Question

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. 

(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.

Answer 1

We have given correlation coefficients (r), regression equations in the two scatter plots. First scatter plot is Violent crime rates Vs Unemployment rates and second scatter plot is property crime rates and unemployment rates. Using given information we will answer questions.

(a) There is no significant linear correlation between violent crime rates and unemployment rates.

Correlation coefficient r between violent crime rates and unemployment rates is 0.058 which is not that significant. Correlation coefficient lies between -1 and 1. Correlation coefficient near to 1 or -1 is is highly significant and correlation coefficient near to zero is not significant.

(b) There is a significant linear correlation between property crime rates and unemployment rates.

Correlation coefficient r between property crime rates and unemployment rates is 0.577 which is significant. Significant linear correlation can be observed from scatter plot also.

(c) Generally, slope of regression line represents change in the dependent variable (y) for unit change in the regressor variable (x).

With respect to property crime rates the slope of regression equation is 270.07 which represent increase in the property crime rate by 270.07 (per 100,000) for unit increase in the unemployment rate.

It represents increase because slope has positive sign.

(d) Generally, y-intercept represents the mean of dependent variable (y) if data on regressor(x) takes value zero.

With respect to property crime rates intercept is 2766.3 which represents average property crime rate (per 100,000) for the zero unemployment rate.

This is not meaningful because we can observe that there is a significant linear correlation between property crime rates and unemployment rates so 2766.0 average property crime rates for zero unemployment rates is not meaningful.

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