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# Forecasting

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In the volume, Consumer Demand in the United States: Analyses and Projections
(Cambridge, Mass.: Harvard University Press, 1970), H.S. Houthakker and L.D. Taylor presented the following results for their estimated demand equation from 1929 to 1961 (excluding the 1942 through 1945 war year in the United States:

Qt = 19.575 + 0.0289Xt - 0.0923Pt - 99.568Ct - 4.06Dt
(9.3125) (-1.7682) (-9.8964) (23.50)
R² = 0.857 D-W = 1.86

Where Qt = per capita personal consumption expenditures on shoes and other footwear during year t, at 1954 prices

Xt= total per capita consumption expenditures during year t, at 1954 prices

Pt= relative prices of shoes in year t, at 1954 prices

St= stock of automobiles per capita in year t

Dt= dummy variable to separate pre-from post-World war II years:
Dt= 0 for year 1929 to 1941 and
Dt= 1 for years 1946 to 1961

The number of parentheses below the estimated slope coefficients refer to the estimated t statistics.

Using the above estimated regression equation, forecast the demand for shoes for (a) 1962 and (b) 1972 if the forecasted values of the independent or explanatory variables are those given in the following table. (c) Why would you expect the error for the 1972 forecast to be larger than for the 1962 forecast?

https://brainmass.com/economics/regression/forecasting-122818

#### Solution Preview

Qt = 19.575 + 0.0289Xt - 0.0923Pt - 99.568Ct - 4.06Dt

(a) For 1962 we are given the following values:
X = 1,646
P=20
C=0.4
D=1
Putting these numbers in the regression equation we get:
Q(1962) = 19.575 + ...

#### Solution Summary

The solution performs demand analysis and forecasting for the scenarion provided in the question. It also goes in a lot more detail about other aspects of regression analysis.

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## Moving Average Forecast, Exponential Smoothing Forecast, Adjusted Exponential Smoothing Forecast, MAD, MAPD, Cumulative Error, Comparison among different Forecast Techniques and Regression Analysis

1. The saki motorcycle dealer in Minneapolis wants to make an accurate forecast of demand for the Saki Super TXII motorcycle during the next month.
Because the manufacturer is in Japan, it is difficult to send motorycles back or reorder if the proper number is not ordered a month ahead.
From sales records, the dealer has accumulated the following data for the past year:

Month Motorcyle Sales
January 9
February 7
March 10
April 8
May 7
June 12
July 10
August 11
September 12
October 10
November 14
December 16

a) Compute a 3-month moving average forecast of demand for April thru January of the next year
b) Compute a 5-month moving average forecast for June thru January
c)Compare the two forecasts computed in (a) and (b) using MAD-which should be used next year January?

2. The chairperson of the department of management at State University wants to forecast the number of students
who will enroll in production and operations mgmt next semester-- in order to determine how many sections to schedule.
The chair has acumulated the following enrollment data for the past 8 semesters:

Semester Students enrolled
1 400
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3 350
4 420
5 500
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a) Compute a three semester moving average forecast for semesters 4 thru 9
b)compute the exponentially smoothed forecast for the enrollment data &#945; = 0.20
c) compare the two forecasts using MAD-which is more accurate?

3. Whistle Stop Café is well known for its homemade ice cream, made in a small plant in back of café. People drive
all the way from Atlanta and Macon to buy the ice cream. The two women who own the cafe want to develop a forecasting model
so they can plan their ice cream production operation and determine the number of employees they need to sell ice cream in the café.
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Year Quarter Ice Cream sales(gallons)
2003 1 350
2 510
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2004 5 370
6 480
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2005 9 450
10 550
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Develop an adjusted exponential smoothing model with &#945; = 0.50 and &#946; = 0.50 to forecast demand and assess
its accuracy using cumulative error(e) and average error. Does there appear to be any BIAS in the forecast?

4. Aztec Industries has developed a forecasting model that was used to forecast during a 10-month period.
The forecasts and actual demand were as follows:

Month Actual Demand Forecast Demand
1 160 170
2 150 165
3 175 157
4 200 166
5 190 183
6 220 186
7 205 203
8 210 204
9 200 207
10 220 203

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Does forecasting method appear to be accurate?

5. The manager of Ramona Hotel believes that how well the local Blue Sox professional baseball team is has an impact on the occupancy rate at the hotel during summer months.
Following are the number of victories for the Blue Sox( in a 162-game schedule) for the past 8 years and the hotel occupancy rates:

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1 75 83
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