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Margins of Error for PredictionsIt should be clear to you from what you have already learned that, in general:
Whilst this is useful to know, you really need to be able to QUANTIFY the margin of error for a given prediction. Provided that the assumptions of regression analysis hold, you can calculate: 1. a confidence interval (CI) for the mean value of y expected when x=x0:
Both intervals are centred on the value predicted by the regression equation, namely y0 = a + bx0, but the prediction interval has a bigger standard error. The t-value is calculated from (n-2) degrees of freedom with tail area (a/2). Use the spreadsheet to investigate how the intervals depend on the many different quantities involved.
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