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?
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter3: Straight Lines And Linear Functions
Section3.CR: Chapter Review Exercises
Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...
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