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. Estimate Std. Error t value Pr(>jtj) (Intercept) -29.901 7.789 -3.839 0.001 poverty% 2.559 0.390 6.562 0.000 s = 5.512 R2 = 70.52% R2adj = 68:89%

Solution

  1. Write out the linear model.
  1. Linear Model, \(AnnualMurders(perMillion) = 2.559\times poverty\% - 29.901\)
  1. Interpret the intercept.
  1. If There is no poverty, the Expected murders in the cites will be -29.901 This value does not make any sense. It just serves to ajust the height of the regression line.
  1. Interpret the slope.
  1. When there is an increase in poverty percentage of 1%, the expected number of murders per million increase of 2.556.
  1. Interpret R2.
  1. Poverty level explains 70.52% of the variability in murder rates in metropolitan areas.
  1. Calculate the correlation coefficient.
  1. correlation coefficient \(r=\sqrt{R^2}\)
sqrt(.7052)
## [1] 0.8397619

The correlation coefficient is 83.98%