Chapter Four Problems 4.23, 4.27, 4.33, and 4.35.
4.23
a) Compute MAD and MAPE for management’s technique.
Ans:
2009-2010
Period
Unit Sales
July
100
August
93
September
96
October
110
November
124
December
119
January
92
February
83
March
101
April
96
May
89
June
108
Management's Forecast
Forecast
120
114
110
108
Total
Average
Abs Pct
Error
Absolute Squared Err
-19
19
361
18.81%
-18
18
324
18.75%
-21
21
441
23.60%
0
0
0
0
-58
58
1126
61.16%
-14.5
14.5
281.5
15.29%
Bias
MAD
MSE
MAPE
b) Do management’s results outperform (i.e., have smaller MAD and MAPE than) a naive
forecast?
Ans:
Data
2009-2010 Unit
Period
Sales
July
August
September
October
November
December
January
February
March
April
May
June
100
93
96
110
124
119
92
83
8
10
15
9
Naive
Forecast
Abs Pct
Forecast Error
Absolute Squared Err
5
3
3
9
37.50%
6
4
4
16
40.00%
11
4
4
16
26.67%
12
-3
3
9
33.33%
Total
8
14
50 137.50%
Average
2
3.5
12.5
34.38%
Bias
MAD
MSE
MAPE
Management’s Forecast, MAD = 14.5 and MAPE = 15.29%
As per the Naive Forecast, MAD = 12.25 and MAPE = 12.12%
Using the Naive Forecast, the MAD and MAPE value is lower compared to Management’s
Forecast.
c) Which forecast do you recommend, based on lower forecast error?
Ans:
I would recommend that the firm should use the Naive Forecast method to forecast for the 4
months.
4.27
Ans:
Year
2006
2008
2009
Season
Demand 2007 Demand
Demand Demand
Winter
1400
1200
1000
900
Spring
1500
1400
1600
1500
Summer
1000
2100
2000
1900
Fall
600
750
650
500
Total average annual
demand
Average
Average
2006-2009
Seasonal
Seasonal
Demand
Demand
Index
1125
1250
0.9
1500
1250
1.2
1750
1250
1.4
625
1250
0.5
1250
As per Mark’s forecast, annual demand for his sailboats in 2011 will equal 5,600 sailboats.
Demand level for Mark’s sailboats in the spring of 2011 = (5600/4) * 1.2 = 1680 sailboats
4.33
a) Forecast the number of transistors to be made next year, using linear regression.
Ans:
Period
Year 1
Year 2
Year 3
Year 4
Year 5
Intercept
Slope
Abs Pct
Demand
Period
Forecast Error Squared Err
140
1
144
-4
16
02.86%
160
2
162
-2
4
01.25%
190
3
180
10
100
05.26%
200
4
198
2
4
01.00%
210
5
216
-6
36
02.86%
126
18
Total
Average
0
160
13.23%
0
32
02.65%
Bias MSE
MAPE
Number of transistors to be made next year, using linear regression = 126 + 18*6 = 126 +
108 = 234
b) Compute the mean squared error (MSE) when using linear regression.
Ans: Mean squared error (MSE) when using linear regression = 32
c) Compute the mean absolute percent error (MAPE).
Ans: Mean absolute percent error (MAPE) = 2.65 %
4.35
a) Use the model to predict the selling price of a house that is 1,860 square feet.
Ans:
The model is:
Y = 13,473 + 37.65X
The price (Y) of the house = 13473 + 37.65 * 1860 = $ 83502
b) A 1,860-square-foot house recently sold for $95,000. Explain why this is not what the
model predicted.
Ans:
Coefficient of correlation measure expresses the degree or strength of the linear relationship.
The coefficient of correlation for the model is 0.63. The strength of relationship as per the
model is not that significant and so there is a difference in the model prediction and the actual
sale value of the house.
c) If you were going to use multiple regression to develop such a model, what other
quantitative variables might you include?
Ans:
Multiple regressions is an associative forecasting method with more than one independent
variable. Other quantitative variables that can be considered for this multiple regression
would be:
-
Nos. of floors in the house
Distance of the house from major hospital
Average distance between two adjacent houses in that area
Rent prevailing in the surrounding areas
Distance from the Walmart or major shopping complex in the town
d) What is the value of the coefficient of determination in this problem?
Ans:
Coefficient of determination = 0.63 * 0.63= 0.3969