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Logistic Regression
Introduction
How It Works
Scoring Our Model
Finding the Best S-Curve
Understanding Our S-Curve
Code with Python
Summary
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Glossary

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Logistic RegressionUnderstanding Our S-Curve

Reading time: ~10 min

The numbers w and b of a straight line were easy to read. Inside an S-curve they are read through odds: the chance that something happens divided by the chance that it does not.

\text{odds} = \dfrac{p}{1 - p}

A 0.75 chance of passing gives odds of 0.75 \div 0.25 = — we say "3 to 1". A 0.5 chance gives odds of , or "1 to 1". A 0.2 chance gives 0.2 \div 0.8 = 0.25, or "1 to ".

The Doubling Ladder

Suppose a model has w = 0.69. Since e^{0.69} \approx 2, every extra hour of study multiplies the odds of passing by 2. At 2 hours the odds are 1 to 8. Climb the ladder.

Equal steps in hours multiply the odds by the same number each time — but the chance itself climbs fast in the middle and slowly at the ends. That is the S-shape again.

Reading the Coefficients

In general, a coefficient w means: one more unit of the feature multiplies the odds by e^w. For Kavya ma'am's 14 students, gradient descent found w \approx 1.02, so each extra hour multiplies the odds of passing by about e^{1.02} \approx .

Select a tab to read other kinds of coefficients.

Yes/No features

A feature such as "attended the doubt-clearing class" is 1 or 0. If its coefficient is 1.1, then e^{1.1} \approx 3: a student who attended has three times the odds of passing of a student who did not.

Negative coefficients

A feature such as "hours spent on the phone" might get a coefficient of −0.7. Since e^{-0.7} \approx 0.5, each extra hour on the phone halves the odds of passing. A negative coefficient shrinks the odds; zero leaves them unchanged.

Many features

With several features, each coefficient is read with every other feature held fixed: the hours coefficient tells you what one more hour of study does for two students who are alike in everything else.

Speed Round: Odds and Chances

Get five right to move on.

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