2. Associative Forecasting
Associative models assume that there is a causational relationship between the variable of interest and other variables called predictors
Price of beef and price of chicken
Crop yields and soil condition
Crop yields & timing of water
Profits and sales
Price of products and energy cost
Predictor variables - used to predict values of variable of interest
Regression - technique for fitting a line to a set of points
Regression Methods - Regression (or causal ) methods that attempt to develop a mathematical relationship between the item being forecast and factors that cause it to behave the way it does.
13 October 2020
Dr. Abdulfatah Salem

3. Simple Linear Regression
Forecasting
Simple Linear Regression
The simplest and most widely used form of regression involves a linear relationship between two variables.
The objective in linear regression is to obtain an equation of a straight line that minimizes the sum of squared vertical deviations of data points from the line (i.e., the least squares criterion)
This least squares line has the form:
y = a + bx
Where:
Y = predicted (dependent or response) variable
X = predictor (independent or explanatory) variable
a = intercept
b = slope (change rate)
13 October 2020
Dr. Abdulfatah Salem

4. Forecasting Conditions required for predictor to be valid
The relationship between movements of an indicator and movements of the variable should have a logical explanation.
Movements of the indicator must precede movements of the dependent variable by enough time so that the forecast isn’t outdated before it can be acted upon.
A fairly high correlation ( r ) should exist between the two variables.
Correlation factor r is a measure of the strength and direction of relationship between two variables
Correlation r close to zero indicate weak linear relationship between two variables
Correlation r close to +1 indicate strength linear relationship between two variables (directly change)
Correlation r close to -1 indicate strength linear relationship between two variables (inversely change)
13 October 2020
Dr. Abdulfatah Salem

5. Simple Linear Regression
Forecasting
Simple Linear Regression
Assumptions
For best results
Variations around the line are random
Deviations around the line normally distributed
Predictions are being made only within the range of observed values
Always plot the data to verify linearity
Check for data being time-dependent
Small correlation may imply that other variables are important
13 October 2020
Dr. Abdulfatah Salem

6. Forecasting
Ex.
Carrefour has a chain of 10 stores in Egypt. Sales figures and profiles for the stores are giving in the following table. Obtain a regression for the data, and predict profit for a store assuming sales of 30 million.
13 October 2020
Dr. Abdulfatah Salem

7. Forecasting
Sol.
13 October 2020
Dr. Abdulfatah Salem

8. Forecasting
13 October 2020
Dr. Abdulfatah Salem

9. Forecasting
Ex.
The following table shows the profits (in EGP) resulting from the weekly sales (in tons) of candy in a confectionery factory in Tanta city.
Discuss the possibility of forecasting profits using sales
Build a forecasting model
Forecast the weekly profit resulting from sales of 60 tons
13 October 2020
Dr. Abdulfatah Salem

10. Forecasting Sol. 13 October 2020
If sales is 10.3 then profit will be =
13 October 2020
Dr. Abdulfatah Salem

11. Forecasting
Ex.
A multi-hospital system (MHS) owns 12 hospitals. Revenues and profits for each hospital are given below.
All figures are in millions of dollars.
Predict profits for a hospital with $10 million in revenues.
Hospital 1 2 3 4 5 6 7 8 9 10 11 12
Revenue 14 15 16 20
Profit
0.15
0.1
0.13
0.25
0.27
0.24
0.2
0.44
0.34
0.17
13 October 2020
Dr. Abdulfatah Salem

12. Forecasting
Sol.
Profit
Revenue
13 October 2020
Dr. Abdulfatah Salem

13. Multi Hospital System Revenues and Profits Data
Forecasting
Cont
Multi Hospital System Revenues and Profits Data
Hospital
Revenue (x)
Profit (y)
x*y x2 1 7
0.15
1.05 49 2
0.10
0.2 4 3 6
0.13
0.78 36
0.6 16 5 14
0.25
3.5
196 15
0.27
4.05
225
0.24
3.84
256 8 12
0.20
2.4
144 9
3.78 10 20
0.44
8.8
400 11
0.34
5.1
0.17
1.19
Total
132
2.71
35.29
1796
13 October 2020
Dr. Abdulfatah Salem

14. Forecasting
Cont
y = x.
To predict the profits for a hospital with $10 million in revenue,
simply plug 10 in as the value of x in the regression equation:
Profit = (10) =
Multiplying this value by one million,
the profit level with $10 million in revenue is found to be $209,903.
13 October 2020
Dr. Abdulfatah Salem

