Crime

Fifty states in America were investigated in terms of their crime rates and percentage of high school dropouts. The crime rate per 100,000 people included: murder, rape, robbery, aggravated assault, burglary, larceny-theft and motor vehicle theft. The state high school dropout rate comprised the percentage of current 16-19 year old people who were not in school and had not finished the 12th grade. The data are plotted below.

Since Dropout is a continuous explanatory variable, this model (indicated by the blue line in the plot below) is of the form \[y_i = \alpha + \beta x_i+ \epsilon_i\] for \(i=1,\dots,n\). We can estimate \(\alpha\) and \(\beta\) using the usual formula \((X^TX)^{-1}X^TY\) but for now assume we found

\[\begin{eqnarray*} \hat{\alpha}&=&2197\\ \hat{\beta}&=&282\\ \end{eqnarray*}\]

Interpreting these estimates,

• For a 0% dropout, the average crime rate is 2197 (per 100,000 people).

• For every 1% increase in dropout, the average crime rate increases by 282 (per 100,000 people).