Regression

A method that fits the line, or plane, that best explains one variable from one or more others, usually by minimising the sum of squared errors. The slope says how much the dependent variable moves, on average, for a one-unit move in an explanatory one.

A stock's beta is a regression slope. Regressing its monthly returns on the Nifty's, with a slope of 1.2 and an intercept of 0.1%, says that in a month when the index rises 2% the stock is expected to rise about 2.5%. Scatter around the line is the stock's own risk, which diversification removes.

Regression measures association, not cause. It's sensitive to outliers and to the period chosen. It's also sensitive to variables left out, and a relationship found by testing many candidate variables will often fail on new data. Read the slope with its standard error and the R-squared before believing it.

A slope without its uncertainty is half an answer.