10 Gun Ownership in the U.S. Consider the following 2008 scatterplot, comparing

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10 Gun Ownership in the U.S. Consider the following 2008 scatterplot, comparing the percentage of a state's population that lives in rural areas to the percentage of their population who owns a registered gun. A logarithmic regression model has been added to the graph for your use. [Source: fiveninetyseven.com Gun Ownership in the U.S. 70 60 y17.188inf)- 16.896 R 0.6742 50 Percentage of 40 Owning a Gun 30 20 10 Residents 0 20 40 50 60 70 Percentage of Residents Living in Rural Areas 1. If we work on the assumption that a regression model with a correlation coefficient of 0.8 or higher is a decent fit, is the logarithmic regression model above one that we should give any credence to? Explain 2. Arizona has 11.8 percent of its population classified as living in rural areas. What percentage of residents does the logarithmic regression model predict own a registered gun? 3. If a state were to have 50 percent of its residents owning a registered gun, what percentage of residents does the logarithmic regression model predict will live in rural areas? Show your work. 4. Discuss whether the predictions you made were interpolation or extrapolation. Explain. 131

Explanation / Answer

1.

Yes, we can accept the model because the threshold is kept at r = 0.8, which means r2 threshold is 0.64

and as can be seen in he graph, the r2 is 0.6742

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