16. You conduct a study to show that number of crimes (Yi) across cities varies with expenditure on police force (Xti), median income (X2i), unemployment rate (X3i) and population density (X4i). You collect data for several cities in Northern and Southern India and estimate this model. (i) Specify a dummy variable model to incorporate the following and mention the null and alternate hypothesis and the expected decision if your data has to support the following: (a) Different intercepts for North and South. (b) As Northern India is less developed than Southern India and it has low expenditure on police while Southern India has more population density in its cities compared to Northern India so the impact of these two variables are different for North and South. (5 marks) (ii) You suspect heteroscedasticity and specify the appropriate test for the same given so many regressors and what will happen to the results in (i) above if you ignore to adjust for heteroscedascticity