Question

Association does NOT Imply Causation. In L4.1 Exercise 4(f), we considered the following Observational Study (OS) setup:

EDUC = high school graduation rate (percentage of 25+ year olds who graduated from high school)
CRIME = crime rate (crimes per 1000 residents)
Data. (EDUC, CRIME):5, where the sample 5 is a collection of 41 Florida counties.
LSQ Line: CAIME =−42.9+1.44 EDUC
The main goal of this exercise is to interpret the slope coefficient b=1.44 in the LSQ line [for CAaME regressed on EDUC over sample 5 ].
Note: The EDUC values ranged from about 55 to 85 , so an increment of 5 units ( −5 percentage points) is reasonabie; it's 1/6 ih the range. An increment such as 10 units would also be reasonable.

(a) Below are candidate interpretations (A-1) of the slope coefficient b=1.44. Order them from "least causal" (best) to "most causal" (worst).
A. Consider two counties; one with graduation rate x and the other with graduation rate x+5 (i.e., 5 percentage points higher). For whatever reason, the predicted crime rate is 7.2 units (or 7.2 crimes per 1000) higher for the county with the higher graduation rate than for the county with the lower graduation rate.
B. An increase of 5 percentage points in graduation rate is, for whatever reason, associated with an increase of 7.2 units in the predicted crime rate.
C. If araduation rate increases by 5 percentage points, the predicted crime rate increases by 7.2 units.
D. If graduation rate is increased by 5 percentage points, the predicted crime rate increases by 7,2 units.
E. If graduation rate is increased by 5 percentage points, the predicted crime rate will increase by 7.2 units.
F. If we increase graduation rate by 5 percentage points, then the predicted crime rate will increase by 7.2 units.
G. If we increase graduation rate by 5 percentage points, then we expect the crime rate to increase by 7.2 units.
H. If the gaduation rate of a county were to increase by 5 percentage points, then this county's crime rate would be expected to increase by 7.2 units.
I. If we increase the graduation rate of a county by 5 percentage points, then we would expect this county's crime rate to increase by 7.2 units.

(b) Choose the candidate interpretation of b=1.44 that you think is most reasonable and WRITE IT OUT..

Answer 1

The most reasonable interpretation that avoids causal implications is that an increase of 5 percentage points in graduation rate is associated with an increase of 7.2 units in the predicted crime rate, acknowledging association without causation.

Step-by-step explanation:

The phrase 'association does not imply causation' reminds us that just because two variables have a relation, it doesn't mean that one causes the other. In the linear regression equation “CRIME = -42.9 + 1.44 EDUC,” given with the example of the 41 Florida counties, the slope coefficient (b=1.44) tells us that for each increment of 5 percentage points in the high school graduation rate (EDUC), the crime rate (CRIME) is predicted to increase by 7.2 crimes per 1000 residents on average.

Considering the interpretations of the slope coefficient, the most reasonable interpretation that avoids implying causation would be:

B. An increase of 5 percentage points in graduation rate is, for whatever reason, associated with an increase of 7.2 units in the predicted crime rate.

This statement communicates that there is an association between high school graduation rates and crime rates, without asserting that one causes the other. It also aligns with the understanding that there could be many lurking or confounding variables affecting both education and crime rates such as police expenditures, unemployment levels, and regional differences.