You're interested in looking at whether air pollution has effect on violent crime rates. More precisely, you believe that everything else being equal the more polluted is the air, the more aggressive people become which results in higher violent crimes. Let APi represent the average June air pollution in city i, and CRi be the violent crime rate in city i (again in June).
(a) Write the simple linear regression model (i.e. population model)
(b) Provide two variables that could possibly affect the violent crime rate, but are not accounted for in the simple linear regression model (i.e. are in the u term).
(c) In order to "reasonably" estimate the parameter of interest, we must make certain assumptions. Provide TWO such assumptions. Make sure to relate these assumptions to the problem at hand.