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Statistics for Lawyers
Problem Set # 4– Due /04
Name_________________________________(Please Print)
1. A study of schools categorized school districts in one of six, 1,...,6, categories by median
family income and school revenues per pupil. In each case higher numbers mean
categories with higher dollar amounts. A sample of three districts had the following
categories for family income and revenues per pupil, respectively: (1,5), (2,4), and (3,6).
(A) Compute the covariance and linear correlation between the category numbers. (B) Is
the positive correlation reduced by the fact that the relationship between family income
and school revenues is invested for the first two districts?
Ans.(A)_____________________________(B)_______________________________________
2. Suppose, in the above problem there were only two districts, (1,5) and (3,6). What would
the correlation be in that case?
Ans.__________________________________________________________________________
3. If the values of one of two variables being correlated is multiplied by a constant c, what
effect does that have on the correlation between them?
Ans.__________________________________________________________________________
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4. If two variables are independent (roughly, knowing one will not help us know the other) it
will usually follow that their linear correlation will be zero. However, the converse is not
true, i.e., if their linear correlation is zero then they are independent. For example, assume
the two variables are x and y with y = x 2 , so they are perfectly dependent. If we pick three
values of x as -3, 0, 3 then the corresponding values for y are 9, 0, 9. Show that the
correlation between x and y in these data is zero.
Ans.__________________________________________________________________________
5. From the Current Population Survey of 1993 the average income and average education
for men 25 to 54 for each state (and D.C.) can be computed. This gives us 51 pairs of
values. The correlation between them is 0.64. On the other hand, for individuals, the
correlation between income and education is 0.44. Explain the reason for this difference.
Ans.__________________________________________________________________________
End of Problem Set # 4