process for quantifying the strength of evidence for a conclusion provided by the available data.

People who are new to statistical modeling often ask me, "What's the difference between plain statistics and modeling?" As you'll see, statistical modeling refers to a set of concepts and techniques that give you more power to analyze complex systems and situations than traditional methods, such as the t-test, taught in introductory statistics.

As you know if you've had an introduction to statistics, a t-test is one method for addressing a simple question: are two groups different? The t-test is kind of like a skateboard. There's nothing wrong with a skateboard, but it has very limited use.

Statistical models, to run with the analogy, are like helicopters. They can get you from place to place, like a skateboard, but let you go much further and faster.

And they're better at handling travel over rugged terrain, those situations where traditional techniques just won't get you where you need to be.

Sometimes skateboards are used in rough circumstances, but this often results in a painful and pointless conclusion.

OK. A statistical model is neither a skateboard or a helicopter. Those are just metaphors. So what is a model?

My favorite definition --- and certainly the most helpful one --- is this: A model is a representation for a purpose. "Representation" means the model stands for something, often something or process in the real world. The "purpose" is central. Without knowing what the model will be used for, you can hardly design an appropriate model.

Here are a few everyday models. Each is a representation.

the blueprint stands for a building
the doll represents a child
the model airplane represents an aircraft
And each of these representations is useful for some purposes but not for others. The blueprint is useful for seeing how space can be subdivided or consolidated. But it is not useful for figuring out how sound in the building will reverberate. The model airplane is useful for showing how the various parts of the plane --- engine, wings, tail --- are related. But it's not useful for safety testing.

We build models because they are much more convenient than the real thing for carrying out the purpose for which the model is intended. It's infinitely easier to add a new wall in a blueprint than it is in a real building.

A mathematical model is simply a model built from mathematical stuff: numbers, model formulas, equations, and so on.

A statistical model is a special kind of mathematical model. It is informed by data and is often built to predict future events or to test out hypotheses about how the system being modeled actually works.

In this course, you'll learn how to design, train, and use statistical models. This will, of course, involve data. But, since a model is a representation for a purpose, it's important that you have always in mind what purpose your model is intended to serve so that you can build a model that does the job it's meant for.

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