(SHOW ALL WORK) Records comparing unemployment rates, violent crime rates (per 1
ID: 3155858 • Letter: #
Question
(SHOW ALL WORK)
Records comparing unemployment rates, violent crime rates (per 100,000) and property crime rates (per 100,000) were gathered in the state of Illinois for the years 1975 - 2005 (n = 31). The correlation coe cients and regression equations are given in the scatter plots below.
(a) Is there a significant linear correlation between violent crime rates and unemployment rates?
(b) Is there a significant linear correlation between property crime rates and unemployment rates?
(c) With respect to property crime rates, what does the slope of the regression equation represent?
(d) With respect to property crime rates, what does the y-intercept represent? Is it meaningful?
(e) The average unemployment rate in 2008 for the state of Illinois was 6.4%. Use this value and the regression equation to predict the property crime rate of Illinois for 2008.
(f) It turns out that the property crime rate in 2008 for the state of Illinois was 2,932.6 property crimes per 100,000 people. How well does that fit with your prediction from the previous question?
(g) The average unemployment rate in 2009 for the state of Illinois was 10.1 %. Use this value to predict the property crime rate of Illinois for 2009. Is this a risky prediction?
(h) What percentage of the variation in property crime rate can be explained by the linear relation to unemployment?
(i) What is the natural choice for the causative variable and the response variable.
Property Crime Rates-vs- Unemployment Rates Violent Crime Rate -vs- Unemployment Rates r=0.058 y 5.67 x + 733.4 un | r 0.577 y = 270.07 x + 2766.3 1300 1200 1100 1000 4500 900 700 500 2,500 Unemployment Rate Unemployment RateExplanation / Answer
a & b) Since n=31, df = n-2 = 31-2 = 29. The critical value of r at df = 29 is 0.349. Correlation between violent crime rates and unemployment rates is 0.058 which is less than 0.349. The correlation between violent crime rates and unemployment rates is not significant. Correlation between property crime rates and unemployment rates is 0.577 which is greater than 0.349. The correlation between property crime rates and unemployment rates is significant.
c) As unemployment rate increases by 1%, property crime rates increases by 270.07 per 100,000.
d) When unemployment rate is 0%, property crime rates would be 2766.3 per 100,000. Yes, its meaningful.
e) y=270.07x+2766.3. Plug x=6.4.
y=270.07(6.4)+2766.3 = 4494.748
f) The prediction error = 4494.748 - 2932.6 = 1562.148
g) y=270.07x+2766.3. Plug x=10.1.
y=270.07(10.1)+2766.3 = 5494.007
This rate does not lie too far from data values. its not a risky prediction.
h) r² = 0.577² = 0.332929. Only 33% of the variation in property crime rate can be explained by the linear relation to unemployment.
i) Response variable = property crime rate and causative variable = unemployment rate
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