Regression analysis across National Transit Database operating cost numbers on 76 large bus agencies nationwide indicates King County Metro and other large systems in Washington State are relatively high cost operations.

In cooperative and voluntary support of the King County Regional Transit Task Force, Public Interest Transportation Forum on May 13, 2010 ran a least squares regression analysis on 2008 National Transit Database (NTD), in an attempt to establish a robust formula for bus agency annual operating costs as a function of various cost drivers.

The simple linear equation that was derived works well as an explanation for the operating costs of the 76 largest bus transit agencies in America, measured by the number of vehicles in maximum operation (VMO), using 2008 data and excluding New York City.  Trolley bus operations of San Francisco and Seattle are counted as separate agencies in addition to the many motor bus operations, since NTD separates the data on these. The analysis was carried down the list of agencies from larger to smaller for a total of 76 data points, stopping at Spokane and including it as the smallest agency in the set.  The agencies and their data are displayed lower on this page as Appendix A; Washington State agencies are highlighted.

These are bus operations only; there is no rail transit, no demand responsive transit, and no van pools included.

For the 76 largest USA bus agencies, not including NYC, and including trolley bus operations in San Francisco and King County as separate data points from the rest of the motor bus operations, the following formula was derived using the multiple variable regression analysis capabilities of Excel spreadsheet software:

Annual operating expenditures =
(# of vehicles X 204) + [annual passenger boardings (000) X 0.46] + (# of full time employees in operations X 50)
- (# of part time employees in operations X 54) - a constant of 11,263.

Adjusted R squared is 0.98.  The equation overall and all coefficients are highly significant, p<.02  Appendix C below shows the statistics.  However, there is high multicollinearity, meaning the input variables are highly correlated.  This condition means the coefficients of the input variables cannot be considered as measuring independent influences on the operating costs.  However, the complete equation is valid.  An earlier run on a larger set of agencies yielded a similar equation.

Notice some terms are positive and some negative in the equation.

Notice how a greater number of part time employees (in combination with the other influences) tends to reduce expenditures, shown by the negative sign on the part time employees variable. 

If one plugs into the formula the actual inputs for each of the agencies listed in the table in Appendix A, a calculated estimate is obtained, as shown below in the fifth column of the table in Appendix B.  About half the estimates are higher than actual, and half are lower than the actual.  That's how regression works. In 46 out of 76 of the agencies, the formula provides an estimate that is within 15% of the actual, marked in green in the Appendix B table.  

Regression based estimates lower than the actual indicate a relatively high cost agency.  Perhaps wages and salaries are higher in these agencies, or they are paying more for fuel.  These are cost issues not directly included in the estimating equation.  Maybe the tires are changed more often on the buses.  Some of the lower cost agencies are in right-to-work states where the influence of collective bargaining on wage rates is lower than in states like Washington and California where labor unions are stronger.

What's of immediate interest with this sample is that plugging in the input number for the King County motor bus operation shows that the estimated expenditure from the formula based on all the agencies is 16% lower than the actual 2008 expenditures. For King County Trolley bus, the formula estimate is 30% lower.

The excess of actual over estimated combined from these two parts of King County Metro bus operations comes to about $75 million dollars over a year.

King County is not the highest cost agency with regard to operations expenditure for transit in Washington State, as shown by the ranking in Appendix B.  Some are higher, and some are lower, by this measure of comparing actual operating expenditures to what is estimated by the regression equation above.

Not surprisingly, Sound Transit's bus estimated expenditures are in percentage terms the most below actual of any agency in America in this sample: 37%. This is a result of Sound Transit funding the full costs of Metro (and Pierce Transit and Community Transit) for operating buses under contract on Sound Transit's behalf.  Sound Transit is thus a major subsidizer of the county bus agencies, including King County Metro.  

PITF recommends that the Regional Transit Task Force should replicate and extend this analysis with other cost influencing input variables, different years, and different samples.  Input variable that are less correlated with each other would likely provide greater insight into a variety of influences on operating costs.

In any event, the problem of above average costs revealed using 2008 data as demonstrated here should provide motivation to demonstrate cost control steps being addressed in the subsequent years (2009 and 2010) and in upcoming years.  Cost control steps should be documented prior to the planned coalition of King County leaders heading to the Washington State Legislature to ask for more revenue authority.

Addendum note: Since preparing this analysis, a regional colleague in the professional data analysis community prepared an alternative analysis that examined operating expenditures as a function of full-time employees per passenger boarding.  Once again, King County Metro was revealed as showing above average costs.