Amusement Park: Coffee and Crime
Directions: Answer the following problems showing as much work as you can.
As you are drawing up the plans to build a coffee shop in your amusement park, a co-worker comes to you with a concern. He heard a news report that indicated that a coffee shop would bring more crime into the amusement park. To support this claim, your co-worker presented the following data and scatterplot (with the least squares line shown) for 8 counties in the state:
County
Shops
Crimes
A
9
4000
B
1
2700
C
0
500
D
6
4200
E
15
6800
F
50
20800
G
5
2800
H
24
15400






The scatterplot shows the positive linear relationship between “Shops” (the number of coffee shops of this particular chain in the county) and “Crimes” (the number of annual property crimes for the county). In other words, counties with more of these coffee shops tend to have more property crimes annually.
Does the relationship between Shops and Crimes appear to be linear? Would you consider the relationship between Shops and Crimes to be strong, moderate, or weak?
Compute the correlation coefficient. Does the value of the correlation coefficient support your choice in part (a)? Explain.
The equation of the least-squares line for these data is: Predicted Crimes = 1434 + 415.7(Shops). Based on this line, what is the estimated number of additional annual property crimes for a given county that has 3 more coffee shops than another county?
Do these data support the claim that building a coffee shop will necessarily cause an increase in property crimes? What other variables might explain the positive relationship between the number of coffee shops for this coffee shop chain and the number of annual property crimes for these counties?
If the following two counties were added to the data set, would you still consider using a line to model the relationship? If not, what other types (forms) of model would you consider?
County
Shops
Crimes
I
25
36900
J
27
24100