Forecasting

Handy Notes on
Forecasting
Compiled & Prepared By
SOMASHEKAR S M

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Contents:
 Introduction to forecasting
 Steps in forecasting process
 Approaches to forecasting
 Forecasts based on judgment and opinion
 Analysis of time series data
 Accuracy and control of forecasts
 Choosing a forecasting technique
 Elements of Good forecast
Introduction to “Forecasting”
One of the steps, nay the very first one, in the process of management is planning. “Planning is
understood as the process of setting goals and choosing the means to achieve these goals.” Planning is essential for,
without it, managers cannot organize people and resources effectively. In any business planning is done
based on the estimation of future events.
Forecasting is fundamental to planning. Forecasts are statements about future, specifying the volume
of sales to be achieved and equipment, materials and other inputs needed to realize the expected sales.
Forecasting is different from “prediction”. While forecasting is systematic and scientific projection of the
future event, prediction is a subjective estimation of the future event. Forecasting is done based on past data,
prediction is purely based on managers skill, experience and judgment.
Definition: A popular definition for forecasting is that, “It is estimating the future demand for products and
services and resources necessary to produce these outputs”
Need for forecasting:
Following are some of the reasons, why operation managers must develop forecasts
1. New facility planning: Strategic activities such as designing and building a new factory or designing and
implementing a new production process, might take a long time. This requires long range of forecasts of
demand for existing and production of new products.
2. Production planning: Rate of production keep varying to meet the fluctuating demand from time to time,
which demands several months of time period to change processes and capacities of production processes.
Intermediate range demand forecast, helps operating managers get the necessary lead time to provide the
capacity to produce the products to meet variable demands.
3. Work-force scheduling: According to varying demands for production and services, it is necessary to vary the
work force levels to meet the fluctuations by using overtime, lay-offs or hiring. For this, operation managers
need short-range demand forecasts to enable them have necessary lead time to provide work force to meet
the fluctuations.
4. Financial planning: Sales forecasts are the driving force in budgeting. Budgeting is used by many
operations managers to plan and control the financial performance of their production department.
Types of forecasts:
There are three types of forecasting:
i) Short term forecasting
COMPLIED & PREPARED BY

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ii) Intermediate forecasting
iii) Long term forecasting
Short term forecasting: It may be defined as forecasting done on relatively shorter period. The period may
be one moth to one year depending upon the nature of the product.
Purposes of short forecasting:
 Production policy: By knowing the future demand, the decision regarding production policy can be
taken so that there is no problem of over production and short supply of input materials.
 Material requirement planning (MRP): By knowing the future demand, the availability of right quantity
and quality of the material could be ensured.
 Purchase procedure: The purchase programme could be decided depending upon the material
requirements.
 Inventory control: Proper control of inventory could be ensured, so that inventory carrying cost is
minimum or optimum.
 Equipment requirement: The decision regarding procurement of new equipment is view of the capacity
and capability of the existing equipment can be taken.
 Human-power requirement: The decision regarding recruitment of extra labor on full time or part time
could be taken.
 Finance: The agreement of funds for purchase of raw materials, machines and parts could be made.
Intermediate range forecasting: Intermediate range covers three to five years; it is especially valuable in
formulating a capital expenditure programme and the related financial plan for research and product
development. Intermediate forecasts must consider the problem of cyclic fluctuation, if they are to be
meaningful.
Long range forecasting: Long range forecasts provide, operations mangers, with information to make
important decisions such as the following;
 Selecting a product design. The final design is dependent on expected sales volume.
 Selection a production processing scheme for a new product.
 Selecting a plan for the long range supply of scarce materials.
 Selecting a long range production capacity plan.
 Selecting a long range financial plan for acquiring funds for capital investment.
 To build a new buildings and to purchase new machines.
 To develop new sources of materials and new sources of capital funds.
Difference between planning and forecasting:
 Planning commits individuals to certain goals. It also calls for some activity to achieve the planned
goals. Forecasting does not commit individuals to any goals nor does it stimulate any activity among
them.
 Planning is done with the help of forecasting which provides assumptions about the future
environment of a plan. Forecasts made about the kind of markets, quality of sales, process, products,
technical developments, costs, wage rates, taxes, political and social environment and similar other
matters, become premises for the future. Forecasting is thus only a tool of planning.
Importance of forecasting in Operations Management
 Departments throughout the organization depend on forecasts to formulate and execute their plans.

