A scatter plot of sixty input–output pairs. Nature produced each output from its input by a smooth hidden rule plus random noise. A button reveals the rule as a dashed curve. A slider freezes one input value; a button drops twenty more outputs at exactly that input. Those outputs scatter vertically, and readouts track how many were dropped, their running average, their spread, and the rule's value there. The average settles onto the rule's value while the spread stays about one unit: the rule is the average at each input, and the noise is the leftover.
Sixty observations, each generated by y = f(x) + noise. Hold x fixed and sample more outputs to compare their average and spread.