Full text: The Personal Distribution of Income

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

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