Real data almost never lands perfectly on a line — but when it comes close, a line becomes a machine that predicts. Drag a line onto the data yourself, then step through the algebra that turns two points into a model, and learn to say out loud what the slope means.
Fare vs. distance
Typical miss per data point—
Build a linear modelpick a situation below
The situation
Slope — the rate—
Intercept — the start—
Show the misses as
Why square the misses?
A miss above the line and a miss below it would cancel each other if we just added them up — a terrible line could score zero. Squaring makes every miss positive, and it punishes one big blunder far more than several small ones. The best-fit line is the single line that makes the total of those squares as small as it can possibly be.
Snap to it and you will notice it is close to, but not exactly, the line built from two points in the other tab. That is expected: a two-point model hears only two measurements, while the best-fit line listens to all five at once.