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Could you please explain for me what's the difference between model prediction and model estimation ? What is the difference between a prediction interval and an estimation interval?

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marked as duplicate by whuber Feb 12 at 16:18

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    $\begingroup$ In a regression context, a model postulates how the values of an outcome variable (Y) vary as a function of one or more predictor/explanatory variables for subjects in a target population. The model is then estimated using the data from a representative sample drawn from that population. In this context, model estimation refers to the process of guessing the likely values of the parameters describing how that variation plays out. $\endgroup$ – Isabella Ghement Feb 12 at 17:34
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    $\begingroup$ Once the model is estimated, it can be used to predict the value of the outcome variable for subjects in the target population who were NOT included in the original sample used to estimate the model, given that we know the values of their predictor/explanatory variables. So model prediction always follows model estimation. $\endgroup$ – Isabella Ghement Feb 12 at 17:35
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    $\begingroup$ In model estimation, we estimate unknown model parameters which describe how the outcome variable is related to the predictor/explanatory variables based on data from a representative sample. In model prediction, we predict the unknown values of the outcome variable based on the estimated model as well as known values of the predictor/explanatory variables. Frequentist statistics considers the unknown model parameters to be fixed quantities but the unknown values of the outcome variable to be random quantities. $\endgroup$ – Isabella Ghement Feb 12 at 17:42
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    $\begingroup$ An "estimation interval" is a range of likely values for an unknown (fixed) model parameter. A "prediction interval" is a range of likely values for an unknown (random) outcome value. $\endgroup$ – Isabella Ghement Feb 12 at 17:43