Question

Sociology/Criminology/Economics: Records comparing unemployment rates and property crime rates (per 1,000) were gathered in a state for the years 1975 - 2005 (n = 31). Below is the scatterplot, regression line, and corresponding statistics for these 31 years.

Property Crime -vs- Unemployment x = Unemployment Rate (in %) y = Property Crime Rate (in crimes per 1,000 people) correlation coefficient: r = 0.8140 regression equation: ŷ = 2.59x + 28.8 sample size: n = 31

Answer the following questions regarding this relationship.

(a) Is there a significant linear correlation between these variables?

YesNo    

(b) What percentage of the variation in property crime rate can be explained by the linear relation to the unemployment rate? Express you answer as a percentage with one decimal place.
%

(c) What is the expected property crime rate (in crimes per 1,000 people) if the unemployment rate is 5.50 percent? Round your answer to one decimal place.
crimes per 1,000 people

Answer 1

a)

Yes

b)

percentage of the variation in property crime rate can be explained by the linear relation to the unemployment rate =r²*100 =(0.8140)^2*100=66.3 %

c)

expected property crime rate=2.59*5.5+28.8=43.0