Wk5 LecNotes Regression and Forecasting(1)

7/28/2019 Wk5 LecNotes Regression and Forecasting(1)

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Regression and Forecasting

Prof Narayan Janakiraman


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Forecasting Techniques

Markets

Products

Existing

Existing

New

New

Time Series AnalysisRegression Analysis

Delphi Technique

Diffusion ModelsCustomer Survey

Sales Force Composite


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For existing companies the need is to determinehow much of the current product they are likely to

sell..

Markets

Products

Existing

Existing


New

New


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Time Series

Simplest Method is EXTRAPOLATION

Time

Volume

of Sales

PresentPast Future


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Typical Time Series Data

Set of evenly spaced numerical data Obtained by observing response

variable at regular time periods

Forecast based only on past values Assumes that factors influencing

past and present will continueinfluence in future

Year Sales

1996 37

1997 40

1998 41

1999 372000 45

2001 50

2002 43

2003 47

2004 56

2005 52

2006 55

2007 54

2008


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What would a plot of the data tell you?

Year Sales

1996 37

1997 40

1998 411999 37

2000 45

2001 50

2002 43

2003 472004 56

2005 52

2006 55

2007 54

2008

Chart Title


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Plot data and connect the dots

Year Sales

1996 37

1997 40

1998 41

1999 37

2000 45

2001 50

2002 43

2003 472004 56

2005 52

2006 55

2007 54

2008

Chart Title


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Lets try moving averages, lag functions

Chart TitleYear Sales 3 year

1996 37

1997 40

1998 41 39.331999 37 39.33

2000 45 41.00

2001 50 44.00

2002 43 46.00

2003 47 46.672004 56 48.67

2005 52 51.67

2006 55 54.3

2007 54 53.7

2008


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Weighted Average

Weighted Avg'Period Year Sales

1 1996 372 1997 40

3 1998 41 39.9

4 1999 37 38.8

5 2000 45 41.8

6 2001 50 45.9

7 2002 43 45.5

8 2003 47 46.4

9 2004 56 50.7

10 2005 52 52.2

11 2006 55 54.3

12 2007 54 53.9

13 2008

Moving Average weights all previousdata equally

What would happen if you differentiallyweighted the data?

t-1 0.5

t-2 0.3

t-3 0.2


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Exponential Smoothing

Sophisticated weighted average

Forecast =

last period forecast + alpha * (last perioddemand - last period's forecast)

ExpSmoothYear Sales

1996 37 37

1997 40 37.01998 41 39.7

1999 37 40.9

2000 45 37.4

2001 50 44.2

2002 43 49.4

2003 47 43.6

2004 56 46.7

2005 52 55.1

2006 55 52.3

2007 54 54.7

2008 54.1


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Exponential Smoothing Tool

The image part with relationship ID rId3 was not found in the file.

Single-parameter exponential smoothing is easy with Excels ToolPak.

Click on Tools on the menu bar, select the Data Analysis option, and then

in the Data Analysis dialog box, click on Exponential Smoothing.


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Single-ParameterExponential Smoothing (Figure 7-4 )

The image part with relationship ID rId3 was not found in the file.

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A B C D E F

= 0.2

Period Actual Forecast

Month t Sales, Yt Sales, Ft

January 2000 1 4,890

February 2 4,910 4890.0

March 3 4,970 4894.0

April 4 5,010 4909.2

May 5 5,060 4929.4

June 6 5,100 4955.5July 7 5,050 4984.4

August 8 5,170 4997.5

September 9 5,180 5032.0

October 10 5,240 5061.6

November 11 5,220 5097.3

December 12 5,280 5121.8

January 2001 13 5,330 5153.5

February 14 5,380 5188.8

March 15 5,440 5227.0

April 16 5,460 5269.6May 17 5,520 5307.7

June 18 5,490 5350.2

July 19 5,550 5378.1

August 20 5,600 5412.5

September 21 5450.0

MSE = 24,254

Forecast of Blitz Beer Sales by Single-Parameter Smoothing

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D

=SUMXMY2(D7:D25,E7:E25)/COUNT(E7:E25)

1. Enter the

smoothingconstant in D2.

2. Enterproblem

information inrange. NoticeD26 does not

have a valuebecause it is to

be forecast.

3. Click on Tool,Data Analysis,

and the

ExponentialSmoothing to

get theExponentialSmoothingdialog boxshown next.


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Exponential Smoothing DialogBox

1. In the InputRange line enterthe range of thedata. The result

shown is $D$6:$D$25

2. Enter theDamping factor.

It is 1 - .

3. In the OutputRange enter thelocation of the

results.

4. Click the OK button to get the

results shown previously in Figure 7-4.


