Advertisements
Advertisements
Question
The following table shows the number of salesmen working for a certain concern:
| Year | 1992 | 1993 | 1994 | 1995 | 1996 |
| No. of salesman |
46 | 48 | 42 | 56 | 52 |
Use the method of least squares to fit a straight line and estimate the number of salesmen in 1997
Solution
Computation of trend values by the method of least squares (ODD Years)
| Year (x) |
No. of Salesman (y) |
X = (x – 1994) | x2 | XY | Trends Value (Yt) |
| 1992 | 46 | – 2 | 4 | – 92 | 44.8 |
| 1993 | 48 | – 1 | 1 | – 48 | 46.8 |
| 1994 | 42 | 0 | 0 | 0 | 48.8 |
| 1995 | 56 | 1 | 1 | 56 | 50.8 |
| 1996 | 52 | 2 | 4 | 104 | 52.8 |
| N = 5 | `sum"Y"` = 244 | `sum"X"` = 0 | `sum"X"^2` = 10 | `sum"XY"` = 20 | `sum"Yt"` = 244 |
a = `(sum"Y")/"n" = 244/5` = 48.8
b = `(sum"XY")/(sum"X"^2) = 20/10` = 2
Therefore, the required equation of the straight line trend is given by
Y = a + bX
Y = 48.8 + 2X
i.e Y = 48.8 + 2(x – 1994)
When x = 1992
Yt = 48.8 + 2(1992 – 1994)
Y = 48.8 + 2(– 2)
= 48.8 – 4
= 44.8
When x = 1993
Yt = 48.8 + 2(1993 – 1994)
Y = 48.8 + 2(– 1)
= 48.8 – 2
= 46.8
When x = 1994
Yt = 48.8 + 2(1994 – 1994)
Y = 48.8 + 2(0)
= 48.8
When x = 1995
Yt = 48.8 + 2(1995 – 1994)
Y = 48.8 + 2(1)
= 50.8
When x = 1996
Yt = 48.8 + 2(1996 – 1994)
Y = 48.8 + 2(2)
= 48.8 + 4
= 52.8
When x = 1997
Yt = 48.8 + 2(1997 – 1994)
Y = 48.8 + 2(3)
= 48.8 + 6
= 54.8
APPEARS IN
RELATED QUESTIONS
Compute the average seasonal movement for the following series
| Year | Quarterly Production | |||
| I | II | III | IV | |
| 2002 | 3.5 | 3.8 | 3.7 | 3.5 |
| 2203 | 3.6 | 4.2 | 3. | 4.1 |
| 2004 | 3.4 | 3.9 | 37 | 4.2 |
| 2005 | 4.2 | 4.5 | 3 | 4.4 |
| 2006 | 3.9 | 4.4 | 4.2 | 4.6 |
The sales of a commodity in tones varied from January 2010 to December 2010 as follows:
| In Year 2010 | Sales (in tones) |
| Jan | 280 |
| Feb | 240 |
| Mar | 270 |
| Apr | 300 |
| May | 280 |
| Jun | 290 |
| Jul | 210 |
| Aug | 200 |
| Sep | 230 |
| Oct | 200 |
| Nov | 230 |
| Dec | 210 |
Fit a trend line by the method of semi-average
Choose the correct alternative:
A time series is a set of data recorded
Choose the correct alternative:
A time series consists of
Choose the correct alternative:
The components of a time series which is attached to short term fluctuation is
Choose the correct alternative:
The additive model of the time series with the components T, S, C and I is
Choose the correct alternative:
The component of a time series attached to long term variation is trended as
Choose the correct alternative:
The seasonal variation means the variations occurring with in
Fit a straight line trend by the method of least squares to the following data
| Year | 1980 | 1981 | 1982 | 1983 | 1984 | 1985 | 1986 | 1987 |
| Sales | 50.3 | 52.7 | 49.3 | 57.3 | 56.8 | 60.7 | 62.1 | 58.7 |
Sum of the first n terms of the series `1/2 + 3/4 + 7/8 + 15/16 +`......... is equal to:
