You have data on the number of crimes per capita and the size of the police force from counties in the U.S. There is also information on wages, unemployment, education, and lots of other characteristics of the population. You estimate the following relation using ordinary least squares regression:

Ci =+Pi +Xi +i

Here Ci is the crime rate per capita in county i, Pi is police per capita in i, Xi represents the other variables characterizing county i that you put in the regression and i.

a. What do you think the sign of the estimated parameter * will be? Do you think that the estimate of * will differ from the true ? If so, how will it differ, and why will it differ (provide a formal rational for your answer)