Brian, Marta, Chris, and Carrie U.S. Murder Rates by Brian, Marta, Chris, and Carrie Copyright (c) 2008 by The McGraw-Hill Companies. This material is intended solely for educational use by licensed users of LearningStats. It may not be copied or resold for profit.

High Murder Rates Average Rates Low Murder Rates

Principle of Parsimony: Deleting Useless Predictors What Predictors Did We Start With? Which Ended Up The Best Predictors? Principle of Parsimony: Deleting Useless Predictors

Murder Rate’s Best Predictors’ T-Statistics Black%Pop Hispanic%Pop Smoking Unemployment SouthEast PopDensity NorthEast 8.155 3.535 2.375 2.134 -1.695 -1.675 -1.532

Logic General Demographic Anticipated Sign= ? We thought living in the South could have a higher murder rate, but, otherwise we didn’t have any idea how location or size of a state could effect murder rate and thought it would be interesting to find out. Anticipated Sign= + We figured the more diverse or highly populated an area becomes, the more likely there are to be confrontations that could result in murder.

Logic Anticipated Sign= +/- Economic Others Logic Anticipated Sign= +/- We thought as Unem. Or Pov. Goes up, people result to crime for survival (+), and as income and homeown% go up there’s less need for crime and violence (-). Anticipated Sign= +/- College Grad% we expected to have a negative effect b/c most of the time more knowledge gets you ahead in life. The other 3 we expected to have slightly positive effects, if any at all.

Fit: 1st Run R2 is high, at close to 0.79 showing the fit was good. S should be low. See how it changes in subsequent runs. The adjusted R2 was .10 below the original, which suggests useless predictors.

Fit: 10th Run R2 is lower by .006 from the first run, but the adjusted R2 is much closer to the original, which means the relationship has become more parsimonious from deletion of unnecessary predictors. Standard Error dropped by almost 0.2 from the first run, to back up the fact that deleting predictors makes a better fit.

Stability The Correlation Matrix The VIF Method Because multicollinearity is often a cause of instability, we tested for it with two methods. The Correlation Matrix The VIF Method

Multicollinearity Some large correlations between predictors reveal possible multicollinearity.

Stability? No individual VIF has a value greater than ten, so no major worries for multicollinearity The sum of the VIF’s is above ten, at 13.1, which means we should maybe worry about multicollinearity, and as a result, worry about instability

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