Page 419 - DMTH404_STATISTICS

Unit 30: Method of Least Square

30.4 Self Assessment Notes

1. Fill in the blanks:
(i) Series of figures arranged in chronological order is known as ........ .
(ii) ........ is that irreversible movement which continues in the same direction for a
considerable period of time.
(iii) The trend equation fitted by the method of least squares is known as the equation of
........ fit.
(iv) In case of ........ trend, the successive observations differ by a constant number.
(v) In the case of an exponential trend, the successive observations differ by a constant
........ .
(vi) In the case of linear trend Y = a + bX, a is termed as the ........ value in the year of ..........

30.5 Review Questions

1. Determine the trend and short-term fluctuations, assuming additive model, from the
following data by calculating 3 yearly moving averages. The figures of profit are in
Rs '000.
Years : 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990
Profits : 34 46 52 55 58 61 58 61 64 55

2. Calculate the long-term trend and short-term oscillations, assuming multiplicative model,
with a three-year period from the following data on output (in tonnes) of tea.

Year Output Year Output
1969 1632 1973 2620
1970 1557 1974 3120
1971 1652 1975 3236
1972 2100 1976 3562

3. Construct a four-year moving average from the following data on the consumption
(in '000 bales) of imported cotton in India.
Year : 1920 1930 1940 1950 1960 1970 1980
Consumption : 129 131 106 91 95 84 93
4. Determine trend values by method of moving average if the observations, given below,
are known to have a business cycle of 4 years.
Year : 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
Values : 41 61 55 48 53 67 62 60 67 73 78 76 84
5. Assuming five-yearly cycle, determine trend of bank clearings (in Rs crores) by moving
average method:
Years : 1 2 3 4 5 6 7 8 9 10 11 12
Bank Clearings : 53 79 76 66 69 94 105 87 79 104 97 92
6. Find trend of the following series using a three-year weighted moving average with
weights 1, 2, 1.
Year : 1 2 3 4 5 6 7
Value : 2 4 5 7 8 10 13

LOVELY PROFESSIONAL UNIVERSITY 411