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 over the past seven years: YearPeriod (t)Expense (%)2003113.92004212.22005310.52006410.42007511.52008610.0200978.5 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 year 8.d. If SCF can maintain its current trend in reducing administrative expenses, how long will it take for SCF to achieve a level of 5% or less?

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 over the past seven years:

Year	Period (t)	Expense (%)
2003	1	13.9
2004	2	12.2
2005	3	10.5
2006	4	10.4
2007	5	11.5
2008	6	10.0
2009	7	8.5

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 year 8.
d. If SCF can maintain its current trend in reducing administrative expenses, how long
will it take for SCF to achieve a level of 5% or less?

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