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Forecast usingRegression Models

Regression

Models

LinearNon-

Linear

2+ ExplanatoryVariables

Simple

Non-Linear

Multiple

Linear

1 ExplanatoryVariable


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Linear Regression

( )( )

=

XXX

YXXYb

2

Identifydependent (y) andindependent (x) variables

Develop your equation for thetrend line

Y = a + bX


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Interpretation of Coefficients

Slope (b) Estimated Ychanges by b for each 1 unit increase in X Ifb = 2, then sales (Y) is expected to increase by 2 for each 1 unit increase in

advertising (X)

Y-intercept (a) Average value ofYwhen X= 0 Ifa = 4, then average sales (Y) is expected to be 4 when advertising (X) is 0

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Y = a+ bX


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Regression is to understandrelationships

b< 0b > 0Y

X

Y

X

E(Y) = a + bXi


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A maker of golf shirts has been tracking sales andadvertising dollars.

Predict sales for $53,000 advertising

Y = 92.9 +1.15X

Sales $ (Y) Adv.$(X)

1 130 32

2 151 52

3 150 50

4 158 55

5 ? 53

Y5 = 92.9+1.15 53( ) =153.85


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Regression

Regression is easy with Excels Regression Tool. Click on

Tools on the menu bar, select the Data Analysis option, and

then in the Data Analysis dialog box select Regression. This

yields the Regression dialog box shown next.

3 Click on the1 In the Input Y


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Regression Dialog Box

3. Click on theOK button to getthe Regression

Summary Outputshown next.

2. In the Input XRange line enterthe range of the

X data. The

result hereshown is $B

$7:$B$16

1. In the Input YRange line enter therange of the Y data.

The result shownhere is $C$7:$C$16


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Excels Regression Tool

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A B C D E F G

Fitting Trend Line to BriDent Toothpaste Sales Using Regression

Year in Unit

Transformed Sales

Units (thousands)

Year X Y

1992 0 72.9

1993 1 74.4

1994 2 75.9

1995 3 77.91996 4 78.6

1997 5 79.1

1998 6 81.7

1999 7 84.4

2000 8 85.9

2001 9 84.8

SUMMARY OUTPUT

Regression Statist ics

Multiple R 0.98

R Square 0.96

Adjusted R Square 0.96

Standard Er ror 0.90

Observat ions 10

ANOVA

df SS MS F Significance F Regression 1 177.47 177.47 219.86 0.00

Resi dual 8 6.46 0.81

Total 9 183.92

Coeff ic ients Standard Er ror t Stat

Inter cept 72.96 0.53 138.17

X 1.47 0.10 14.83

The slope and intercept are read from E15:E16 and yield the

regression equation below. The multiple R, R squared, adjusted R,

standard error, and F and t statistics are shown also.

XY 47.196..72 +=


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What if you had data like this?

Y

X1


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Second-Order Model

E(Y) = a + bX1i+ cX

1i

2

Linear

effect

Curvilinear

effect


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Second-Order Model Worksheet

Case, i Yi X1i X1i2

1 1 1 1

2 4 8 643 1 3 9

4 3 5 25

: : : :

Create X12 column.

Run regression with Y,X1,X12.


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Non Linear Regression

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Multiple Regression Example: Toy Manufacturer Sales Hypothesis How is weekly toy sales affected by

changes in levels of advertising, the use of sales reps vs. agents for calling on retailers, and local school enrollments?

Toy Sales = Advertising(X1)+ sales rep/agent(X2)+ school enrollment(X3) + eTo do this, we need to dummy code: sales rep = 1 or agent = 0.

Y = 102.18 + 3.87X1 + 115.2X2 + 6.73X3

So what does this mean?


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Multiple Regression

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A B C D E F G

Monthly

Monthly Floorspace Advertising

Sales (square feet) Expenditure

Store Y X1 X2

1 20,100 3,050 350

2 14,900 1,300 980

3 16,800 1,890 830

4 9,100 1,750 760

5 15,500 1,010 930

6 26,700 2,690 7707 34,600 4,210 440

8 7,200 1,950 570

9 21,800 2,830 310

10 23,400 2,030 920

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.89332611

R Square 0.798031538

Adjusted R Sq 0.740326264

Standard Error 4168.371133Observations 10

ANOVA

df SS MS F Significance F

Regression 2 480581774.7 240290887.3 13.8294383 0.003702478

Residual 7 121627225.3 17375317.9

Total 9 602209000

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept -22979 10546.50 -2.18 0.07 -47917.10 1959.87

X1 11.42 2.29 4.98 0.00 5.99 16.84X2 23.41 8.64 2.71 0.03 2.99 43.84

Multiple Regression for the Deuce Hardware Store Excelsregression toolcan be used to

do multipleregression. Just

list ALL the X

variables whendesignating theInput X Range;C7:D16 in this

example.

21 41.2342.11979,22 XXY ++

=


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Forecasting29Advanced Marketing BiMBA 2006

Model-based forecasting methods

Regression with other factors Sales = a intercept + b (advertising) + c (price) Develop model on half of past data Test model on other half of data


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PROS AND CONS?

Markets

Products

Existing

Existing


New

New

Documents

Wk5 LecNotes Regression and Forecasting(1)