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 Finance needs forecasts to project crash flows* and capital requirements.
 Human resources need forecasts to anticipate hiring needs.
 Production needs forecasts to plan production levels, workforce, material requirements, inventories,
etc.
 Manufacturers also forecast worker absenteeism, machine availability, material costs, transportation
and production lead times, etc.
 Besides demand, service providers are also interested in forecasts of population, of other
demographic variables, of weather, etc.
Project crashing* is a method for shortening the project duration by reducing the time of one (or more) of the critical
project activities to less than its normal activity time.
Limitations:
 Forecasts are always estimates, they rarely accurate and not realistic in practice.
 Usage of assumptions and guess work leads to the possibility of errors
 Forecast of new products are always difficult, in the absence of past data.
Applications of forecasting:
 Operations management: forecast of product sales; demand for services
 Marketing: forecast of sales response to advertisement procedures, new promotions etc.
 Finance & Risk management: forecast returns from investments
 Economics: forecast of major economic variables, e.g. GDP, population growth, unemployment
rates, inflation; useful for monetary & fiscal policy; budgeting plans & decisions
 Industrial Process Control: forecasts of the quality characteristics of a production process
 Demography: forecast of population; of demographic events (deaths, births, migration); useful for
policy planning
Steps in forecasting process

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Step 1: Determine purpose of forecast: Any forecast at first establish the variables which are to be forecast.
Variables could be either controllable or un-controllable (uncertainties). Controllable variables are those
which can be reasonably monitored at management level such as budgeting, inventory levels, etc, whereas
uncontrollable variables such as product demand, competition, raw material cost etc are not in hand of the
management.
Step-2: Time horizon: Forecasting can be made for different range of time periods and can be can be classified
as short term, intermediate term and long term forecasts. Forecast techniques can change with changes in
time horizon.
Step-3: Select a forecasting technique: There are essentially two types of forecasting techniques used in the field
of forecasting. They are,
 Qualitative technique (Used when situation is vague and little data exist New products, New
technology, includes people opinions, judgments and surveys)
 Quantitative technique (Used when situation is ‘stable’ and historical data exist. It involves
mathematical calculations)
Step-4: Gather and analyze data: One of the most difficult and time consuming part of forecasting is the
collection of valid and reliable data. Forecast can be no more accurate than the data on which it is based
Data can be collected from- primary source and secondary source. Four criteria can be applied to the
determination of whether the data will be useful-
 Data should be reliable and accurate
 Data should be relevant
 Data should be consistent
 Data should be timely
Sometimes accurate data may be available but only in certain historic periods.
Step-5: Prepare the forecast: Draw up the forecast of each product or service over the appropriate planning
period using any of the above technique. It may be wise to develop a range of possible forecast outcomes,
with the use of different scenarios.
Step-6: Monitor the forecast: Forecasts can be evaluated by comparing with actual historical values. Most
forecasts go wrong because it is futuristic. To monitor forecast accuracy it is necessary to use right forecast
models. To identify what adjustments are needed to the forecast models and to project expected deviation
from the planned forecast.
Approaches to forecasting
A large number of forecasting techniques are available to the operations manager these days. The
availability of computer programs has further eased the task of forecasting. In general, two fundamental
approaches are used in forecasting,
1. Subjective approach (Qualitative in nature and usually based on the judgment and opinions of people)
Subjective methods are those in which the processes used to analyze the data have not been well
specified. These methods are also called implicit, informal, clinical, experienced-based, intuitive methods,
guesstimates or gut feelings. They may be based on simple or complex processes; they may use objective
data or subjective data as inputs; they may be supported by formal analysis; but the critical thing is that the
inputs are translated into forecasts based on judgments/opinions. This method is useful for intermediate to

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long-range forecasting tasks. The use of judgment in forecasting sounds unscientific. But, where new
products are sought to be introduced, there are few alternatives other than using the informed opinion of
knowledgeable people. However, to obtain better results, judgmental methods are used in conjunction with
other categories of methods.
2. Objective approach (Incorporates Quantitative/Mathematical models, Statistical analyses and other formulations)
Objective methods are those that use well-specified processes to analyze the data. Ideally, they have
been specified so well that other researchers can replicate them and obtain the same forecasts. These have
also been called explicit, statistical, or formal methods. They may be simple or complex; they may use
objective data or subjective data; they may be supported by formal analysis or they may not; but the critical
thing is that the inputs are translated into forecasts using a process that can be exactly replicated by other
researchers. Furthermore, the process could be done by computer.
In this, analysts plot demand data on a time scale, study the plots and look for consistent shapes or
patterns as shown in fig
Demand patterns become continuous when it is constant and does not consistently increase or
decrease. The sales of a product in the mature stage of its life cycle may show a horizontal demand pattern.
Linear trend (the systematic increase or decrease tendency of demand is known as trend) emerges
when, demand increases or decreases from one period to the next. The sales of products in the growth stage
of the product life cycle tend to show an upward trend.
Time
ProductionDemand
Linear
Irregular

