Page 318 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 24: Time Series Methods—Principle of Least Square and Its Application

Solution: Notes

Fitting of Straight Line Trend by the Method of Least Squares
Year Earnings Deviations Deviations XY X 2
(Rs. Lakhs) from 1990-5 multiplied by 2
Y X

1987 38 – 3.5 – 7 – 266 49
1988 40 – 2.5 – 5 – 200 25
1989 65 – 1.5 – 3 – 195 9
1990 72 – 0.5 1 – 72 1
1991 69 + 0.5 + 1 + 69 1
1992 60 + 1.5 + 3 + 180 9
1993 87 + 2.5 + 5 + 435 25
1994 95 + 3.5 + 7 + 665 49
N = 8 ∑Y = 526 ∑X = 0 ∑XY = 616 ∑X = 168
2
Y = a + bX
c
∑Y 526
a = = = 65.75
N 8
∑XY 616
b = 2 = = 3.67
∑X 168
Y = 65.75 + 3.67 X.
For 1998 X will be + 15
When X is + 15, Y will be
Y = 65.75 + 3.67 (15)
= 65.75 + 55.05 = 120.8.
Thus the estimated earnings for the year 1998 are Rs. 120.8 lakhs.
The same result will be obtained if we do not multiply the deviations by 2. But in that
case our computations would be more difficult as would be seen below
Year Sales in thousands Deviations XY X 2
of rupees from 1991-5
Y X
1987 38 – 3.5 – 133.00 12.25
1988 40 – 2.5 – 100.00 6.25
1989 65 – 1.5 – 97.50 2.25
1990 72 – 0.5 – 36.00 0.25
1991 69 + 0.5 + 34.50 0.25
1992 60 + 1.5 + 90.00 2.25
1993 87 + .5 + 217.50 6.25
1994 95 + 3.5 + 332.50 12.25
N = 8 ∑Y = 526 ∑X = 0 ∑XY = 308 ∑X 2 = 42.00

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