15. Forecasting Ex. 13 October 2020 Dr. Abdulfatah Salem
Sales of new houses and three-month lagged unemployment are shown in the following table.
Determine if unemployment levels can be used to predict demand for new houses.
If so, derive a predictive equation.
period
units sold
Unemp.
rate 1 20
7.2 2 41 4 3 17
7.3 35
5.5 5 25
6.8 6 31 7 38
5.4 8 50
3.6 9 15
8.4 10 19 11 14
13 October 2020
Dr. Abdulfatah Salem

16. Forecasting
r = − 0.97
b =
a = 71.85
(Unit sold) = *(Unemp. rate)
13 October 2020
Dr. Abdulfatah Salem

17. Forecasting Seasonality Def. Ex.
Seasonality is a characteristic of a time series in which the data experiences regular and predictable changes that recur every fixed interval of time. Any predictable change or pattern in a time series that recurs or repeats over a one-time period can be said to be seasonal.
Ex.
If you live in a climate with cold winters and warm summers, your home's heating costs probably rise in the winter and fall in the summer. You reasonably expect the seasonality of your heating costs to recur every year.
10/13/2020
Dr. Abdulfatah Salem

18. Forecasting
Seasonality
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Dr. Abdulfatah Salem

19. Forecasting
Seasonality
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Dr. Abdulfatah Salem

20. Forecasting
Seasonality
10/13/2020
Dr. Abdulfatah Salem

21. Forecasting Seasonality 10/13/2020 Dr. Abdulfatah Salem Seasonality
Repetition at Fixed Intervals
Seasonal variations
Regularly repeating movements in series values that can be tied to recurring events.
It is applied to annually, monthly, weekly, daily and other regularly recurring patterns in data.
Seasonality is
The amount that the actual values deviate from the average value of a series.
Seasonal relative
Percentage of average or trend
Centered moving average
A moving average positioned at the center of the data that were used to compute it.
10/13/2020
Dr. Abdulfatah Salem

22. FORECASTING METHODS FOR SEASONAL SERIES
House Cleaning Services Company needs a quarterly forecast of the number of customers expected next year. The business is seasonal, with a peak in the third quarter and a trough in the first quarter.
Forecast customer demand for each quarter of year 5, based on an estimate of total year 5 demand of 2,600 customers.
10/13/2020
Dr. Abdulfatah Salem

23. Forecasting Multiplicative Seasonal Influences 10/13/2020
A seasonal influence is multiplicative if the quarterly demand forecast of a quarter
= Projected average quarterly demand  Average seasonal index of that quarter.
Quarter Year Year Year Year 4
1 45/250 = /300 = /450 = /550 = 0.18
2 335/250 = /300 = /450 = /550 = 1.32
3 520/250 = /300 = /450 = /550 = 2.11
4 100/250 = /300 = /450 = /550 = 0.39
10/13/2020
Dr. Abdulfatah Salem

24. Additive Seasonal Influences
Forecasting
Additive Seasonal Influences
A seasonal influence is additive if the quarterly demand forecast of a quarter
= projected average quarterly demand + average seasonal index of that quarter.
Quarter Year Year Year Year 4
= = = = -450
= = = = 175
= = = = 610
= = = = -335
10/13/2020
Dr. Abdulfatah Salem

25. Techniques for Seasonality
Forecasting
Techniques for Seasonality
Step 1:
Find average seasonal demand for each period.
Step 2: Compute Seasonal Index (SI) for each season for each period.
Step 3: Calculate the average SI for each season.
Step 4: Calculate the average seasonal demand for next period.
Step 5: Forecast demand for each seasons of next period.
10/13/2020
Dr. Abdulfatah Salem

26. Forecasting
Quarterly demand for last four years is given in the table below.
use a 5-step process to forecast.
Ex.
Quarter
Year 1
Year 2
Year 3
Year 4
Fall
2530
2690
2790
2860
Winter
2300
2420
2410
2600
Spring
1900
2000
2105
2175
Summer
1510
1775
1875
1945
10/13/2020
Dr. Abdulfatah Salem

27. Forecasting
Sol.
Step 1: Find average quarterly demand for each quarter.
Quarter
Year 1
Year 2
Year 3
Year 4
Fall
2530
2690
2790
2860
Winter
2300
2420
2410
2600
Spring
1900
2000
2105
2175
Summer
1510
1775
1875
1945
Average
2060
2221
2295
2395
Formula
= ( )/4)
= 2060
= ( )/4)
= 2221
= ( )/4)
= 2295
= ( )/4)
= 2395
10/13/2020
Dr. Abdulfatah Salem

