What Is a Model, Really?
You'll hear the word model in every ML course, blog post, and product spec — usually without anyone defining it. Here's the unflashy truth:
A model is a small bag of numbers. Nothing more. Not an algorithm. Not code. Not a black box. Just numbers stored in memory that, together, describe a function from input to output.
For linear regression that bag has exactly two numbers: a weight and a bias. They define a single straight line:
response_time = (weight * requests_per_second) + biasThat equation IS the model. When you save a trained linear regression to disk, those two numbers are what get saved.
Algorithm vs Model
The two words get used interchangeably and they shouldn't be. Here's the split:
| Algorithm | Model | |
|---|---|---|
| What it is | A procedure (a recipe) | A bag of tuned numbers (the cake) |
| When it runs | Once, during training | Every time you call .predict() |
| Linear regression example | "Find w and b that minimise squared error" | w = 1.82, b = 29.5 |
| What you ship to prod | Nothing | The numbers |
The algorithm runs once, looks at all your data, picks the best numbers, and then it is done. The model — those numbers — is the thing you actually use in production.
How Big Is a "Model"?
The number of parameters in the bag depends on what kind of model it is. The mental model is the same at every scale:
| Model | Parameter count | What they represent |
|---|---|---|
| Linear regression (this lesson) | 2 | 1 weight + 1 bias |
| Digits classifier (Lesson 1.1) | ~640 | 64 pixels × 10 digit classes |
| ResNet-50 (image classifier) | ~25 million | Convolutional filter weights |
| GPT-4 (LLM) | ~1.7 trillion | Transformer attention + feed-forward weights |
Same idea, twelve orders of magnitude apart. The bag of numbers gets bigger; what it is doesn't change.
Be the Algorithm — Drag Two Knobs
Reading about this is the wrong way to learn it. Run the explore script and physically tune the model by hand: drag two sliders, watch the red line move across the data cloud, watch the error metric (RMSE) climb and fall. Then click "Let the algorithm do it" and watch sklearn snap the knobs to the optimal values in one shot.
After you've tuned the model by hand, the next step in this lesson — model.fit() — stops being magic. .fit() is doing exactly what you just did, just analytically and instantly.
python curriculum/stage1_classic_ml/02_linear_regression/0_interactive_intro/explore_model_knobs.pyChallenges to attempt before clicking "Let the algorithm do it":
- What is the RMSE of a totally random model (the starting position)?
- How low can you push the RMSE by hand? Write your best score down.
- By how much does the algorithm beat your best score?
- The optimal values are roughly
w ≈ 1.8andb ≈ 30. Translate them into plain English for a SOC analyst monitoring the server.
Think Deeper
Run <code>explore_model_knobs.py</code>. By hand, try to push the RMSE below 20 ms. Then click "Let the algorithm do it". By how much did the algorithm beat your best score, and why?
w, b analytically (the normal equation) instead of guessing. The key insight isn't that the algorithm is smart — it's that the model is just those two numbers, and the algorithm's only job is picking them. Once it has, the algorithm is done; you ship the numbers.