Advertisements
Advertisements
प्रश्न
Explain the method of fitting a straight line
Advertisements
उत्तर
The method of fitting a straight line is as follows
Procedure:
(i) The straight-line trend is represented by the equation Y = a + bX ........(1)
Where Y is the actual value, X is time, a, b are constants.
(ii) The constants ‘a and ‘b’ are estimated by solving the following two normal Equations
`sum"Y"` = na + b `sum"X"` ........(2)
`sum"XY" = "a"sum"X" + "b"sum"X"^2` .........(3)
Where ‘n’ = number of years given in the data.
(iii) By taking the mid-point of the time as the origin, we get `sum"X"` = 0
(iv) When `sum"X"` = 0, the two normal equations reduces to
`sum"Y"` = na + b(0), a `(sum"Y")/"n" = bar"Y"`
`sum"XY"` = a(0) + `"b"sum"X"^2`, b = `(sum"XY")/(sum"X"^2)`
The constant ‘a’ gives the mean of Y and ‘b gives the rate of change (slope),
(v) By substituting the values of ‘a and ‘b’ in the trend equation (1), we get the Line of Best Fit.
APPEARS IN
संबंधित प्रश्न
State the uses of time series
The following figures relates to the profits of a commercial concern for 8 years
| Year | Profit (₹) |
| 1986 | 15,420 |
| 1987 | 15,470 |
| 1988 | 15,520 |
| 1989 | 21,020 |
| 1990 | 26,500 |
| 1991 | 31,950 |
| 1992 | 35,600 |
| 1993 | 34,900 |
Find the trend of profits by the method of three yearly moving averages
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
Choose the correct alternative:
Factors responsible for seasonal variations are
Choose the correct alternative:
The component of a time series attached to long term variation is trended as
Using three yearly moving averages, Determine the trend values from the following data.
| Year | Profit | Year | Profit |
| 2001 | 142 | 2007 | 241 |
| 2002 | 148 | 2008 | 263 |
| 2003 | 154 | 2009 | 280 |
| 2004 | 146 | 2010 | 302 |
| 2005 | 157 | 2011 | 326 |
| 2006 | 202 | 2012 | 353 |
The sum of the infinite series `x + (1 + 2)/(2!) x^2 + (1 + 2 + 3)/(3!) x^3 +` .... equals
Sum of n terms of series 1.3 + 3.5 + 5.7 + ______ is
Sum of the first n terms of the series `1/2 + 3/4 + 7/8 + 15/16 +`......... is equal to:
The sum of the series 3.6 + 4.7 + 5.8 + ....... upto (n – 2) terms
