Problem

8.25 Murders and poverty, Part I. The following regression output is for predicting annual murders per million from percentage living in poverty in a random sample of 20 metropolitan areas.

Charts

Questions

  1. Write out the linear model.

    We get the values from the chart. The intercept is -29.901 and the slope is 2.559

    \(\hat{y} = -29.901 + 2.559x\)

    (i.e.) \(\hat{murders} = -29.901 + 2.559 \times poverty\)%

  2. Interpret the intercept.

    The model predicts an expected murder rate of -29.901 per million if the percentage living in poverty is 0%.

    Note: 0% is outside the range of values for poverty% for the data: this is an example extrapoliation. Anywho, how can you have a negative murder rate?

  3. Interpret the slope.

    On average, we expect the murders per million to go up by 2.559 as the poverty percentage increases.

  4. Interpret \(R^2\).

    In the chart, \(R^2 = 70.52\)%: the poverty level explains 70.52% of the variation in annual murders per million.

  5. Calculate the correlation coefficient.

    The correlation coefficient is given by \(\sqrt{R^2}\) = \(\sqrt{0.7052}\) = \(\pm0.8397619\).

    By looking at the scatter plot, we know we are looking for the positive value so the correlation coefficient is +0.8397619.