City Cicles

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  • Topic: Errors and residuals in statistics, Exponential smoothing, Regression analysis
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  • Published : May 16, 2013
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Pràctica 2:

Organització de la producció.

Carles Ramírez Estrada
Marcel Subirana Florats
Curs 2011-2012
G23
22/03/2012

4.47 City Cycles has just started selling the new Z-10 mountain bike, with monthly sales as show in the table. First, co-owner Amit wants to forecast by exponential smoothing by initially setting February’s forecast equal to January’s sales with α=1. Co-owner Barbara wants to use a three-period moving average.

1. Is there a strong lineal trend in sales over time?

2. Fill in the table with what Amit and Barbara each forecast for May and the earlier months, as relevant.

3. Assume that May’s actual sales figure turns out to be 405. Complete the table’s columns and then calculate the mean absolute deviation for both Amit’s and Barbara’s methods.

4. Based an these calculations, which method seems more accurate?

1. Naive forecast:

| Sales| Naive Forecast| Error| |Error|| Error^2| %| January| 400,00| -| 400,00| 400,00| 160000,00| 100,00| February| 380,00| 400,00| -20,00| 20,00| 400,00| 5,26| March| 410,00| 380,00| 30,00| 30,00| 900,00| 7,32|

April| 375,00| 410,00| -35,00| 35,00| 1225,00| 9,33| May| 405| 375,00| 30| 30| 900| 7,41|
| | CFE| 405| 405| 163425| 129,32|
| | MFE| 81| 81| 32685| 25,86|
| | | | MAD| MSE| MAPE|

TS = CFE/MAD| 5|

* This graph shows sales:

The resulting equation of figure use to give different values to "x" and find the slope of the regression line.

y = -4,5x + 402,5
R² = 0,123

Months| Sales| “X”|
January| 400| 398|
February| 380| 393.5|
March| 410| 389|
April| 375| 384.5|
May| 405| 380|

2. Exponential smoothing:

| Sales| Exponential| Error (α=0,1)| |Error|| Error^2| %| January| 400,00| 394,00| 6,00| 6,00| 36,00| 1,50|
February| 380,00| 394,60| -14,60| 14,60| 213,16| 3,84| March| 410,00| 393,14| 16,86| 16,86| 284,26| 4,11|...
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