Errors of prediction and least-squares estimation
From a statistical point of view, the goal of simple regression analysis is to find the slope coefficient and the intercept for the linear function that best describes the relationship between two variables. The slope coefficient, which is also known as the regression coefficient, is important because it measures the amount of change in the dependent variable associated with a one unit change in the independent variable. In the example used earlier, a regression coefficient of 1.5 suggests that income can be expected to increase by $1,500 for every one year increase in education. However, this arbitrary regression coefficient is only one of any number of regression coefficients that one might employ to describe these data. The best way to choose between alternative regression coefficients is to compare the errors of prediction associated with different linear regression equations. Errors of prediction are defined as the differences between the observed values of the dependent variable and the predicted values for that variable obtained using a given regression equation and the observed values of the independent variable.
KeywordsRegression Coefficient Regression Line Linear Regression Equation Unit Change Slope Coefficient
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