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  2. Regression validation - Wikipedia

    en.wikipedia.org/wiki/Regression_validation

    An illustrative plot of a fit to data (green curve in top panel, data in red) plus a plot of residuals: red points in bottom plot. Dashed curve in bottom panel is a straight line fit to the residuals. If the functional form is correct then there should be little or no trend to the residuals - as seen here.

  3. Partial regression plot - Wikipedia

    en.wikipedia.org/wiki/Partial_regression_plot

    The residuals from the least squares linear fit to this plot are identical to the residuals from the least squares fit of the original model (Y against all the independent variables including Xi). The influences of individual data values on the estimation of a coefficient are easy to see in this plot.

  4. Errors and residuals - Wikipedia

    en.wikipedia.org/wiki/Errors_and_residuals

    The residual is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis , where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals .

  5. Statistical model validation - Wikipedia

    en.wikipedia.org/wiki/Statistical_model_validation

    Residual plots plot the difference between the actual data and the model's predictions: correlations in the residual plots may indicate a flaw in the model. Cross validation is a method of model validation that iteratively refits the model, each time leaving out just a small sample and comparing whether the samples left out are predicted by the ...

  6. Partial residual plot - Wikipedia

    en.wikipedia.org/wiki/Partial_residual_plot

    In applied statistics, a partial residual plot is a graphical ... a scatter plot of the response variable against the independent variable provides a good indication ...

  7. Linear regression - Wikipedia

    en.wikipedia.org/wiki/Linear_regression

    A plot of the absolute or squared residuals versus the predicted values (or each predictor) can also be examined for a trend or curvature. Formal tests can also be used; see Heteroscedasticity. The presence of heteroscedasticity will result in an overall "average" estimate of variance being used instead of one that takes into account the true ...

  8. Least squares - Wikipedia

    en.wikipedia.org/wiki/Least_squares

    The result of fitting a set of data points with a quadratic function Conic fitting a set of points using least-squares approximation. The method of least squares is a parameter estimation method in regression analysis based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the ...

  9. Studentized residual - Wikipedia

    en.wikipedia.org/wiki/Studentized_residual

    The residuals, unlike the errors, do not all have the same variance: the variance decreases as the corresponding x-value gets farther from the average x-value. This is not a feature of the data itself, but of the regression better fitting values at the ends of the domain.