Statistics: an assumption of the linear regression model

Tutoring statistics, linear regression is perennial. The tutor mentions an assumption it includes.

When appropriate, linear regression models data by the equation

y = a + bx + e,

e being an error term due to variability.

An inherent assumption of linear regression modelling is that the error term, e, does not depend on the actual data value, x.

In many lab environments, the assumption that error magnitude does not depend on the measurement’s magnitude makes sense. For instance, measuring with a ruler, the error is often set to ± 0.5mm, regardless of the length measured.

For some types of data, however, the measurement’s magnitude seems to impact its error magnitude. An example might be inventory counting. One imagines that, counting only three items, the error would likely be 0. Counting a thousand, however, would more likely yield an observation a few off from the real number present, and so on.

Perhaps the point is that the data has to be measured or observed, which itself brings error, perhaps dependent on the size of the measurement itself.

Source:

Harnett, Donald L. and James L. Murphy. Statistical Analysis for Business and Economics. Don Mills: Addison-Wesley, 1986.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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