virhejäännös

Virhejäännös refers to the part of a statistical model's prediction that cannot be explained by the independent variables included in the model. In simpler terms, it is the difference between the actual observed value of a dependent variable and the value predicted by the regression model. This remaining variation is often attributed to factors not accounted for in the model, random error, or measurement inaccuracies.

In regression analysis, a model aims to explain the variance in a dependent variable by using one or more independent variables. The model generates a predicted value for the dependent variable based on the values of the independent variables. The virhejäännös for a specific observation is calculated as the actual value minus the predicted value. Mathematically, if y is the actual value and ŷ (y-hat) is the predicted value, then the residual is y - ŷ.

The analysis of virhejäännös is a crucial step in model evaluation. By examining the residuals, statisticians can assess the adequacy of the model. Ideally, residuals should be randomly distributed around zero, indicating that the model has captured the systematic relationships in the data. Patterns in the residuals, such as a curved shape or increasing variance, suggest that the model assumptions might be violated or that important variables are missing. This can prompt model refinement, such as transforming variables, adding interaction terms, or incorporating new predictors.