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Question
Explain the method of fitting a straight line
Solution
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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