Q3: Time Series Analysis (linear regression model). 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. Period (t) Expense (%) Year 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?
Q3: Time Series Analysis (linear regression model). 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. Period (t) Expense (%) Year 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?
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Transcribed Image Text:Q3: Time Series Analysis (linear regression model).
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.
Period (t) Expense (%)
Year
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?
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