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3. Sociology /Criminology/ Economics: 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 coefficients and regression equations are given in the scatter plots below. Violent Crime Rate -vs- Unemployment Rates Property Crime Rates -vs- Unemployment Rates r = 0.058 y = 5.67 x + 733.4 6.500 r = 0.577 y = 270.07 x + 2766.3 450 Violent Crime rate (per 100,000) Property crime rate( per 100,000) 2 5 6 7 9 2000 10 11 Unemployment Rate Unemployment Rate (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? F 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