A study was conducted to examine the roles of firearms and various other factors in the rate of homicides in the city of Detroit. Information for the years 1961 to 1973 is provided in the Detroit dataset. Dataset is provided.

Homicide - the number of homicides per 100,000 population

Police - the number of full-time police officers per 100,000 population

Unemp - the percentage of adults who are unemployed

Register - the number of handgun registrations per 100,000 population

Weekly - the average weekly earnings for city residents.

1. In excel. Run simple linear regression for each of the four predictors listed here and provide the R² for each of the four models.

2. Which variable explains the greatest proportion of the observed variation among the values of homicide rate?

3. In excel, Build a multiple regression model - start with all four predictor variables and determine the 'best' model based on p-values and R-squared values. List which variables remain in your model.

4. Provide the regression equation for predicting homicide that you found in your excel output. Provide the appropriate numbers in the regression equation. yhat = b₀ + b₁x₁ + ..+ b₄x_4. This will include however many predictors you found in the model in Question 3 - no more than 4 but 4 predictors may not be the most parsimonious model.

5. What is the adjusted R-squared for your final model from Question 3?

6. Plugging in whichever values you need, what is the expected number of homicides when the number of police per 100,000 population is 352, the percent of unemployed people is 8, the number of handgun registrations per 100,000 population is 650, and weekly average earnings for city residents is $132 for the model you selected in Question 3?

7. For the residual plots and describe what you see.