How do observations become a model—and how much should we trust it? Start with probability, learn what a prediction estimates, then fit a model and evaluate it on new observations.
Learning modules
| Sequence | What you will learn | Open |
|---|---|---|
| Probability foundations | Describe randomness, averages, spread, and conditioning. | Lessons · Practice |
| Module 2 · Learning from data | Fit a prediction, evaluate new observations, and separate bias, variance, and noise. | Lessons · Worked questions |
| Module 3 · Linear regression | Work with matrices, fit a line, measure its errors, and judge coefficient uncertainty. | One-page guide + practice |
| Module 4 · Flexible regression | Add categories, interactions, and curves; compare models on training and test data. | One-page guide + practice |
| Module 5 · Logistic regression | Turn scores into class probabilities, fit by likelihood, and read odds. | One-page guide + practice |
| Module 6 · LDA and classification errors | Compare class distributions, count mistakes, and choose a threshold. | One-page guide + practice |
| Midterm practice | Build each idea from first principles, solve the supplied problems, and check your understanding. | Practice module |
| XOR · A first neural network | See why one line fails, then build two simple checks that solve the problem. | Interactive page |
Where to begin
Start with probability for randomness and conditioning, or learning from data for fitting and evaluating predictions.
If the symbols are the obstacle, use worked notation questions.
Try each lesson’s question before opening the worked answer. The goal is to be able to reconstruct the calculation and recognize it when a new problem changes the notation.