Page 197 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 7. If X is independent variable then we can estimate the average values of Y for a given value
of X. The relation used for such estimation is called regression of ..............................
(a) X on X (b) Y on Y

(c) X on Y (d) Y on X
8. If Y is used for estimating the average values of X, the relation will be called regression of
................................

(a) X on X (b) Y on Y
(c) X on Y (d) Y on X
9. For a bivariate data, there will always be .............................of regression.
(a) Single line (b) Two lines

(c) Three lines (d) Four lines
10. Derivation of each line is dependent on a different set of ...............................
(a) Functions (b) Assumptions
(c) Symbols (d) Presumptions

9.2 Least Square Methods

This is one of the most popular methods of fitting a mathematical trend. The fitted trend is
termed as the best in the sense that the sum of squares of deviations of observations, from it, are
minimised. We shall use this method in the fitting of following trends:
1. Linear Trend
2. Parabolic Trend

3. Exponential Trend
9.2.1 Fitting of Linear Trend

Given the data (Y , t) for n periods, where t denotes time period such as year, month, day, etc., we
t
have to find the values of the two constants, a and b, of the linear trend equation Y = a + bt.
t
Using the least square method, the normal equation for obtaining the values of a and b are:
Y = na + b t and
t
2
tY = a t + b t
t
Let X = t – A, such that X = 0, where A denotes the year of origin.
The above equations can also be written as

Y = na + b X
XY = a X + b X 2
(Dropping the subscript t for convenience).

Y XY
Since X = 0, we can write a and b 2
n X

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