Logistic Regression: The Bouncer Who Gives Probability of Entry Instead of Just Yes/No

Linear regression predicts numbers. But what if you need to predict Yes/No? Pass/Fail? Spam/Not Spam? You can't just draw a straight line through 0s and 1s — you'll get predictions of 1.7 (170% spam??) or -0.3 (negative probability??). Logistic regression fixes this by squishing predictions into proper probabilities between 0 and 1.