The $100 million levy

The council put out a flyer claiming the town would have a $100 million dollar tax levy (total property taxes collected) in 15 years. For this to happen, they had to assume that the levy would grow by 4%, the maximum increase allowed, for the next 15 years.

A more careful analysis using a linear model showed that a constant growth rate model does not fit the data well, underpredicting the levy at both ends and overpredicting in the center:


Examining the residuals confirms this:


Adding a quadratic term to the model produces a better fit:

The residuals do not exhibit any systematic pattern this time:

Because the graph is concave down, the rate of growth is slowing. This shows that the model needed to get to a $100 million dollar levy in 15 years does not fit the data, because that curve would be concave up.

The R code and output are posted here.