Question

Explain the method of fitting a straight line

Answer 1

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.