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Seasonal: The most common periodic variation is the seasonal variation which occurs with some
regularity in a span of time. These variations are caused by climatic conditions such as effect of the sun and
weather conditions, social customs and festivals etc. e.g: the demand for woolen wear will be high in winter
and low during summer, sale of refrigerator, sale of soft drinks etc
The cyclic pattern pertains to the influence of seasonal factors that have impact on demand, either
positively or negatively. But whereas seasonal variations occur within a period of one year or less cyclic
variations repeat at intervals of 5 to 10 years. Cyclical: patterns related to changes of the market size, due to,
e.g., prices of some metals and gross national products etc.
Irregular variations, these variations occur without any particular rhythm. They can be caused by
causes operating in a casual and irregular fashion. Causes may be like droughts, floods, wars, strikes and
earthquakes etc.
Forecasts based on Judgment and Opinion:
Judgmental forecasting methods are, by their very nature, subjective, and they may involve such qualities
as intuition, expert opinion, and experience. They generally lead to forecasts that are based upon qualitative
criteria.
These methods may be used when no data are available for employing a statistical forecasting method.
However, even when good data are available, some decision makers prefer a judgmental method instead of a
formal statistical method. In many other cases, a combination of the two may be used.
Here is a brief overview of the main judgmental forecasting methods.
1. Manager’s opinion: This is the most informal of the methods, because it simply involves a single manager
using his or her best judgment to make the forecast. In some cases, some data may be available to help make
this judgment. In others, the manager may be drawing solely on experience and an intimate knowledge of
the current conditions that drive the forecasted quantity.
2. Jury of executive opinion: This method is similar to the first one, except now it involves a small group of
high-level managers who pool their best judgment to collectively make the forecast. This method may be
used for more critical forecasts for which several executives share responsibility and can provide different
types of expertise.
3. Sales force composite: This method is often used for sales forecasting when a company employs a sales force
to help generate sales. It is a bottom-up approach whereby each salesperson provides an estimate of what
sales will be in his or her region. These estimates then are sent up through the corporate chain of command,
with managerial review at each level, to be aggregated into a corporate sales forecast.
4. Consumer market survey: This method goes even further than the preceding one in adopting a grass-roots
approach to sales forecasting. It involves surveying customers and potential customers regarding their future
purchasing plans and how they would respond to various new features in products. This input is particularly
helpful for designing new products and then in developing the initial forecasts of their sales. It also is
helpful for planning a marketing campaign.
5. Delphi technique: Delphi technique is a subjective method relying on the opinions of few experts or an
“organized method” for collecting views and information pertaining to forecast events and assess complex
issues. This method designed in such a way to minimize bias and error of judgment by comparing with other

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expert-opinion methods. In this technique panel of experts are gathered/constituted to tackle the problem of
forecasting. These experts can be both inside and outside of the organization, each being expert on some
aspect of the problem. The efforts of this expert’s panel can be coordinated and facilitated by an impartial
leader known as the coordinator. Problems that are generally addressed by this technique can be anything-
technological, economical or social. Some typical problems of forecasting that can be tackled by Delphi
technique are;
 When could the petroleum reserves of the country be exhausted?
 When will Indian population overtake that of the Chinese?
 What would be the effect of free basics in India?
The Delphi technique procedure works as follows:
 The coordinator prepares a questionnaire in writing and sends it to each expert in the panel. Each
expert makes independent predictions not knowing about others.
 The coordinator consolidates the collected predictions and summarizes them.
 On the basis of summary, the coordinator writes a new set of questionnaires and passed to the same
panel of experts.
 Again coordinator collects their opinions, consolidates and summarizes it till he satisfied by the
overall consensus arrived by the experts.
 Opportunities are also provided to the panel to revise their decisions by coordinator before he
consolidates the consensus of final round.
Advantages:
 The panel of experts in Delphi technique has diverse backgrounds and each can contribute in a
specialized way.
 Eliminates subjective bias and influencing by members through anonymity.
Disadvantages
 It is tedious and time consuming method.
 Coordinator must possess effective summarizing skills.
Analysis of time series data:
Definition of Time Series: An ordered sequence of values of a variable at equally spaced time intervals.
A time series is a sequence of data points that
1) Consists of successive measurements made over a time interval
2) The time interval is continuous
3) The distance in this time interval between any two consecutive data point is the same
4) Each time unit in the time interval has at most one data point
Examples of time series are ocean tides, counts of sunspots etc
Time series forecasting is the use of a model to predict future values based on previously observed values.
This method of forecasting is considered similar to economic indicator method (GDP Annual Growth Rate
GDP Growth Rate, GDP per capita, Unemployment Rate, Youth Unemployment Rate, Long Term
Unemployment Rate) since it also requires regression analysis (regression analysis is a statistical process for
estimating the relationships among variables).

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Basic Model:
Advantages of Time series analysis:
 This technique is less subjective than collective opinion method and its application is not dependent
on the organization’s performance.
 In comparison with collective opinion method which may yield annually, time series analyses past
annual sales month by month or even week by week.
Limitations:
 This technique is not useful in establishing of new product which do not have past data.
 The impact of changes in selling prices, product quality, economic conditions
Components of Time series:
The time series analysis consists of determining the trend underlying the demand and extrapolating
the future trend. Statistical methods are actually used to determine the trend. The components of a time
series are generally classified as
 Trend(T)
 Cyclical (C)
 Seasonal (S)
 Random/Irregular(R)
 Horizontal
Note: All the above are discussed in regarding with demand patterns
The most common and relatively easiest methods for developing forecast from past data are;
 Simple moving averages
 Weighted moving averages
 Exponential smoothing
 Regression analysis.
 Correlation
Simple moving average: In this model, the arithmetic average of the actual sales for specific number of recent
past time periods is taken as the forecast for the next time period. Extending the moving average to include
more periods may increase the smoothening effect but decreases the sensitivity of the forecast. Long periods
provide too many opportunities for significant changes to occur in demand pattern. To reduce this risk, the
organizations can base its forecast on average demand during short periods say three months.
n= number of periods, Di=demand in the ith period

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A T.V manufacturer has experienced following demands for T.V sets during the past six months:
The plant manager desires a forecast for July, using a six period moving average. The forecast for July shall
be:
Using a six month moving average, the July forecast is 36,700. Using a three months data, the forecasts for
July shall be,
Three months moving averages
Month T.V Sets
January 20,000
February 30,000
March 20,000
April 40,000
May 50,000
June 60,000
Time
(Month)
(t)
Demand
for month
(D)
Moving
Average M(t)
Forecast
(Ft)
Error
(et)
1 95
2 100
3 87 94.00
4 123 103.33 94.00 29.00
5 90 100.00 103.33 -13.33
6 96 103.00 100.00 -4.00
7 75 87.00 103.00 -28.00
8 78 83.00 87.00 -9.00
9 106 86.33 83.00 23.00
10 104 96.00 86.33 17.67
11 89 99.67 96.00 -7.00
12 83 92.00 99.67 -16.67

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Time
(Month)
(t)
Demand for
month (D)
3- month
Moving
Average, M(t)
4- month
Moving
Average, M(t)
5- month
Moving Average,
M(t)
1 95
2 100
3 87 94
4 123 103.33 101.25
5 90 100 100 99
6 96 103 99 99.2
7 75 87 96 94.2
8 78 83 84.75 92.4
9 106 86.33 88.75 89
10 104 96 90.75 91.8
11 89 99.67 94.25 90.4
12 83 92 95.5 92
 In most cases, this method is applied to forecast for only one period in to the future.
 The forecaster must wait until demand entries are available for making the first forecast.
Advantages
 This technique is simpler than the method of any regression analysis or method of least squares.
 This method is not affected by the personal prejudice of the people using it.
 If the trend in the data is linear the moving average gives good picture of long term movement in data.
 This technique has the merit of flexibility.
Limitations
 It is very sensitive even to small movement in data.