28. Forecasting
Step 2: Compute Seasonal Index (SI) for each quarter for each year.
Quarter
Year 1
Year 2
Year 3
Year 4
Value
Si1
Si2
Si3
Si4
Fall
2530
1.228
2690
1.211
2790
1.216
2860
1.194
Winter
2300
1.117
2420
1.090
2410
1.050
2600
1.086
Spring
1900
0.922
2000
0.900
2105
0.917
2175
0.908
Summer
1510
0.733
1775
0.799
1875
0.817
1945
0.812
10/13/2020
Dr. Abdulfatah Salem

29. Forecasting Step 3: Calculate the average SI for each quarter.
Fall
1.228
1.211
1.216
1.194
Winter
1.117
1.090
1.050
1.086
Spring
0.922
0.900
0.917
0.908
Summer
0.733
0.799
0.817
0.812
Average Si
1.212
1.086
0.912
0.790
10/13/2020
Dr. Abdulfatah Salem

30. Forecasting
Step 4: Calculate the average quarterly demand for next year.
First, the yearly demand has to be estimated or calculated for next year using one of the forecasting techniques.
Year 1
Year 2
Year 3
Year 4
2060
2221
2295
2395
Year 5
2500
Year 1
Year 2
Year 3
Year 4
Year 5
10/13/2020
Dr. Abdulfatah Salem

31. Forecasting
Step 5: Forecast demand for the four quarters of next year.  
Multiply the average demand by the SI for each quarter.
Quarter
Fall
Winter
Spring
Summer
Average Si
1.212
1.086
0.912
0.790
Formula
2500x1.212
2500x1.086
2500x0.912
2500x0.790
Year 5
3030
2715
2280
1975
10/13/2020
Dr. Abdulfatah Salem

32. Forecasting
Ex.
A furniture manufacturer wants to predict quarterly demand for certain seats for periods 15 and 16, which happen to be the second and the third quarters for a particular year. The series consists of both trend and seasonality. The trend portion of the demand is projected using the trend equation Ft = t. Quarter relatives are Q1 = 1.2 , Q2 = 1.1, Q3 = 0.75 and Q4 = use this information to predict demand for periods 15 and 16.
Sol.
The trend values at t = 15 and t = 16 are:
F15 = (15) = 236.5
F16 = (16) =
Multiplying the trend value by the appropriate quarter relatives yield a forecast that includes both trend and seasonality.
Given that t = 15 is a second quarter and t = 16 is a third quarter,
The forecast will be:
Period 15: (1.1) =
Period 16: (0.75) =
10/13/2020
Dr. Abdulfatah Salem

33. Forecasting 10/13/2020 Dr. Abdulfatah Salem
Ex.
The manager of a parking lot has computed daily relatives for the number of cars per day in the lot. The computations are repeated here (about three weeks are shown for illustration). A seven period centered moving average is used because there are seven days (seasons) per week
Sol.
10/13/2020
Dr. Abdulfatah Salem

34. Forecasting The estimated relatives will be:
Monday: ( )/2 = .745
Tuesday: ( )/2 = .865
Wednesday: ( )/2 = 1.045
Thursday: ( )/2 = 1.195
Friday: ( )/3 = 1.36
Saturday: ( )/2 = 1.24
Sunday: ( )/2 = 0.535
Note
The sum of the relatives must equal the number of periods (i.e., 7 in this example). If it is not, you have to multiply by a correction factor. In this example the sum is 6.985, therefore you have to multiply each factor by (7/6.985)
13 October 2020
Dr. Abdulfatah Salem

35. Forecasting Performance
(How good is the forecast?)
13 October 2020
Dr. Abdulfatah Salem

36. Forecasting
Ex.
The following table shows the actual sales of upholstered chairs for a furniture manufacturer and the forecasts made for each of the last eight months. Calculate MFE, MSE, MAD, and MAPE for this product.
13 October 2020
Dr. Abdulfatah Salem

37. Forecasting
Sol.
13 October 2020
Dr. Abdulfatah Salem

38. Forecasting Ex. Use The Following Methods To Calculate The
Forecast Values for the shown table:
1-period Moving Average
3-period Weighted Moving Average
( W1 = W2 = 0.2 W3 = 0.1 )
Exponential Smoothing ( α = 0.1 )
Then measure the performance for each method
and compare the result
13 October 2020
Dr. Abdulfatah Salem

39. Forecasting
Ex.
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Dr. Abdulfatah Salem

40. Forecasting
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Dr. Abdulfatah Salem

41. Forecasting model selection
13 October 2020
Dr. Abdulfatah Salem