I started following the debate on differential minimum wage for youth (15-19 year old) and adults in New Zealand. Eric Crampton has written a nice series of blog posts, making the data from Statistics New Zealand available. I will use the nzunemployment.csv data file (with quarterly data from March 1986 to June 2011) and show an example of multiple linear regression with autocorrelated residuals in R.
A first approach could be to ignore autocorrelation and fit a linear model that attempts to predict youth unemployment with two explanatory variables: adult unemployment (continuous) and minimum wage rules (categorical: equal or different). This can be done using: