Statistical method 2

(a) Graphical Method: - under this method, annual
sales data is plotted on a graph paper and a line is
drawn through the plotted points. Then a free hand
line is so drawn that the total distance between the
line and the point is minimum.
Sale Years
Trend Projection
Although this method is very simple and least
expensive, the projections made through this method
are not very reliable. The reason is that the
extension of the trend line involves subjectivity and
personal bias of the analysis.
(b) Fitting Trend Equation: Least square method: -
Fitting trend equation is a formal technique of
projecting the trend in demand. Under this method,
a trend line (or curve) is fitted to the time – series
data with the aid of statistical techniques. The
form of the trend equation that can be fitted to
the time series data is determined either by
plotting the sales data or by trying different forms
of trend equations for the best fit.
When plotted, a time series date may show various
trends. The most common types of trend equation
are 1) liner and 2) exponential trends
Linear Trend: - When a time series data reveals a
rising trend in sales than a straight-line trend
equation of the following form is fitted
S =  A  + BT
Where S = annual sales
T = Time (in year)
A & B are constant. The parameter b
given the measure of annual increase in sales
Exponential trend:- When sales ( or any dependent
variable) have increased over the past years at an
increasing rate or at a constant percentage rate,
than the appropriate trend equation to be used is an
exponential trend equation of any of the following
type
1. Y = aebt
Or its semi – logarithmic for
Log y = = log a + bt
This form of trend equation is used when growth
rate is constant.
2. Double log trend equation of equation
Y = aTB
Or it’s double logarithmic form
Log y = log a + b log t
This form of trend equation is used when growth
rate is increasing.
Limitation The first limitations of this method arise
out of the assumption that the past rate of change
in the dependent variable will persist in the future
too. Therefore, the forecast based on this method
may be considered to be reliable only for the period
during which this assumption holds.
Second, this method cannot be used for short-term
estimates. Also it cannot be used where trend is
cyclical with sharp turning points of trough and
perks.