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प्रश्न
Explain the method of fitting a straight line
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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.
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संबंधित प्रश्न
State the uses of time series
Write a brief note on seasonal variations
State the different methods of measuring trend
Determine the equation of a straight line which best fits the following data
| Year | 2000 | 2001 | 2002 | 2003 | 2004 |
| Sales (₹ '000) | 35 | 36 | 79 | 80 | 40 |
Compute the trend values for all years from 2000 to 2004
Calculate the seasonal indices from the following data using the average method:
| Year | I Quarter | II Quarter | III Quarter | IV Quarter |
| 2008 | 72 | 68 | 62 | 76 |
| 2009 | 78 | 74 | 78 | 72 |
| 2010 | 74 | 70 | 72 | 76 |
| 2011 | 76 | 74 | 74 | 72 |
| 2012 | 72 | 72 | 76 | 68 |
Choose the correct alternative:
A time series is a set of data recorded
Choose the correct alternative:
Factors responsible for seasonal variations are
Choose the correct alternative:
The value of ‘b’ in the trend line y = a + bx is
Choose the correct alternative:
The seasonal variation means the variations occurring with in
The sum of the infinite series `x + (1 + 2)/(2!) x^2 + (1 + 2 + 3)/(3!) x^3 +` .... equals
