1. The following contains data from the Chicago Public School system (CPS) on 6th

graders who were retained (forced to repeat grade) or promoted (successfully advanced to the

next grade).

fraction of students dropped out that were retained is .572, fraction of students who dropped that were promoted is .527

A. Calculate the difference in the fraction of students who drop out, comparing students

who were retained versus those who were promoted.(Here I got .527 - .572 = -.045)

B. Explain why the difference you calculated does not represent the causal effect of being

retained.

C. Provide one example of an omitted variable that could be driving/biasing this relationship.

Justify your answer clearly, explaining how the variable is related to both graduation rates and

grade retention

D. Determine the sign/direction of the bias (is the true/causal relationship greater or less than the

number that you calculated in A).