Qustion 2:

The crime rate (dependent variable) is influenced by the opportunity cost of potential offenders and other socio-economic factors.

The following model can be constructed：

CrimeRate_i = β₀ + β₁AverageWage_i + β₂X_i + α_i

1. Dependent variable (CrimeRate_i): Crime rate in area i. (For example: Number of crimes per 10,000 people)

2. Core independent variable (AverageWage_i): Average wage (For example: Hourly or annual salary) in area i, with an expected negative sign. (Higher wages lead to higher opportunity costs of crime)

3. Control variable (X_i): Other factors that may affect the crime rate.

For example:

-Unemployment rate: The higher the unemployment rate, the stronger the incentive to commit crime is likely to be. (Positive expected sign)

-Education level: The average number of years of education. It may reduce the propensity to commit crimes. (Expected sign is negative)

-Population density: More opportunities for crime in densely populated areas. (Expected sign may be positive)

-Police investment: Number of police officers per 10,000 people, may deter crime. (Expected sign may be negative)

-Poverty rate: The proportion of low-income groups, which may correlate crime. (Expected sign may be positive).

4. Error term (α_i): Unobserved factor.

The variables were selected on the basis of:

1. The core explanatory variable (AverageWage): It directly corresponds to the influence of Becker's theory of  “legitimate income”  on the decision to commit a crime.

2. Control variables: It needs to cover other drivers of crime to avoid omission bias.

For example:

-Unemployment and poverty rates reflect economic pressures

-Educational level may affect crime preferences

-Police commitment represents law enforcement deterrence

Final model：

CrimeRate_i = β₀ + β₁AverageWage_i + β₂UnemploymentRate_i + β₃PopulationDensuty_i + α_i