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# Lesson06

## on Sep 14, 2011

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Statistics for International Business School, Hanze University of Applied Science, Groningen, The Netherlands

Statistics for International Business School, Hanze University of Applied Science, Groningen, The Netherlands

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## Lesson06Presentation Transcript

• IBS Statistics
Year 1
Dr. Ning DING
n.ding@pl.hanze.nl
I.007
• What we are going to learn?
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
• Review
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Why Dispersion?
Central Tendency?
• Review
Dispersion
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Range Variance Standard Deviation
• Review
Dispersion
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
• Review
Don’tcompare the dispersion in data sets byusingtheir Standard Deviationsunlesstheirmeans are close to eachother.
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Whichone has more variation in the data?
Example :
20 poundsoverweight
Mean=120 pounds
Mean=170 pounds
CV=20/120 =16.7%
CV=20/170 =12.5%
Coefficient of Variation (CV)= Standard Deviation / Mean
• Review
2
3
4
5
6
7
10
13
2
3
4
4.25
4.75
7
8
9
2
3
4
5
6
7
8
9
2
3
3.25
3.50
3.75
4
5
9
Median= 5.5 5.5 4.5 3.38
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Mean= 5.5 6.25 5.25 4.19
• Review
Most skewed?
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Median= 5.5 5.5 4.5 3.38
Mean= 5.5 6.25 5.25 4.19
• Review
Positive Correlation
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Negative Correlation
• Review
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Secular trend
Seasonalvariation
Sales
Q4
Q2
Q3
Cyclicalfluctuation
Q1
Irregularvariation
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Years
• Review
Applicable when time series follows fairly linear trendthat have definite rhythmic pattern
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
• Seven-Year Moving Total
Moving Average
1+2+3+4+5+4+3=22
/ 7 = 3.143
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
2+3+4+5+4+3+2=23
/ 7 = 3.286
3+4+5+4+3+2+3=24
/ 7 = 3.429
SevenYearMoving Average
• Ŷ = a + bt
Review
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
= 1.73
a = 22.67 -1.73*4 = 15.75
a = Y - bX
P152 N6 Ch16
• Ŷ = a + bt
Review
= 1.73
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
a = 22.67 = 22.67
a = Y - bX
a = Y
Ŷ = 22.67 + 1.73t
• Ŷ = a + bt
Review
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
a = Y
Odd-numbered
Even-numbered
• Seasonal Variation
Understanding seasonal fluctuationshelp plan for sufficient goods and materials on hand to meet varying seasonal demand
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
• Seasonal Variation
Seasonal variations are fluctuations that coincide with certain seasons and are repeated year after year
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
• Seasonal Variation
Seasonal Index:
A number, usually expressed in percent, that expresses the relative valueof a season with respect to the average for the year(100%)
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
SalesforJuly are 14% belowan average month.
Sales for December are 26.8% above an average month.
• Seasonal Variation
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Sales Report: in \$ millions
2005
2006
2007
2008
2009
2010
• Seasonal Variation
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Step 1: Re-organize the data
2005
2006
2007
2008
2009
2010
• Seasonal Variation
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
6.7+4.6+10.0+12.7=34
/4=8.50
4.6+10.0+12.7+6.5=33.8
/4=8.45
Step 2: Moving Average
• Seasonal Variation
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Step 3: Centered Moving Average
• Seasonal Variation
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Step 4: SpecificSeasonal Index
• Seasonal Variation
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
10/8.475=1.180
12.7/8.45=1.503
6.5/8.425=0.772
Step 4: Specific Seasonal Index
• Seasonal Variation
2005
2006
2007
2008
2009
2010
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
+ + + =
*(0.9978)
*(0.9978)
*(0.9978)
*(0.9978)
Step 5: TypicalQuarterly Index
• Seasonal Variation
Sales for the Winter are 23.5% below the typical quarter.
2005
2006
2007
2008
2009
2010
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Salesfor the Fall are 51.9% above the typicalquarter.
Step 6: Interpret
• Exercise
Appliance Center sells a variety of electronic equipment and home appliances. For the last four years the following quarterly sales (in \$ millions) were reported.
Determine a typical seasonal index for each of the four quarters.
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
P161 No.10 Ch16
• Exercise
Step 1: Reorganize the data
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Step 2: Moving Average
Step 3: Centered Moving Average
Step 4: Specific Seasonal Index
P161 No.10 Ch16
• Step 5: Reorganize the data
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Step 6: Calculate the mean for each quarter
Step 8: Divide 4 by Total of four means to get Correction Factor
Step 7: Sum up the four means
Step 9: Mean * Correction Factor
P161 No.10 Ch16
• DeseasonalizingData
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to develop seasonally adjusted forecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
To remove the seasonal fluctuations so that the trend and cycle can be studied.
Ŷ = a + bt
Ŷ = a + bX
• 76.5
57.5
114.1
151.9
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
/ 0.765
= 8.759
/ 0.575
= 8.004
/ 1.141
= 8.761
/ 1.519
= 8.361
/ 0.765
/ 0.575
/ 1.141
/ 1.519
/ 0.765
/ 0.575
/ 1.141
= 8.498
= 9.021
/ 1.519
= 8.004
= 8.700
= 8.586
= 9.112
= 8.953
= 9.283
• DeseasonalizingData
Ŷ = a + bt
Chapter 16: Time Series & Forecasting
76.5
57.5
114.1
151.9
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
Ŷ = 8.1096 + 0.0899 t
Sale increased at a rate of 0.0899 (\$ millions) per quarter.
Ŷ = 8.1096 + 0.0899 * 25
= 10.3571 \$ millions
10.3571*0.765 = 7.9232 \$ millions
• Home Assignment
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to develop seasonally adjusted forecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
1. Calculate the seasonal indices for each quarter, express them as a ratio and not as a %. You may round to 4 dec. places.
Wed, 06, 12:00 a.m. 2011
Pigeon hole Ning Ding
2. Interpret the seasonal index quarter II.
3. Deseasonalized the original revenue for 2008 quarter I.
4. For 2011 quarter II the forecasted revenue from the trend line was 55. Calculate the seasonalized revenue for 2011 quarter II.
• What we have learnt?
• Review
• Chapter 16:
• Use a trend equation to forecast future time periods
• Use a trend equation to developseasonallyadjustedforecasts
• Determine and interpret a set of seasonal indexes
• Desearsonalize data using a seasonal index
• Step 7: Sum up the four means
Step 1: Reorganize the data
Step 8: Divide 4 by Total of four means to get Correction Factor
Step 2: Moving Average
Step 3: Centered Moving Average
Step 9: Mean * Correction Factor
Step 4: Specific Seasonal Index
Step 5: Reorganize the data
Step 6: Calculate the mean for each quarter
Hint