Univariate vs. multivariate regression

Univariate (simple) regression has one input: $\hat{y}=wx+b$ — a line in 2-D. It is easy to plot and reason about: $w$ is the slope, $b$ the intercept.

Multivariate (multiple) regression has many inputs: $\hat{y}={\mathbf{w}}^{\top }\mathbf{x}+b$ — a plane in 3-D, a hyperplane in general. Each weight is a *partial* effect: the change in $\hat{y}$ per unit of $x_j$ with the other features held constant.

A feature can look important alone but unimportant in a multivariate model, because another correlated feature already explains the same variation. With strongly correlated features (multicollinearity), individual weights become unstable and hard to interpret, even if predictions are fine.