How communities respond to a disaster or a violent crime was the subject of research published in the American Journal of Community Psychology (Vol. 44, 2009). Psychologists at the University of California tracked monthly violent crime incidents in two Texas cities, Jasper and Center, before and after the murder of a Jasper citizen that had racial overtones and heavy media coverage. (Center, Texas, was selected as comparison city since it had roughly the same population and racial makeup as Jasper.) Using monthly data on violent crimes, the researchers fit the regression model:
E(y) = β0 + β1x1 + β2x2 + β3x1x2,
where y = violent crime rate (number of crimes per 1,000 population), x1 = {1 if Jasper, 0 if Center}, and {x2 = 51 if after the murder, 0 if before the murder}.
a. In terms of the β's in the model, what is the mean violent crime rate in Center, Texas, for months following the murder?
b. In terms of the β's in the model, what is the mean violent crime rate in Jasper, Texas, for months following the murder?
c. For months following the murder, find the difference between the mean violent crime rate for Jasper and Center. (Use your answers to parts a and b)
d. Repeat part c for months before the murder.
e. Note that the differences, parts c and d, are not the same. Explain why this illustrates the notion of interaction between x 1 and x 2.
f. A test for H0: β3 = 0 yielded a p-value | < .001. Using α = .01, interpret this result.
g. The regression resulted in the following β-estimates:
β̂1 = 429, β̂2 = 169, β̂3 = 255. Use these estimates to illustrate that average monthly violent crime decreased in Center after the murder but increased in Jasper.