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# what would you expect the relationship between u1 and u2 to be? Why?

INSTRUCTIONS TO CANDIDATES

This assignment requires only simple steps, but this may take time if you have not imple- mented these in Stata before. Please start early to avoid last minute rushes.

1. using Stata:

(a) set seed 260722;

(b) generate N = 100 observations of two random variables, u1 and u2 uniformly dis- tributed in the [0, 1] interval;

2. what would you expect the relationship between u1 and u2 to be? Why?

3. using Stata, regress u1 on u2 (including a constant term). What is the probability that the coefficient on u2 is non-zero? Comment in light of your answer to the previous question.

4. rerun your previous code, this time generating k = 10, 100 and 1000 trial pairs of random u1 and u2. For each such pair, perform the regression above. Do this for each of N = 10, 100 and 1000. Fill in Table 1, indicating in each cell the number of significant coefficients (at the 5% level) you find for each trial. (To illustrate, one cell is already filled in.)

k

10 100 1000

10 0

N 100

1000

Table 1: Number of trials with regressor significantly different from zero at 5% level

5. do you notice anything unusual about the completed table? How do you make sense of this?

6. using Galton’s height data from the Harvard dataverse (click this link):

(a) generate the ‘midparent’ height, the average of the mother’s and father’s height;

(b) regress the child’s height on the midparent height;

(c) comment on the sign and significance of parental height as an explanatory variable for a child’s height.

The assignment is due on 10 August; it must not exceed 1000 words, including the Stata

.do file containing all your code.

Do not worry if some of these questions ‘stump’ you: while some questions are ‘mechanical’, others are designed to deepen your intuitions.

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