A graphical display used to assess the appropriateness of a linear regression model typically involves plotting residuals against predicted values. These diagrams, often generated using a calculating device, aid in determining if the assumptions of linearity, constant variance, and independence of errors are met. For example, after performing a linear regression on a data set relating study hours to exam scores, the difference between each student’s actual score and the score predicted by the regression equation is calculated. These differences, the residuals, are then plotted against the corresponding predicted scores, visually representing the model’s fit.
The practice of examining such diagrams is critical for validating the reliability of statistical inferences drawn from regression analysis. A random scatter of points around zero suggests that the linear model is suitable. Conversely, patterns such as curvature, increasing or decreasing spread, or outliers indicate violations of the model’s assumptions. Detecting and addressing these violations improves the accuracy and validity of the analysis, leading to more reliable conclusions. Initially, such assessments might have been performed manually, but the evolution of electronic calculators has streamlined the process, providing efficient visual representations of the data.