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 A great deal of care is needed for the selection of the period of moving average since the wrong periods
selected would not give the correct picture of the trend.
The table below shows the monthly demand over 6 month’s period for a product.
Determine the sales forecast for the 7th month, using 3 month simple moving average method.
The forecast for the 7th month based on 3 month moving average is 126.67 units
Weighted moving averages (WMA):
The moving averages as calculated in the preceding part are known as unweighted because the same weight
is assigned to each of the numbers whose average is being ascertained. Some enterprises base their forecast
on a weighted moving average. In this method, except that, instead of an arithmetic average of past sales, a
weighted moving average of past sales is the forecast for the next time period. A WMA allows for varying,
not equal weighting of old demands.
Following table shows the computation for a three moths weighted moving average with a weight of 0.5
assigned to the most recent demand value, a weight of 0.30 assigned to the next most recent value and
weight of 0.20 assigned to the oldest of the demand value included in the average.
Month Demand (units)
1 120
2 130
3 110
4 140
5 110
6 130
Month Demand (units) Three month moving total (Total
demand during the past 3 months (units)
Three month
moving average
method
1 120
2 130
360 (120+130+110)
3 110
380 (130+110+140)
4 140
360 (110+140+110)
5 110
380 (140+110+130)
6 130

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The table below indicates the monthly demand for the 6 month’s period. The weightage given is 3 for the
most recent demand value, 2 for the next most recent value and 1 for the oldest demand value. Determine
the 3 month-weighted average and the demand forecast for the 7th month.
The forecast for the 7th month is 125 units
Time
(Month) (t)
Demand,
D
Moving average
M(t)
Forecast,
Ft
1 120
2 130
3 110 118
4 140 129 118
5 110 119 129
6 130 126 119
Month Demand (units)
1 120
2 130
3 110
4 140
5 110
6 130
Month Demand (units) Three month weighted moving total
Three month weighted
moving average.
1 120
2 130
3 110
4 140
5 110
6 130

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The past data for sales of wet grinders of particular company in an area is shown below.
Forecast the demand for the month of July 2001 using
a) Simple average for all previous methods
b) A Three month moving average
c) A three-month moving average where the weights are 0.5 for the latest month 0.3 and 0.2 for the moths
previous to that respectively.
a)
Forecast for July 2001 using Simple average =741 units
b)
Forecast for July 2001 using 3-month Moving Average=860 units
c)
3-month weighted moving average where weights are June=0.5, May=0.3, April=0.2
Forecast for July 2001 using a 3 month Weighted moving average =893 units
Since different methods give different forecasts, it is obvious that a certain method is selected based on its
performance as a forecast
Simple Exponential Smoothing
In these methods, the forecast sales for the last period are modified by information about the forecast error of
the last periods. This modification of the last year’s forecasts is the forecasts for the next time periods.
In this methods, the weight assigned to a previous period’s demand decreases exponentially as that data gets
older. Thus, recent demand data receive a higher weight than does the older demand data.
Month Sales
Jan-01 585
Feb 610
March 675
April 750
May 860
June 970

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A simple exponential smoothing technique considers only trend values and does not take into account seasonal
indexes or seasonal adjustments.
ABC company used a simple exponential smoothing method using an exponential smoothing constant of 0.2 (i.e.,
α=0.2) to forecast the short term demand. The forecast for the month of July was 500 units whereas the actual sales
were only 450 units. What is the forecast for the month of August?
Sales forecast for August is 490 units
A hospital has 9 month moving average forecasting method to predict particular drug requirements. The actual
demand for the item is shown in the table below.
Month 1 2 3 4 5 6 7 8 9
Demand 80 65 90 70 80 100 85 60 75
Using the 9 month moving average, find the exponential smoothing forecast for the 10th month.

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Regression Analysis
Regression analysis is a forecasting technique that establishes a relationship between variables – one
dependent and other(s) independent. In simple regression, there is only one independent variable. In multiple
regressions there is more than one independent variable. If the historical data set is a time series, the independent
variable is the time period and the dependent variable in sales forecasting. A Regression model doesn’t have to be
based on a time series, in such cases, the knowledge of the future values of the dependent variable. Regression is
normally used in long-range forecasting, but if care is taken in selecting number of periods included in the historical
data and the set of that data is projected only a few periods in to the future, then regression may also be used for short
range forecasting.
Least squares concept is used for regression and correlative analysis between any set of dependent and independent
variables. Least squares is a widely used mathematical method of obtaining line of best fit between the dependent
variable (usually demand) and an independent variable. It is so called as least squares method since the sum of the
squares method since the sum of the square of the deviations of the various points from the line of best fit is minimum
or least. It gives the equations of the line for which the sum of the squares of vertical distance between the actual
values and line values are at minimum.
In least squares or regression analysis, the relationship between the dependent variables Y and some
independent variable X can be represented by a straight line.

