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Suppose the World Health Organization collected data from 3,000 male indonesians
aged 40 through 65. The sample means, sample variances, and sample covariances of
In ( wages), height, and In(height) are reported in Table 2. Note that wages are measured
in Rupiah and height is measured in centimeters.
Table 1
Sample Mean
Sample Variance and Covariance
Mean
In (wage) height
In (height)
In (wage)
5.8
2.2
height
160
2
40
In (height )
5.1
0.005
0.19
0.001
(1) Since In(height) is a transformation of height, if one knows height then one can
perfectly predict In(height). As a result, would you expect the correlation coefficient
between these two variables to be 1? (5pts)
(2) Given the information in Table 1, calculate the corelation coefficient between height
and In(height)? (10pts) Does this correspond with your answer to part (a)? (5pts)
(3) Suppose you are a researcher at the World Health Organization (WHO) and you
want to examine the theory that healthier people are more productive and thus earn
higher wages. Since height is determined by one's nutritional intake in childhood, you
use height as a measure of health. To test your theory, you come up with the following
regression model:
log(wage) = do + 1 height + u,
what is the assumptin of u we make here (5pts)? What's the economic meaning of it
(5pts)?
(4) Using the information in Table 1, calculate the OLS estimator of a, in the above
regression model (10pts).

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