The difference between an observed value and the predicted value in a regression model is termed a residual. Determining this difference is a crucial step in evaluating the fit of the model. In spreadsheet software, specifically Microsoft Excel, this calculation involves subtracting the predicted y-value for each data point from its actual y-value. For instance, if the actual sales figure for a particular month is $10,000 and the regression model predicts $9,500, the residual is $500, representing the unexplained variation in that specific observation.
Understanding and analyzing residuals provides critical insights into the appropriateness of the chosen regression model. Small residuals indicate a good model fit, while large residuals might signify outliers or suggest that the chosen model is not the most suitable for the data. Analyzing residual patterns, such as plotting them against the predicted values, helps to detect heteroscedasticity or non-linearity, potential violations of the assumptions underlying linear regression. Historically, manual residual calculation was tedious and error-prone. Modern spreadsheet functionalities enable rapid and accurate assessment of model adequacy.
