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).