Interactive — fit the line by hand

Drag w and b until the line runs through the cloud of dots. Watch the right-hand panel — dark means low loss, bright means high loss, and the white cross is the best line that exists for this data.

Hours studied → Marks

The error landscape

low losshigh loss
2.00
40.0
Loss—
Best possible—
Predict 5.5 hrs—
input x=5.5 × 2.00 the weight add bias + 40.0 output ŷ 51.0

One input, one weight, one bias — this is a neuron. It updates live with the sliders above: it isn't an analogy, it's the same equation, redrawn.