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Consider an example as illustrated below,
Obviously the given data represents increasing/linear trend with slight scattering
here and there. If we asked to forecast this data by using available method such as
SMA and Exponential smoothing, the final forecast value lies in between the range
of the given data, which may not be true always. Since the trend following
increasing path, chances are there future demand may also increase. For this we
cannot adopt available models rather than one need to use best fit model.
The above scatter diagram gives inofrmation about location of points at different time periods. Since the marked
points are not collinear, we cannot draw exact straight line. But we can draw a line which is as close as to these
marked points.
As shown above errors exist between the Linear curve and points near to the curve. Sum of these errors at different
points is given by
The method of least squares is to find the parameters m and c such that sum of squares of the errors is minimum.
Let,
Time (t), in
months
Actual Demand
(D), in units
Jan-2001 26
Feb 28
March 29
April 31
May 32
June 35
July 38

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With the help of least squares method, develop a linear trend equation for the data shown in the table and

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i) Compute the constants (m & c) in the regression equation
ii) Forecast a trend value for the year 2002 and 2008
Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Shipments
(Tons)
2 3 6 10 8 7 12 14 14 18 19
Year X
Year Coded
Y
Shipments (tons)
XY X2
1991 -5 (1-6) 2 -10 25
1992 -4 (2-6) 3 -12 16
1993 -3 (3-6) 6 -18 9
1994 -2 (4-6) 10 -20 4
1995 -1 (5-6) 8 -8 1
1996 0 (6-6) 7 0 0
1997 1 (7-6) 12 12 1
1998 2 (8-6) 14 28 4
1999 3 (9-6) 14 42 9
2000 4 (10-6) 18 72 16
2001 5 (11-6) 19 95 25
From the above table it is seen that the demand ( or shipments) is shown as a function of time i.e., successive years. In
such a case the time periods are coded in such a way that . It should be noted here that if there are odd number
of periods, the median year may become zero and the periods above and below it may assume negative and positive
but equal values. If the number periods are even, then median value cannot be zero. But care should be taken to see
that in each of the above cases, the difference between any two successive periods must be the same. In table above,
the years can also be coded as -10, -8, -6, -4, -2, 0, +2, +4, +6, +8, +10. Any set of values for X can be assumed as
long as
i) To find constants m & c
The straight line equation is
Where
ii) To forecast for the years 2002 and 2008
It is observed that from the table that if year is coded as +5, year 2002 would be +6 and year 2008 would be +12
For year 2002, Put X=6
Forecast for the year 2002=19.9 tons of shipment
For the year 2008, Put X=12
Forecast for the year 2008 = 29.5 tons of shipment

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The table below gives the sales record of a firm. Using Regression Analysis forecast the sales in the month of January
and February next year.
Months Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
Sales
(in units)
90 111 99 89 87 84 104 102 95 114 103 113
Month X
Month coded
Y
Sales (units)
X2 XY
January -5.5 (1-6.5) 90 30.25 -495
February -4.5 (2-6.5) 111 20.25 -499.5
March -3.5 (3-6.5) 99 12.25 -346.5
April -2.5 (4-6.5) 89 6.25 -222.5
May -1.5 (5-6.5) 87 2.25 -130.5
June -0.5 (6-6.5) 84 0.25 -42
July 0.5 (7-6.5) 104 0.25 52
August 1.5 (8-6.5) 102 30.25 561
September 2.5 (9-6.5) 95 20.25 427.5
October 3.5 (10-6.5) 114 12.25 399
November 4.5 (11-6.5) 103 6.25 257.5
December 5.5 (12-6.5) 113 2.25 169.5
To find constants m and c
Forecast for the months January and February of next year
From the table if the value of X for December is +5.5, the value of X for January would be +6.5 and that of February
would be +7.5.

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Normally the demand of any product would vary with time but in reality it depends on variety of factors like
quantity of the product, effectiveness of sales force, advertisement strategies and budgets, distribution efficiencies,
and so on. In such as case we consider demand to be dependent on a quantity other than time. The procedure followed
is the same as the previous case, but only the formulae used to calculate the constants m and c are differ. In Case 2
also a straight line is fit whose equation is,
From Equn (1)

