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Introdução à Análise de Resíduo

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  • Nota de Estudos
  • Rever Tópicos
    Samkeliso R S.
    SZ
    Samkeliso R S.

    analysis of errors

    Henock A.
    ET
    Henock A.

    done

    Rachel N.
    IE
    Rachel N.

    Residual analysis is an analysis of 'errors'.

    Jahidul I.
    BD
    Jahidul I.

    Residual analysis is an analysis of 'errors'. The error is the difference between the actual value and the value predicted using a regression line. A very general way of describing what statistical tools do is: data = summary + summary data = summary + residual data = structure + structure y = a + b·x + residual i.e. they separate the data (the variation we are interested in) into two parts, one that we are able to summarize (structure, explain, describe, and another part that is not (yet?) summarized (structured, explained, described), i.e. the remaining residual part of the variation. Generally analyzing the residuals produced by any statistical tool, provides us with a general approach to assess the quality and diagnose possible problems with the summary, as whenever you are able to discover any kind of systematic aspect (groups, outliers, any structure) you will know that the summary did not succeed in catching all systematic elements in the data. Below we will consider residuals from regression; you should however be aware that the general principles can be applied to any statistical tool; no matter what tool you are using, a residual is always: residual = data - summary Analyse residuals from regression An important way of checking whether a regression, simple or multiple, has achieved its goal to explain as much variation as possible in a dependent variable while respecting the underlying assumption, is to check the residuals of a regression. In other words having a detailed look at what is left over after explaining the variation in the dependent variable using independent variable(s), i.e. the unexplained variation. Ideally all residuals should be small and unstructured; this then would mean that the regression analysis has been successful in explaining the essential part of the variation of the dependent variable. If however residuals exhibit a structure or present any special aspect that does not seem random, it sheds a "bad light" on the regression. Most problems that were initially overlooked when diagnosing the variables in the model or were impossible to see, will, turn up in the residuals, for instance: Outliers that have been overlooked, will show up ... as, often, very big residuals. If the relationship is not linear, some structure will appear in the residuals Non-constant variation of the residuals (heteroscedasticity) If groups of observations were overlooked, they'll show up in the residuals etc. In one word, the analysis of residuals is a powerful diagnostic tool, as it will help you to assess, whether some of the underlying assumptions of regression have been violated.

    Jahidul I.
    BD
    Jahidul I.

    what is analyzing ?

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