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Confidence Prediction

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This topic contains 2 replies, has 2 voices, and was last updated by  AT 14 years, 1 month ago.

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  • #40711

    AT
    Participant

    What’s the difference between confidence and prediction intervals? Why does fitted regression plot show wider prediction intervals than confidence intervals?

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    #126961

    Mike Walmsley
    Participant

    I hope this helps. It is an excerpt from Statsofts electronic textbook.
     
    Confidence Interval vs. Prediction Interval. In regression, it is possible to predict the value of the dependent variable based on given values of the independent variables. When these values are predicted, it is also possible to calculate confidence intervals and/or prediction intervals for the dependent variable.
    The confidence interval gives information on the expected value (mean) of the dependent variable. That is, a confidence interval for a predicted value of the dependent variable gives a range of values around which the “true” (population) mean (of the dependent variable for given levels of the independent variables) can be expected to be located (with a given level of certainty, see also Elementary Concepts).
    The prediction interval gives information on individual predictions of the dependent variable. That is, a prediction interval for a predicted value of the dependent variable gives us a range of values around which an additional observation of the dependent variable can be expected to be located (with a given level of certainty, see also Elementary Concepts).
    Note that the confidence interval will produce a smaller range of values, because it is an interval estimate for an average rather than an interval estimate for a single observation. See Neter, Wasserman, & Kutner, 1985.

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    #126966

    AT
    Participant

    Thanks very much for the clear explanation.

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