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 Weighting in multiple regression

It is often useful to differentially weight the data points. Learn why.

Prism offers four choices on the Weight tab of multiple regression:

No weighting. Regression is most often done by minimizing the sum-of-squares of the vertical distances of the data from the line or curve. Points further from the curve contribute more to the sum-of-squares. Points close to the curve contribute little. This makes sense, when you expect experimental scatter to be the same, on average, in all parts of the curve.

Weight by 1/Y^2. In many experimental situations, you expect the average distance (or rather the average absolute value of the distance) of the points from the curve to be higher when Y is higher. The points with the larger scatter will have much larger sum-of-squares and thus dominate the calculations. If you expect the relative distance (residual divided by the height of the curve) to be consistent, then you should weight by 1/Y2.

Weight by 1/Y. This weighting is sometimes used when the scatter follows a Poisson distribution -- when Y represents the number of objects in a defined space or the number of events in a defined interval. Since Prism offers Poisson regression (a choice on the Model tab), there is little use for 1/Y weighting.

Weight by 1/YK. Also called "General weighting". Read more.