Page 319 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes ∑Y 526
a = = = 65.75
N 8
∑XY 308
b = 2 = = 7.33
∑X 42
The advantage of this method is that the value of b gives annual increment of charge
rather than 6 monthly increment, as in the first method discussed above. Hence, we
will not have to double the value of b to obtain yearly increment. It is clear from the
above illustration that in the first case the value of b is half of what we obtain from the
second method. (b) was 3.67 in the first case and 7.33 in the second case.
24.2 Merits, Demerits and Limitations of the Method of Least Squares

Merits

1. This is a mathematical method of measuring trend and hence there is no possibility of
subjectiveness.
2. The line obtained by this method is called the line of best fit because it is this line from where the
sum of the positive and negative deviations is zero and sum of the squares of the deviations
least, i.e., (Y – Y ) = 0 and (Y – Y ) least.
2
c c
Demerits
Mathematical curves are useful to describe the general movement of a time series, but it is doubtful
whether any analytical significance should be attached to them, except in special cases. It is seldom
possible to justify on theoretical grounds any real dependence of a variable on the passage of time.
Variables do change in a more or less systematic manner over time, but this can usually be attributed
to the operation of other explanatory variables. Thus many economic time series show persistent
upward trends over time due to a growth of population or to a general rise in prices, i.e., national
income and the trend element can to a considerable extent be eliminated by expressing these series
per capita or in terms of constant purchasing power. For these reasons mathematical trends are
generally best regarded as tools for describing movements in time series rather than as theories of the
causes of such movements that follow, that it is extremely dangerous to use trends forecast future
movements of a time series. Such forecasting, involving as it does extrapolation, can be valid only if
there is theoretical justification for the particular trend as an expression of a functional relationship
between the variable under consideration and the time. But if the trend is purely descriptive of past
behaviour, it can give few clues about future behaviour. Sometimes the projection of a trend leads to
absurd results which is prima facie evidence that the trend could not be maintained.
Hence, mathematical methods of fitting trend are not foolproof. In fact, they can be the source of
some of the most serious errors that are made in statistical work. They should never be used unless
rigidly controlled by a separate logical analysis. Trend fitting depends upon the judgement of the
statistician, and a skilfully made free-hand sketch is often more practical than a refined mathematical
formula.
Self-Assessment

1. Gompertz curve is a ............ curve which denoted as ............ .
2. Equation for non-linear curve is ............ .
3. The two normal equations to calculate the values of ‘a’ and ‘b’ in Y = a + bX are ............ and
............ .
4. A polynomial of the form Y = a + bY + CX is called a ............ .
2
5. The line obtained by method of least squares is known as the line of ............ .

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