15
If the mean income in the various wealth classes is
calculated,a linear regression of a very regular pattern
is obtained (fig.l). This "regression of the first kind"
as it is called (Cramer 1946 p.270 )differs from the usual
least sguares regression in that it does not assume a
priori a certain mathematical function for the
regression.If the regression of the means turns out to be
linear as is the case here then we should expect it to be
the same as the result of a least squares regression on
the basis of the full data (a difference may
arise,however, in so far as we do not take into account
the weights for the means corresponding to the frequencies
in the various wealth classes).
If the same regression of the first kind is calculated in
the other dimension,that is , if we take the mean wealth
for each of the various income classes,a completely
different picture emerges:The mean wealth in the lowest
income classes does not increase with income at all; for
higher incomes it increases strongly so that a distinctly
curved regression line results.
The reason - or at least the most important of the reasons
-for the peculiar shape of this regression line lies in
the truncation of the wealth data. In the lower income
classes we find only people who have something like the