Regression Coefficient

A regression coefficient is the number attached to a predictor that says how much the outcome is expected to change when that predictor rises by one unit. In a model with several predictors, each coefficient is interpreted holding the other predictors fixed — the effect of this variable after accounting for the rest.

That little phrase, holding the others fixed, is what makes multiple regression powerful and also easy to misread: a coefficient describes the marginal contribution of one variable within this particular set of variables, so adding or dropping other predictors can change it. Always pair a coefficient with its standard error or confidence interval, because a coefficient of 2.0 means little if it could easily have been anything from -1 to +5.