Question

The slope of a regression line is an indicator of the relationship between the

dependent and independent variable

dependent and independent variable

intercept and the error term

intercept and the independent variable

.

Suppose that a local law enforcement chief wants to decide whether or not to hire more law enforcement officers to patrol area

X.

For​ this, the chief wants to know about the current presence of law enforcement officers in area X and the reduction in the incidence of crime in that area. In the last 3​ years, the total number of law enforcement officers hired for patrolling area X increased from

1,410

to

1,780.

In the same​ span, the number of criminal incidents recorded in area X decreased from

12,855

to

10,985.

The relationship the chief wants to estimate​ is:

Reported Crimes=β0+βOfficers×Officers+μother​,

where

β0

and

βOfficers

are the coefficients of the regression​ line, and

μother

is the error term which includes all other factors which could affect the number of reported crimes apart from the presence of law enforcement officers.

From the given​ information, the distinct effect of changing the number of law enforcement officers on the number of reported​ crimes,

βOfficers​,

is

nothing.

​(Round

your answer to two decimal

places.

Enter a minus sign if your answer is

negative​.)

Answer 1

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.