The Seneca Children’s Fund (SCF) is a local charity that runs a summer camp for disadvantaged children. The fund’s board of directors has been working very hard over recent years to decrease the amount of overhead expenses, a major factor in how charities are rated by independent agencies. The following data show the percentage of the money SCF has raised that was spent on administrative and fund-raising expenses for 2000–2014.
| Year | Period (t) | Expense (%) |
| 2000 | 1 | 18.4 |
| 2001 | 2 | 15.7 |
| 2002 | 3 | 14.8 |
| 2003 | 4 | 13.6 |
| 2004 | 5 | 12.0 |
| 2005 | 6 | 11.3 |
| 2006 | 7 | 10.9 |
| 2007 | 8 | 10.0 |
| 2008 | 9 | 9.2 |
| 2009 | 10 | 8.7 |
| 2010 | 11 | 7.4 |
| 2011 | 12 | 6.5 |
| 2012 | 13 | 5.9 |
| 2013 | 14 | 5.0 |
| 2014 | 15 | 4.8 |
a. Construct a time series plot. What type of pattern exists in the data?
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
c. Forecast the percentage of administrative expenses for 2015.
d. If SCF can maintain its current trend in reducing administrative expenses, how long will it take SCF to achieve a level of 4% or less?