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A manufacturer of children’s cycle believes that a demand for cycles is correlated to a birth of babies in an area during
a previous year. A data given below shows this relationship.
Year No. of births in a previous year Cycles sold during a year
1 40,000 3,000
2 48,000 3,200
3 66,000 4,000
4 78,000 5,200
5 92,000 7,900
6 1,05,000 7,900
7 1,25,000 9,000
8 1,40,000 10,000
Compute a probable sales of cycles in a 9th year given no of births in a previous year as 1,66,000
By Regression analysis,
Year No. of births
in a previous
year, X
Cycles sold
during a year, Y
1 40,000 3,000 1600 1200
2 48,000 3,200 2304 1536
3 66,000 4,000 4356 2442
4 78,000 5,200 6084 3120
5 92,000 7,900 8464 4784
6 1,05,000 7,900 11025 8295
7 1,25,000 9,000 15625 11250
8 1,40,000 10,000 19600 14000
n=8 =694000 =46000 =69058 =46627
i) To find coefficients ‘c” and ‘m’ by regression equation

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For the data given below
a) Discuss the importance of sales forecasting.
b) The quarterly sales for last 3 years is given below. Calculate the quarterly sales of 4th year
Year Quarter Unit Sales
1 20
2 35
3 421
4 29
1 26
2 35
3 50
2
4 34
1 37
2 47
3 55
3
4 44

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Year Quarter, X Unit Sales , Y X2 XY
1 20 1 20
2 35 4 70
3 42 9 1261
4 29 16 116
5 26 25 130
6 35 36 210
7 50 49 3502
8 34 64 272
9 37 81 333
10 47 100 470
11 55 121 6053
12 44 144 528
n=12 =78 =454 =650 =3230

Forecasting
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Correlation: Regression analysis basically tries to express the relationship between two variables in the form of
straight line. The extent to which the two variables are related to each other is explained by correlation analysis. In
other words, correlation is a means of expressing the degree of relationship between two or more variables (i.e.,
Correlation is a statistical technique that can show whether and how strongly pairs of variables are related. For
example, height and weight are related; taller people tend to be heavier than shorter people. The relationship isn't
perfect.)
Coefficient of correlation: Pearson product-moment correlation coefficient, also known as r, R, or Pearson's r, a
measure of the strength and direction of the linear relationship between two variables that is defined as the (sample)
covariance of the variables divided by the product of their (sample) standard deviations.
The correlation coefficient (r) is a number between -1 and +1 and is designated as positive if Y increases with increase
in X and negative if Y decreases with increase in X. If r=0, this indicates the lack of relationship between two
variables.
In Regression analysis problem, Correlation-Coefficient can be found by the relation
Co-efficient of Determination (r2)
r2 is a statistic that will give some information about the goodness of fit of a model. In regression, the r2
coefficient of determination is a statistical measure of how well the regression line approximates the real data points.
An r2 of 1 indicates that the regression line perfectly fits the data.

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Standard deviation of Regression
The following table gives the five months of average monthly temperatures and corresponding monthly resort
attendance.
Months 1 2 3 4 5
Average temperature 24 41 32 30 38
Resort attendance s 43 31 39 38 35
Compute linear regression equation of the relationship between two if next month’s average temperature is forecast to
be 45oC.
1) Use linear regression to develop a forecast
2) Compute a correlation coefficient for the above data and determine the strength of the linear relationship
between average temperature and attendance. How good a predictor is temperature for attendance?
Months Average Temp oC,
X
Resort Attendance,
Y
X2 Y2 XY
1 24 43 576 1849 1032
2 41 31 1681 961 1271
3 32 39 1024 1521 1248
4 30 38 900 1444 1140
5 38 35 1444 1225 1330
n=5 =165 =186 =5625 =6021
1)

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2)
As is indicated by correlation coefficient r=--0.97, the relationship between average temperature and resort attendance
is very strong, in other words it can be concluded that temperature is a good indicator of resort attendance.
Accuracy and control of Forecasts
Demand forecast influences most of the decisions in all the functions. Hence, it must be estimated
with the highest level of precision. Some common measures are inevitable to measure the accuracy of a
forecasting technique. This measure may be an aggregate error (deviation) of the forecast values from the
actual demands. The different types of errors which are generally computed are as presented below
1. Mean absolute deviation (MAD)
2. Mean square error (MSE)
3. Mean forecast error (MFE)
4. Mean absolute percent error (MAPE)
The formula for forecast error is given below,
Mean Absolute Deviation (MAD): It is the mean absolute deviation of forecast demand from actual demand values.
The MAD is sometimes called as the mean absolute error (MAE).

