Sales of vegetable dehydrators at Bud Banis’s discount department store in St. Louis over the past year are shown below. Management prepared a forecast using a combination of exponential smoothing and its collective judgment for the 4 months (March, April, May, and June of 2010):
Month 2009-2010 Unit Sales Management’s Forecast
March 101 120
April 96 114
May 89 110
June 108 108
a) Compute MAD and MAPE for management’s technique.
b) Do management’s results outperform (i.e., have smaller MAD and MAPE than) a naive forecast?
- Which forecast do you recommend, based on lower forecast error?
Mark Cotteleer owns a company that manufactures sailboats. Actual demand for Mark’s sailboats during each season in 2006 through 2009 was as follows:
Season 2006 2007 2008 2009
Winter 1,400 1,200 1,000 900
Spring 1,500 1,400 1,600 1,500
Summer 1,000 2,100 2,000 1,900
Fall 600 750 650 500
Mark has forecasted that annual demand for his sailboats in 2011 will equal 5,600 sailboats. Based on this data and the multiplicative seasonal model, what will the demand level be for Mark’s sailboats in the spring of 2011?
The number of transistors (in millions) made at a plant in Japan during the past 5 years follows:
a) Forecast the number of transistors to be made next year, using linear regression.
b) Compute the mean squared error (MSE) when using linear regression.
- Compute the mean absolute percent error (MAPE).
John Howard, a Mobile, Alabama, real estate developer, has devised a regression model to help determine residential housing prices in South Alabama. The model was developed using recent sales in a particular neighborhood. The price (Y) of the house is based on the size (square footage = X) of the house. The model is: Y = 13,473 + 37.65X
The coefficient of correlation for the model is 0.63.
a) Use the model to predict the selling price of a house that is 1,860 square feet.
b) An 1,860-square-foot house recently sold for $95,000. Explain why this is not what the model predicted.
c) If you were going to use multiple regression to develop such a model, what other quantitative variables might you include?
- What is the value of the coefficient of determination in this problem?
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