Consider a line of regression that fits data points showing crime rate and popul

Question

Consider a line of regression that fits data points showing crime rate and population for all U.S. cities with populations between 1 million and 10 million people.

a. For which U.S. cities would this line of regression not provide very good predictions of crime rate?

b. What advice would you provide to a sociologist from China who would like to use this line of regression to predict the crime rate in Chinese cities?

c. What are some possible confounding variables that might covary with both crime rate and city population?

d. What would you say to someone who was convinced that high birth rates cause an increase in crime approximately 20 years later. Especially if he insists that this particular line of regression proves it (that is, assuming it has a positive slope)?

Explanation / Answer

a)

As the regression line has been modeled for the value of population lying in between 1 million to 10 million, so for every city of US having a population less than 1 million or greater than 10 million, it would not be very good prediction of crime rate using this regression model as it violate the assumptions of linear regression.

b) I would suggest that this model can not be used for the chinese cities because the model has been trained using the data from American cities. So, the behavior of the cities would entirely differ for two countries. There might be less crime or more crime in the chinese cities with same population. A regression model should be only used for the variable it has been trained with. So, chinese sociologist should sample the data for chinese crime rate and population for different cities and then make his own model.

c) There might be several variables confounding which may vary with both population and crime rate. One such example would be the "Per Capita Income" of the city population. Because if the population is high, the per capita income would be low and if there is low per capita income, poor people may tend to use illegal methods to earn more money. Another such variable would be population density. Because if the population is high in a city, it is most likely to have high population density and if the population density is high, the crime rate will be high.

d) Yes, it might be possible. Because with the high birth rate, the population would increase and hence the young population (which are assumed to be more involved with crime) will be more ater 10 years. Hence, there might be strong correlation between birthrate and crime rate.

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