Chapter 16, Problem 22P

1. For the data in problem 21, the correlation between the number of crimes and population is r=0.933,
whichmeans that r ² = 0.8,7 (87%) istheproportion

of variance in the number of crimes that is predicted by popu1ation size. Does adding the amount spent on crime prevention as a second variable in the multiple regression equation add a significant amount tothe

Prediction? Testwith a= 0.05.

Problem 18 in Chapter 15 (p. 526), presenteddata

showing thenumber of crime,the amount spend on crime prevention, and the population for a set n = l2 cities.Atthattime, we used apartialcorrelation to

evaluate the relationship between the amount spent on crime prevention and the number of crimes crime while controlling population. It ispossible touse

multiple regression to accomplish essentially the same purpose. The data are as follows:

Number of

CrimesAmount for PreventionPopulation Size 3 6 1 4 7 1 6 3 1 7 4 l 8 11 2 9 12 2 11 8 2 l2 9 2 l3 16 3 l4 1? 3 l6 13 3 l7 14 3

1. Findthemultipleregressionequationforpredict­ ing the number of crimes using the amount spent on prevention and population as the two predictor variables.

Find the value of R²for the regressionequation.

18. A researcher records the annual number of serious crime and the amount spent on crime prevention for several sma11 town, medium cities, and large cities across the country. The resulting data show a strong positive correlation between the number of serious crimes and the amountspent on crime

prevention. However, the researcher suspectthat the positive correlation is actuallycaused by population as population increases, both the amount spent on crime prevention and the number of crimes will also increase. If population is controlled,there probably should be a negative correlation between the amount spent on crime prevention and the number of seriouscrimes. The following data how the pattern of resultobtained. Note that the municipa1ities are coded in three categories. Use a partial correlation holding population constant to measure the truerelationship

between crime rate and the amount spent on prevention.

Number of

CrimesAmount for PreventionPopulation

Size 3 6 1 4 7 1 6 3 1 7 4 ] 8 l1 2 9 l2 2 11 8 2 12 9 2 13 l6 3 14 l7 3 16 13 3 17 l4 3