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Mean Square Error (MSE): It is mean of squares of the deviation of forecast demands from the actual demand
values. Usually the effects of small errors on operations are not serious. These errors may be smoothed out by
inventory or overtime work. It will be difficult to have smoothed values for forecast even if there are few large errors.
Consequently, a method of measuring errors that penalizes large errors more than small errors is sometime desired.
The mean square error (MSE) provides this type of measure of forecast error.
Mean Forecast Error (MFE): Mean forecast error is the mean of the deviations of the forecast demand s form the
actual demands.
Mean Absolute Percentage Error (MAPE): It is the mean of the percent deviations of the forecast demands from
the actual demands.
Choosing a forecasting technique
There are many forecasting techniques each having its own advantages and limitations. The suitability of any method
basically depends on the potential consumers & enterprise and nature of the product. The important role which
quantity and quality of information plays in selection of the sales/demand forecasting technique cannot be neglected.
In general, an organization or enterprise may utilize several forecasting techniques to anticipate the future demand of
products and services.
Criteria for choosing good forecasting technique;

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 Time available for analysis
 Availability and accuracy of past data about the product.
Cost of developing and employing the forecast method.
Degree of accuracy expected form the forecast.
Complexity of various factors influencing future operations.
Length of forecast period.
Thus in view of the factors mentioned above, the method of forecasting should be evaluated in terms of its
practical application and cost. So, cost v/s benefits of the technique is a critical issue for the management. The
following Fig, help in determining the best use of data available to meet the real requirements and applying
costly methods that provide greater accuracy.
Thus simplicity, accuracy, economy and quick plus easy availability of requisite information form reliable sources are
the four vital elements to be considered in adopting a appropriate forecasting technique.
Forecast Control

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There are several ways to monitor forecast error over time to make sure that the forecast is performing correctly--that
is, the forecast is in control. Forecasts can go "out of control" and start providing inaccurate forecasts for several
reasons, including a change in trend, the unanticipated appearance of a cycle, or an irregular variation such as
unseasonable weather, a promotional campaign, new competition, or a political event that distracts consumers.
A tracking signal indicates if the forecast is consistently biased high or low. It is computed by dividing the
cumulative error by MAD, according to the formula
The tracking signal is recomputed each period, with updated, "running" values of cumulative error (Cumulative
error is computed simply by summing the forecast errors, as shown in the following formula.
A large positive value indicates that the forecast is probably consistently lower than the actual demand, or is biased
low. A large negative value implies the forecast is consistently higher than actual demand, or is biased high. Also,
when the errors for each period are scrutinized, a preponderance of positive values shows the forecast is consistently
less than the actual value and vice versa) and MAD. The movement of the tracking signal is compared to control
limits; as long as the tracking signal is within these limits, the forecast is in control.
Forecast errors are typically normally distributed, which results in the following relationship between MAD and the
standard deviation of the distribution of error, 
This enables us to establish statistical control limits for the tracking signal that corresponds to the more familiar
normal distribution.
Elements of a good forecast
 The forecast should be timely: Usually, a certain amount of time is needed to respond to the information
contained in a forecast. Time necessary to implement necessary change.
 The forecast should be accurate and the degree of accuracy should be stated. This will enable users to plan for
possible errors and will provide a basis for comparing alternative forecast.
 The forecast should be reliable: It should work consistently. A technique that sometimes provides a good
forecast and sometimes a poor but should be reliable.
 The forecast should be expressed in meaningful units: Units depends on user needs. For example: Production
planners need to know how many units will be needed.
 The forecast should be in writing: A written forecast will permit an objective basis for evaluating the forecast.
 The forecasting technique should be simple to understand and use: Fairly simple forecasting techniques enjoy
widespread popularity because of users are more comfortable working with them.
 The forecast should be cost effective: The benefits of implementing the forecast should outweigh the costs of
making forecasts.

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A firm uses exponential smoothing with ∝=0.2 to forecast the demand. The forecast for first week of the January was
400 units whereas the actual demand turned out to be 450 units.
i. Forecast the demand for 2nd week of January
ii. Assume the actual demand for 2nd week of January turned out to be 460 units, Forecast the demand up to 3rd
week of the February, assuming the subsequent demand as 465, 434, 420, 498 and 462 units. Plot the results
graphically showing the actual demand and forecast demand. VTU-Dec/Jan-2010 (12 Marks)
Week Old Forecast Actual Demand New Forecast
Jan 1st week 400 450
Jan 2nd week 410 460
Jan 3rd week 420 465
Jan 4th week 429 434
Therefore forecast for 8th week is 446 units
Alternative:

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The data given below refers to past sales for eleven years. Using least squares estimate sales forecast for next two
years. Also use moving average for 3 years and compare the forecasts.
Years 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991
35 50 48 47 50 55 65 77 92 86 100

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