📊 What is a (Mathematical) Model?

🧒 When I Was a Kid…

When I was a kid, the word “model” meant a toy — something plastic I glued together on weekends.
Later, as a teenager, a model was someone who wore fashionable clothes and walked the runway.

But now that I’m an adult working with data and numbers, the word model has taken on a whole new meaning — one grounded in math and statistics.

For example, I might say:
“I want to model mouse size based on mouse weight.”

But what does that even mean?
And more importantly — why would I want to do that?

🔗 Understanding the Relationship

In this context, a model refers to a relationship — specifically, a mathematical or statistical one.
A model allows us to explore and describe how two (or more) things are related.

So when I say I want to model mouse size based on mouse weight, I’m looking to understand how changes in weight might predict or influence size.
It’s not just about curiosity — it helps us make informed decisions, predictions, and interpretations.

➗ Models as Equations

Often, a model takes the form of an equation.

For example:

Size = a × Weight + b

This simple equation tries to approximate the relationship between weight and size using mathematical terms.
But here’s the catch — real-world data is messy. So no model is perfect.

That’s why a big part of statistics is about evaluating how well a model fits real data.

We ask:

• Does the model predict well?

• Is it useful?

• Is it misleading?

🌀 Not All Models Are Straight Lines

Some relationships are linear — they can be modeled with straight-line equations.
But life isn’t always that simple.

• Some models are curved, like parabolas or exponentials.

• Others are non-linear or even multivariate, involving multiple variables.

And that’s okay.
The key is that a model is a simplified version of reality — useful, but not perfect.

🤯 From Simple to Complex

Models can range from:

• Simple linear models (like the example above),

• to complex machine learning models with thousands of variables and intricate patterns.

The complexity depends on:

• What you’re trying to study,

• How much data you have,

• And how precise you need your predictions to be.

📌 In Summary

• A model is a mathematical way to describe a relationship between variables.

• We use models to understand, explore, and predict.

• We use statistics to judge how useful and reliable those models are.

So next time someone says “model,” think beyond toys or runways.
Think: math, data, relationships, and predictions.

The End — or just the beginning of your modeling journey! 🚀