1) Consider the following time series:

t 1 2 3 4 5 6 7

Yt 120 110 100 96 94 92 88

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. Regression analysis yields the following forecast equation: 119.71-4.929t; what is the MSE for this forecast method? Round to the nearest hundredth.

d. What is the forecast for t=8

2).

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 were spent on administrative and fund-raising expenses for

2003-2009.

Year 2003 2004. 2005. 2006. 2007. 2008. 2009

Period 1. 2. 3. 4. 5. 6. 7

Expense%. 13.9 12.2 10.5 10.4 11.5 10.0 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 2010.

d. If SCF can maintain its current trend in reducing administrative expenses, how long

will it take SCF to achieve a level of 5% or less?

3). FRED (Federal Reserve Economic Data), a database of more than 3000 U.S. economic

time series, contains historical data on foreign exchange rates. The following data

show the foreign exchange rate for the United States and China (http:// .stlouisfed.org/fred2/). The units for Rate are the number of Chinese yuan to one U.S. dollar.

Year Month Rate

2007 October 7.5019

2007 November 7.4210

2007 December 7.3682

2008 January 7.2405

2008 February 7.1644

2008 March 7.0722

2008 April 6.9997

2008 May 6.9725

2008 June 6.8993

2008 July 6.8355

a. Construct a time series plot. Does a linear trend appear to be present?

b. Use simple linear regression analysis to find the parameters for the line that minimizes

MSE for this time series.

c. Use the trend equation to forecast the exchange rate for August 2008.

d. Would you feel comfortable using the trend equation to forecast the exchange rate for

December 2008?