Margins of Error for Predictions

It should be clear to you from what you have already learned that, in general:

interpolation gives better predictions than extrapolation

large samples give better predictions than small samples

high correlation gives better predictions than low correlation

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:

2.  a prediction interval (PI) for an individual value of y 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.

 

To continue on the recommended route click on the Non-linear button at the top of the page.

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Copyright 2001 ©  Neville Hunt, Sidney Tyrrell and James Nicholson
All rights reserved.  Last updated: 03 March 2003 .