Linear modelling

Every time you check how much data you've used on your phone plan , a flat monthly fee plus a charge per GB , you're already thinking in linear models. That's the whole idea: one number changes at a steady, predictable rate relative to another, and you can write that relationship as an equation.

The standard form is $y=mx+c$, where $y$ is your output variable, $x$ is your input variable, $m$ is the gradient (rate of change), and $c$ is the y-intercept (starting value when $x=0$). The gradient tells you how much $y$ shifts each time $x$ goes up by 1. The intercept is what you'd have before $x$ does anything at all.

Linear Model: A relationship where the output variable changes by a fixed amount for every equal step in the input variable, expressed as $y=mx+c$.

Take the equation $C=3+2d$, where $C$ is taxi cost in dollars and $d$ is distance in kilometres. The $3$ is the flat fee just for getting in , you owe it before the car moves an inch. The $2$ means every extra kilometre adds exactly $2 to the bill. That's a linear model doing real work.