Regression Coefficient

The regression coefficient expresses the functional relationship among the response (explained, dependent) variable and one or more explanatory (predictor, independent) variables. Denoting the response variable by Y and the set of explanatory variables by X1, X2, …, Xk, the regression model can generally be formulated as

where k denotes the number of predictor variables and ε denotes the random disturbance or error, representing the discrepancy between the observed response variable and the estimated regression line.

Following the commonly used notational convention in linear regression analysis, which uses Greek letters to denote the unknown parameters, the linear regression model can be written as

where β0 denotes the intercept and β1, β2, …, βk denote the regression coefficients to be estimated from the data. More specifically, the regression coefficients indicate ...