forecasting

1. Ch 3: Forecasting:
Techniques and Routes
Introduction
Forecasting is the establishment of future
expectations by the analysis of past data,
or the formation of opinions.
Forecasting is an essential element of
capital budgeting.
Capital budgeting requires the commitment
of significant funds today in the hope of long
term benefits. The role of forecasting is the
estimation of these benefits. 1

2. Forecasting Techniques and
Routes
Techniqu Routes
es
Top-down
Qualitative route
Quantitativ Bottom-up
e route
Delphi method
Simple Nominal group
regressions technique
Multiple Jury of executive
regressions opinion
Time trends Scenario projection
Moving averages
2

3. Quantitative Forecasting
Quantitative: Regression with related
variable
Data set of ‘Sales’ as related to both time
and the number of households.
HISTORICAL DATA
YEAR HOUSEHOLDS SALES
1991 815 2109
1992 927 2530
1993 1020 2287
1994 987 3194
1995 1213 3785
1996 1149 3372
1997 1027 3698
1998 1324 3908
1999 1400 3725
2000 1295 4129
2001 1348 4532
2002 1422 4487 3

4. Quantitative Forecasting
Quantitative: Sales plotted related to households.
SalesUnits Related to Number of
Households
5000
Sales Units
4000
3000
Sales
2000
1000
0
0 500 1000 1500
Numbe r of Households
4

5. Quantitative Forecasting
Quantitative: Sales regressed on households.
SUMMARY OUTPUT SALES REGRESSED AS A FUNCTION
Edited output OF HOUSEHOLDS
from the Excel regression.
Regression Statistics
Multiple R 0.824389811
R Square 0.67961856
Adjusted R Square 0.644020623 <== "Strength" of the regression
Standard Error 429.2094572
Observations 11
Coefficients Standard Error t Stat P-value
Y Axis Intercept -348.218 913.798 -0.381 0.712
Number of Households 3.316 0.759 4.369 0.002
5

6. Quantitative Forecasting
Quantitative: Sales regressed on households.
Predicting with the regression output.
Regression equation is:
Sales(for year) = -348.218 + ( 3.316 x households).
Assuming that a separate data set forecasts
the number of households at 1795 for the year
2006, then:
Sales(year 2006) = -348.218 + ( 3.316 x 1795)
= 5,604 units.
6

7. Quantitative Forecasting
Quantitative: Multiple Regression
Sales as a function of both time and
the number of households.
HISTORICAL DATA
YEAR HOUSEHOLDS SALES
1991 815 2109
1992 927 2530
1993 1020 2287
1994 987 3194
1995 1213 3785
1996 1149 3372
1997 1027 3698
1998 1324 3908
1999 1400 3725
2000 1295 4129
2001 1348 4532
2002 1422 4487 7

8. Quantitative Forecasting:
Multiple Regression Line Information
From the Excel spreadsheet.
SUMMARY OUTPUT MULTIPLE REGRESSION:
SALES ON YEARS and HOUSEHOLDS
Regression Statistics
Multiple R 0.9216
R Square 0.8494
Adjusted R Square 0.8118 <== "Strength" of regression.
Standard Error 312.1217
Observations 11
Coefficients Standard Error t Stat P-value Lower 95%
Y Axis Intercept -382643.9164 127299.584 -3.006 0.017 -676197.474
Calendar Year 193.3326 64.376 3.003 0.017 44.880
Households 0.1368 1.194 0.115 0.912 -2.616
8

9. Quantitative Forecasting:
Using Multiple Regression
Multiple regression equation is:
Sales in year = -382643.91 +(193.33 x Year)
+ (0.1368 x
Households) sales for the year 2005 is:
Forecast of
Sales in year 2005 = -382643.91 + (193.33 x 2005)
+ (0.1368 x 1586)
= 5200 Units
(Note: the sales forecast relies upon a separate
forecast of the number of households, given as 1 586,
for 2005.) 9

10. Quantitative Forecasting
Quantitative: Time Series Regression
Sales plotted as a function of time.
Plot of Past Sales Units By Year
5000
4000
Sales Units
3000
Sales
2000
1000
0
1990 1995 2000 2005
Year
10

11. Quantitative Forecasting:
Fitted Regression Line
Sales Regression: Line Fit Plot
5000
4000
Actual
3000
Sales
2000
Predicted
1000
0
1990 1995 2000 2005
Year
11

12. Quantitative Forecasting:
Regression Line Information
From the Excel spreadsheet.
EDITED SUMMARY OUTPUT REGRESSION OF SALES ON YEARS
Regression Statistics
Multiple R 0.9215
R Square 0.8492
Adjusted R Square 0.8324 <== "Strength" of regression.
Standard Error 294.5125
Observations 11
Coefficients Standard Error t Stat P-value
Y axis intercept -395541.56 56077.1544 -7.0535 0.0001
Slope of line 199.87 28.0807 7.1178 0.0001
12

13. Quantitative Forecasting:
Regression Line Use
Equation for the regression line is:
Sales in year = -395541.56 + (199.87 x Year)
Forecast of sales for the year 2005 is:
Sales in 2005 = -395541.56 + (199.87 x 2005)
= 5198 Units
(Note: the large negative Y axis intercept results
from using the actual calendar years as the X axis
scale.)
13

14. Quantitative Forecasting:
Regression: Auto Forecast by Excel.
Sales by Year, With Automatic Three
Year Prediction
6000
5000 SALES
4000
Sales
3000
Simple Linear
2000 Regression,
Forecast Out to
1000 Year 2005
0
1990 1995 2000 2005 2010
Year
14

15. Quantitative Forecasting:
Moving Average- Auto Plot
Sales Units Per Year With Fitted Two
Year Moving Average
5000
4000
Sales Units
SALES
3000
2000 2 per. Mov.
Avg.
1000 (SALES)
0
1990 1995 2000 2005
Years
15

16. Quantitative Forecasting:
Notes on Excel Auto Plot.
Excel will plot, and automatically forecast, a
data series which has a functional relationship.
For example, a regression trend line.
The auto plot is driven through the ‘Chart’
menu as ‘Add Trendline’. A particular forecast
is specified via the dialog box.
Future point data values cannot be read
from the automated trendline.
Non-functional relationships, such as a
moving average, can be plotted, but
cannot be automatically forecast.
16

17. Forecasting Routes
Top-Down
where international and national
events affect the future behaviour of
local variables.
17

18. Forecasting Routes
Where local events affect the future
behaviour of local variables.
Bottom-Up
18

19. Forecasting: Summary
 Sophisticated forecasting is essential for
capital budgeting decisions
 Quantitative forecasting uses historical
data to establish relationships and trends
which can be projected into the future
 Qualitative forecasting uses experience
and judgment to establish future
behaviours
 Forecasts can be made by either the‘top
down’ or ‘bottom up’ routes.
Back to the Future! 19