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(>|t|) (Intercept) -29.901 7.789 -3.839 0.001
poverty% 2.559 0.390 6.562 0.000
s = 5.512 R2 = 70.52% R2 adj = 68.89%
(a) Write out the linear model.
(b) Interpret the intercept.
(c) Interpret the slope.
(d) Interpret R2.
(e) Calculate the correlation coefficient.
Percent in Poverty
Annual Murders per Million
14% 18% 22% 26%
10
20
30
40
Murders and poverty, Part II.presents regression output from a model for predicting annual murders per million from percentage living in poverty based on a random sample of 20 metropolitan areas. The model output is also provided below.
Estimate Std. Error t value Pr(>|t|) (Intercept) -29.901 7.789 -3.839 0.001
poverty% 2.559 0.390 6.562 0.000
s = 5.512 R2 = 70.52% R2 adj = 68.89%
(a) What are the hypotheses for evaluating whether poverty percentage is a significant predictor of murder rate?
(b) State the conclusion of the hypothesis test from part (a) in context of the data.
(c) Calculate a 95% confidence interval for the slope of poverty percentage, and interpret it in context of the data.
(d) Do your results from the hypothesis test and the confidence interval agree? Explain.