Most of the analysis in this book focuses on the study of trends over time.  Chapter 7, on the effectiveness of policing, also includses some cross-sectional analyses of relationships at one point of time.

• Graphs are mostly time series graphs.  For these graphs:
• we can compare trends over time for one or more variables
• if two variables move up and down together, they are positively correlated with each other- Figure 2.1 is an example of two that are highly correlated with each other.  Their being correlated means that if you know the value of one for a given year, you can do a pretty good job of predicting the value of the other for that year.
• if they move up and down at opposite times, they are negatively correlated with each other.  A negative correlation also means that if you know the value of one for a given year, you can do a pretty good job of predicting the value of the other for that year.
• if a variable shows a smooth, "linear" trend - going up or down a certain amount each year, this means that it is highly correlated with time - if you know the year you can predict the value of the variable well.
• Some of the graphs are bivariate non-time series graphs.  In some cases, e.g., Figure 2.9, the variables that are plotted are ratios of two years.  This measures how much of a difference there was between two years in the crime rate for each age group.
• These trends can also be measured through regression analysis.  Regression fits a straight line to the trend.  The b coefficient is a measure of the slope of the line.  If you are not familiar with regression from your methods class, check out some of the links on today's home page that explain it:  Tronchim on the General Linear Model  Statsoft on  Multiple Regression.  A more technical treatment of Multiple Regression.  None of these, however, focus on time series analysis when the year is the X variable.
• We will illustrate the use of regression by using the data set.  We will fit a linear curve to different segments of this data set.  I will post the file with our results.  The file is available at:  http://crab.rutgers.edu/~goertzel/regexample.xls
• the discussion on pages 101-105 discusses "elasticities" instead of beta coefficients.  The author explains what this means pretty clearly - it is a more easily understandable way of communicating regression results.  "Elasticity" measures the amount of change in a dependent variable that will result from a certain change in an independent variable.  The beta coefficient measures the same thing, but in a less standardized way.
• Regression Analysis allows us to do two things:
• summarize a lot of data in one table, e.g., table 4.1  Summarizing this with graphs would require a lot of graphs.  However, this kidn of summary table is more difficult for most people to read than a series of graphs.
• make projections of what might have happened under different conditions, or of what will happen in the future if current patterns continue to hold, e.g., Table 4.2
• The big problem with Regression Analysis is that it assumes that trends are linear, i.e., straight lines without turning points.  If there are turning points, we need to control for that and the controls introduce other problems.  For this reason, regression analysis has often led to erroneous results when dealing with this kind of data.