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    Index Numbers & Forecasting

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    Aggregate price indexes

    R & B beverages, Inc., provides a complete line of beer, wine, and soft drink products for distribution through retail outlets in central Iowa. Unit price data for 2003 and 2006 and quantities sold in cases for 2003 follow.
    Item 2003 quantity cases Unit prices
    2003 2006
    Beer 35,000 16.25 17.50
    Wine 5,000 64.00 100.00
    Soft drink 60,000 7.00 8.00

    Compute a weighted aggregate index for the R&B Beverage sales in 2006, with 2003 as the base period.
    Index Numbers

    The median sales prices for new single-family houses for the years 1998-2001are as follows (Statistical abstract of the United States, 2002)
    Year Price ($1000s)
    1198 152.9
    1999 161.0
    2000 169.0
    2001 175.2

    a) Use 1998 as the base year and develop a price index for new single-family homes over this four-year period
    b) Use 1999 as the base year and develop a price index for new single- family homes over this four year period


    The following table reports the percentage of stocks in a typical portfolio in nine quarters from 2005 and 2007
    Quarter Stocks %
    1st-2005 29.8%
    2nd-2005 31.0
    3rd-2005 29.9
    4th-2005 30.1
    1st-2006 32.2
    2nd-2006 31.5
    3rd-2006 32.0
    4th-2006 31.9
    1st-2007 30.0

    A) Use exponential smoothing to forecast this time series. Consider smoothing constants of a=.2, .3and.4. What value of the smoothing constant provides the best forecast?
    B) What is the forecast of the percentage of stocks in a typical portfolio for the second quarter of 2007?
    The following five years of data show the average minimum balance to avoid fees for checking accounts that pay interest (USA Today, December 6, 2005
    Date Balance
    Spring 2000 1522.41
    Fall 2000 1659.63
    Spring 2001 1678.34
    Fall 2001 1707.55
    Spring 2002 1767.36
    Fall 2002 1866.17
    Spring 2003 2015.04
    Fall 2003 2257.82
    Spring 2004 2425.83
    Fall 2004 2086.93
    Spring 2005 2295.85
    Fall 2005 2294.61

    A) GRAPH THIS TIME SERIES. Dose A linear trend appear to be present?
    B) Develop the equation for the linear trend component for the time series.
    C) Use the trend equation to forecast the minimum average balance to avoid account fees for Spring 2006

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    Solution Summary

    The solution provides a step by step method for the calculation of index numbers and time series analysis. Formula for the calculation and Interpretations of the results are also included.