Question

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 in 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 a seven-year period.

Year	Period (t)	Expense (%)
1	1	14.0
2	2	12.1
3	3	10.4
4	4	10.4
5	5	11.6
6	6	10.1
7	7	8.4

(a) Construct a time series plot.

What type of pattern exists in the data?

a)The time series plot shows an exponential trend.

b)The time series plot shows an upward linear trend.  

c)The time series plot shows a quadratic trend.

d)The time series plot shows a downward linear trend.

Develop the linear trend equation for this time series to forecast expense percentage.

T_t = ____?________

(c) Forecast the percentage of administrative expenses for year 8.

____?_____ %

(d) If SCF can maintain their current trend in reducing administrative expenses, during which period will they first achieve a level of 5% or less?

Expenses will first reach a level of 5% or less in period ___________?____________ .

Answer 1

Answer:

a) It seems to be linear trend

b)

c) For 2010, t=8 so for t=8 the percentage of administrative expenses for 2010

   y’ = 13.8 -0.7 * 8

        = 8.2

d) Following table shows the forecasted values:

Year	Period (t)	Forecasted Expense (Y') (%)
2010	8	8.2
2011	9	7.5
2012	10	6.8
2013	11	6.1
2014	12	5.4
2015	13	4.7
2016	14	4
2017	15	3.3

So in year 2015, expenses will be less than 5%.