Correlation and Regression

Using the crime data, create a scatterplot with an appropriate main title, axis labeling (note that "X3" is not an appropriate label), and a regression line (in R, you'll want to pull the variables out of the lm function and then use the abline function) for the reported violent crime rate vs annual police funding. Report the equation of the regression line, the values of r and R squared, and their interpretation. Do this exercise again for the variables X3 and X4. Choose which variable is x and which is y knowing that x should be able to predict the response variable y. Do this for your data set, also ensure that you have one positive correlation and one negative one. Use four different variables and make sure that your y variables are actually "predictable" given your x variables. Last, create the best possible model that uses multiple independent variables to predict the total overall reported crime rate. Plot the independent variables against each other in a scatter matrix in order to assess multicollinearity (and remove variables if needed). Report back why your model is superior with justification (i.e. adjusted R squared, model significance, etc). Summarize your model concisely. As always, do the same exercise for your own data set.