Day 2 · Tuesday

From a fitted line to a decision you can price

Yesterday we agreed what a prediction task is and how to judge one. Today I open the models themselves: how a line and a sigmoid are fitted, what their numbers mean, and when a prediction is enough to act on.

By the end of today

• Read a regression coefficient with its units, its comparison, and its scope;
• Explain what a fitted probability of 0.30 claims, and audit that claim with log loss and calibration;
• Derive a decision threshold from the costs of the two possible errors;
• Say when even a well-audited probability is the wrong decision quantity, and define the uplift that replaces it.

What we cover

• slides 5–22Part I: predicting a numberThe taxi fare. Loss, model, and evaluation for a numerical target.
• slides 23–39Part II: predicting a probabilityThe bank client. The same machinery, rebuilt for a yes/no target.
• slides 40–57Part III: from probability to decisionCosts, thresholds, and the point where prediction stops being enough.

Slides 58–73 are optional appendix material for students who want the full algebra.

Lecture materials

Review questions

• What does least squares minimise, and why does squared error point at the mean?
• The slope 3.6529: state its units, its comparison, and its scope in one sentence.
• A colleague reads $e^{\widehat\beta}\approx19.27$ as "19 times more likely". Correct them, using the doubled-odds table's logic.
• A false positive costs 4 and a false negative costs 80. Derive the threshold and apply it to a fitted 0.30.
• Describe a situation where a calibrated response probability still cannot justify the action, and name the missing quantity.

← Day 1  ·  Day 3 →