Residual Sum of Squares - One Explanatory Variable

One Explanatory Variable

In a model with a single explanatory variable, RSS is given by

where y_i is the i th value of the variable to be predicted, x_i is the i th value of the explanatory variable, and is the predicted value of y_i (also termed ). In a standard linear simple regression model, where a and b are coefficients, y and x are the regressand and the regressor, respectively, and ε is the error term. The sum of squares of residuals is the sum of squares of estimates of ε_i; that is

where is the estimated value of the constant term and is the estimated value of the slope coefficient b.