We are asked to investigate the hypothesis that the number of crimes is related to police expenditures because states with higher crime rates are likely to increase their police force, thereby spending more on the number of officers on the street.
State Number of Crimes (per 100,000 population) Police Protection Expenditures(in millions)
Maine 2,635 221
New Hampshire 2,013 274
Vermont 2,442 136
Massachusetts 2,838 1,673
Rhode Island 2,815 286
a. Construct a scatter diagram of the number of crimes and police expenditures, with number of crimes as the predictor variable. What can you say about the relationship between these two variables based on the scatterplot?
b. Find the least squares regression equation that predicts police expenditures from the number of crimes, What is the slope? What is the intercept?
c. Calculate the coefficient of determination (r2), and provide an interpretation.
d. If the number of crimes increased by 2,000 for a state, by how much would you predict police expenditures to increase?
e. Does it make sense to predict police expenditures when the number of crimes is equal to zero? Why or why not?
The solution gives detailed steps on performing a simple regression analysis including finding intercept, slope and coefficient and determination. All the formula and calcuations are shown and explained.