Question 1

The data set in the worksheet “Question 1” of “MCD2080 FAT 2 Version C.xlsx gives a variety of variables that were recorded across a number of cities in the US.

There are three variables that are believed to influence the crime rate, which are namely;

ExpenditurePol: expenditure (per capita expenditure on police)

High YouthUnemploy: = 1 if > 3 x number of unemployed mature individuals and

                                         = 0 if ≤ 3 x number of unemployed mature individuals.

Below Wage: the number of families below half wage per 1000.

The CrimeRate is defined as number of offences per million population.

Use this data to answer the following questions:

a) (i). Calculate the overall average and standard deviation of the crime rate.

(ii). Calculate the coefficient of correlation for the variables Crimerate and Below Wage; then CrimeRate and ExpenditurePol. In addition, calculate the proportion of cities with high youth unemployment (HighYouthUnemploy).

(iii). Interpret the coefficient of correlation for the CrimeRate and Expenditure Pol.

b) Estimate using the Excel a multiple linear regression model to analyse the impact of the variables

Below Wage, Expenditure Pol and High YouthUnemploy on the Crime Rate. Use your output to answer the following questions (i). Write down the estimated regression equation

(ii). State and Interpret the regression coefficient for the intercept. Discuss its reliability

(iii). State and interpret the regression coefficient for "HighYouthUnemploy"

(iv). Compare the coefficients of High YouthUnemploy and ExpenditurePol to determine which has more of an impact on the crime rates.

c) At the 10% significance level, carry out a hypothesis test to determine if number of high youth unemployment have less impact on the crime rate when the per capita expenditure on police and families below half wage are taken into account.