This example is based on the FBI’s 2006 crime statistics. Particularly we are interested in the relationship between size of the state, various property crime rates and the number of murders in the city. It is our hypothesis that less violent crimes open the door to violent crimes. We also hypothesize that even we account for some effect of the city size by comparing crime rates per 100,000 inhabitants that there still is an effect left.
First we need to check whether there is a linear relationship between the independent variables and the dependent variable in our multiple linear regression model. To do this, we can check scatter plots. The scatter plots below indicate a good linear relationship between murder rate and burglary and motor vehicle theft rates, and only weak relationships between population and larceny.
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Secondly, we need to check for multivariate normality. We can do this by checking normal Q-Q plots of each variable. In our example, we find that multivariate normality might not be present in the population data (which is not surprising since we truncated variability by selecting the 70 biggest cities).
We will ignore this violation of the assumption for now, and conduct the multiple linear regression analysis. Multiple linear regression is found in SPSS in Analyze/Regression/Linear…
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