Diagnosing problems by looking for patterns in residuals The existence of patterns invalidates most statistical tests. Where residuals contain patterns, it implies that the model is qualitatively wrong, as it is failing to explain some property of the data. Where the average residual is not 0, it implies that the model is systematically biased (i.e., consistently over- or under-predicting). In the case of linear regression, the greater the sum of squared residuals, the smaller the R-squared statistic, all else being equal. The further residuals are from 0, the less accurate the model. Where the residuals are all 0, the model predicts perfectly. You can examine residuals in terms of their magnitude and/or whether they form a pattern. Residuals are important when determining the quality of a model. You can read the residuals as being the difference between the observed values of inflation (the dots) and the predicted values (the dotted line). The chart below shows the data in the table. In the case of the data for January 2017, the observed inflation was 0.5%, the model has predicted 1.8%, so the residual is - 1.3%. The residuals are shown in the Residual column and are computed as Residual = Inflation - Predicted. The Predicted column shows predictions from a model attempting to predict the inflation rate. The middle column of the table below, Inflation, shows US inflation data for each month in 2017. They are a diagnostic measure used when assessing the quality of a model. Residuals in a statistical or machine learning model are the differences between observed and predicted values of data.
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