Final Answer:
The distinct effect of changing the number of law enforcement officers on the number of reported crimes, βₒfficers, is -26.18.
Step-by-step explanation:
The regression equation given is: Reported Crimes = β₀ + βₒfficers × Officers + μother.
In this context, the coefficient βₒfficers represents the change in reported crimes associated with a one-unit change in the number of law enforcement officers. From the provided information, we can calculate this coefficient by using the change in officers (ΔOfficers) and the corresponding change in reported crimes (ΔReported Crimes).
ΔOfficers = 1,780 - 1,410 = 370,
ΔReported Crimes = 10,985 - 12,855 = -1,870.
Now, plug these values into the formula: βₒfficers = ΔReported Crimes / ΔOfficers = -1,870 / 370 = -5.05.
Therefore, the distinct effect is -5.05. This implies that for every additional law enforcement officer hired, there is an estimated reduction of 5.05 reported crimes.
However, the question asks for the answer rounded to two decimal places. Therefore, rounding -5.05 to two decimal places gives -5.05.
In conclusion, the final answer is βₒfficers = -5.05, indicating that the distinct effect of changing the number of law enforcement officers on the number of reported crimes is a reduction of 5.05 crimes.