Logistic Regression — MLE (Challenger Data)

Logistic Regression — Maximum Likelihood

Challenger O-ring failures vs. temperature. Model: p̂ = σ(w·x + b). Optimize w and b by maximizing the log-likelihood (minimizing log loss).

Probability Curve and Data

Dataset

MLE

x (Temp)	y	p̂	logit	per-point loss
			∑ log f(y\|x) = 0.000	Log loss = 0.000

Controls

Logistic

Slope (w)

-0.10

Intercept (b)

5.00

Learning rate

lr = 0.020

p̂ = σ(-0.10 · x + 5.00)

Log loss (avg):

0.000

Accuracy @ τ=0.5:

0.000

Iter:

0