The above graph gives the values for 4 items measured by the police department. One represents the number of crimes reported, one represents the number of arrests made, one represents the number of police officers on staff, and one represents the budget surplus for the department (in $1000s).Q. If the impact of a change enacted by the police department takes a month to register, then we can identify a negative linear relationship between B anda)Ab)-c)Cd)DCorrect answer is option 'C'. Can you explain this answer?

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The above graph gives the values for 4 items measured by the police department. One represents the number of crimes reported, one represents the number of arrests made, one represents the number of police officers on staff, and one represents the budget surplus for the department (in $1000s).

Q. If the impact of a change enacted by the police department takes a month to register, then we can identify a negative linear relationship between B and

a)
A
b)
-
c)
C
d)
D

Correct answer is option 'C'. Can you explain this answer?

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The above graph gives the values for 4 items measured by the police de...

If there is a negative linear relationship, that means that when one variable goes up, the other goes down, and vice versa. The new wrinkle introduced by this question is that there can be a one-month lag in seeing this effect. B and D are opposites - when one goes up, the other goes down. If we were to introduce a one-month lag then it’s possible they could correlate directly, not indirectly. With a one-month lag, B and A now seems to be have a negative relationship - when one goes up, the other goes down the following month, and vice versa. But is it a linear relationship - can it be expressed in the form A = mB +c, for some constant values m and c, given a month’s lagtime? You don’t have to do the math, just look at the graph - in the first month, B went up a lot, and in the second month, A went down a little. In the second month, B went down a little, yet in the third month A went up a lot. This is inconsistent - if there’s a linear relationship, then the relative sizes of the changes need to be consistent with each other. Even if you look at the lag in the reverse direction, you’ll notice this same inconsistency.

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The above graph gives the values for 4 items measured by the police department. One represents the number of crimes reported, one represents the number of arrests made, one represents the number of police officers on staff, and one represents the budget surplus for the department (in $1000s).Q. If the impact of a change enacted by the police department takes a month to register, then we can identify a negative linear relationship between B anda)Ab)-c)Cd)DCorrect answer is option 'C'. Can you explain this answer?

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