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Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error 1 F t +1 = F t + a ( Y t – F t ) Y t – F t = e t

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Page 1: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Review

Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2What is α called?

We are weighting the error associated with each time period by α1

Ft+1 = Ft + a(Yt – Ft)

Yt – Ft = et

Page 2: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Review

2

weekActual Sales

(# of units) Yt

Forecast Sales Ft

1 172 213 194 235 186 16

Page 3: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Review

Solve F2, F3, … F7 and e2, e3, … e6

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Page 4: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

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Page 5: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

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Use data table from Quiz #4 to forecast sales using simple linear regressionWe are using ONLY a time variable to

predict sales here!Predict future sales based on correlation

between time (X, independent variable) and sales (Y, dependent variable)

5

Tt = b0 + b1t

Page 6: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

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Regression StatisticsMultiple R 0.205R Square 0.042Adjusted R Square -0.197Standard Error 2.854Observations 6

ANOVAdf SS MS F

Regression 1 1.429 1.429 0.175Residual 4 32.571 8.143Total 5 34

Coefficients Standard Error t Stat P-valueIntercept 20 2.657 7.529 0.002week -0.286 0.682 -0.419 0.697

Page 7: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

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Calculate MSE for the forecast, and calculate T7

7

Page 8: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

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Page 9: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Review

9

weekActual Sales

(# of units) Yt

Forecast Sales Ft

1 172 213 194 235 186 16

Page 10: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

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10

Page 11: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern no trend

11

Year Quarter Sales1 1 1251 2 1531 3 1061 4 882 1 1182 2 1612 3 1332 4 1023 1 1383 2 1443 3 1133 4 804 1 1094 2 1374 3 1254 4 1095 1 1305 2 1655 3 1285 4 96

0

20

40

60

80

100

120

140

160

180

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Um

brel

la S

ales

Time Period

Ubrella Sales

Year 1 Year 2 Year 3 Year 4 Year 5

Page 12: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern no trend

We are saying that umbrella sales are driven by seasonal variability with NO increasing or decreasing trend over time

Every year: 1st and 3rd quarters have moderate sales 2nd quarter has highest sales 4th quarter has lowest sales

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Page 13: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern no trend

If we are using a linear trend to forecast (simple linear regression), we can introduce “season” as a independent categorical variables (X’s)

In statistics, a categorical variable is a variable that can take on a very limited, fixed number of possible values

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Page 14: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern no trend

If k = the # of categories, you will need k – 1 dummy variables

Since there are four seasons (4 categories), we need three dummy variables Qtr1 = 1 if Quarter 1, 0 otherwiseQtr2 = 1 if Quarter 2, 0 otherwiseQtr3 = 1 if Quarter 3, 0 otherwise

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Page 15: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern no trend

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Year t Quarter Yt Q1 Q2 Q31 1 1 125 1 0 01 2 2 153 0 1 0 Regression Statistics1 3 3 106 0 0 11 4 4 88 0 0 02 5 1 118 1 0 02 6 2 161 0 1 02 7 3 133 0 0 12 8 4 102 0 0 03 9 1 138 1 0 03 10 2 144 0 1 03 11 3 113 0 0 13 12 4 80 0 0 04 13 1 109 1 0 04 14 2 137 0 1 04 15 3 125 0 0 14 16 4 109 0 0 05 17 1 130 1 0 05 18 2 165 0 1 05 19 3 128 0 0 15 20 4 96 0 0 0

Yt is the dependent variableQ1, Q2, Q3 are the independent, predictor variables

Dummy or categoricalvariables for seasonal Effects

Q1 = 1 if quarter = 1,otherwise Q1 = 0

Q2 = 1 if quarter = 2,otherwise Q2 = 0

Q3 = 1 if quarter = 3,otherwise Q3 = 0

Q4 = 0

Page 16: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern no trend

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Regression StatisticsMultiple R 0.894R Square 0.799Adjusted R Square 0.761Standard Error 11.325Observations 20

ANOVAdf

Regression 3Residual 16Total 19

CoefficientsIntercept 95Q1 29Q2 57Q3 26

Page 17: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern no trend

What is our model?

17

Page 18: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern no trend

Predict sales in each quarter of year 6 using the model

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Page 19: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern with trend

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0

500

1000

1500

2000

2500

3000

0 1 2 3 4 5 6 7 8 9 10 11 12 13

SalesYear Season Tie Sales

1 1 18562 20123 985

2 1 19952 21683 1072

3 1 22412 23063 1105

4 1 22802 24083 1120

Page 20: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern with trend

We are saying that tie sales are driven by seasonal variability and that there is an increasing trend in sales over time

Every year: Sales are lowest – by far – in 3rd season Sales are highest in 1st season

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Page 21: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern with trend

3 seasons or 3 categories ( k = 3) require the use of 2 dummy variables (k – 1)Seas1t = 1 if Season 1 in time period t, 0

otherwiseSeas2t = 1 if Season 2 in time period t, 0

otherwise We will also need a time variable to address

the trend over time

21

Page 22: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern with trend

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Year Season Sales S1 S2 Time1 1 1856 1 0 1

2 2012 0 1 23 985 0 0 3

2 1 1995 1 0 42 2168 0 1 53 1072 0 0 6

3 1 2241 1 0 72 2306 0 1 83 1105 0 0 9

4 1 2280 1 0 102 2408 0 1 113 1120 0 0 12

Dummy or categoricalvariables for seasonal Effects

S1 = 1 if season = 1,otherwise S1 = 0

S2 = 1 if season = 2,otherwise S2 = 0

Time period variable

Page 23: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern with trend

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Regression StatisticsMultiple R 0.994R Square 0.987Adjusted R Square 0.983Standard Error 73.086Observations 12

ANOVAdf

Regression 3Residual 8Total 11

CoefficientsIntercept 797S1 1095.433S2 1189.467Time 36.467

Page 24: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern no trend

What is our model?

24

Page 25: Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with

Seasonal pattern no trend

Predict sales in each season of year 5 using the model

25


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