5.16\.\* In Example 3.14 we fit the model Rt = b0 + b1St6 + b2Dt6 + b3Dt6 St6 + wt, where Rt is Recruitment, St is SOI, and Dt is a dummy variable that is 0 if St < 0 and 1 otherwise. However, residual analysis indicated that the residuals are not white noise. (a) Plot the ACF and PACF of the residuals and discuss why an AR(2) model might be appropriate. (b) Fit the dummy variable regression model assuming that the noise is correlated noise and compare your results to the results of Example 3.14 (compare the estimated parameters and the corresponding standard errors). (c) Now fit a seasonal model for the noise in the previous part.

A lot of data has some time element to it, and when we are explicitly trying to understand how time is related to our dependent variable, we’re talking about time series analyses. For this simple illustrative case of modeling alcohol related crimes, I’m interested in how many crimes happen per day. The city of Seattle does a great job of making its data available for public use through a Socrata Open Data API, so we’re going to experiment with some data from there. For simplicity’s sake, I’m going to look at only DUIs and ‘liquor law violations’ as my count of alcohol related crimes, but in reality there are probably other crimes you would want to include. This process and all of the exploratory analyses are documented in a Jupyter Notebook in my GitHub repository.