Least Square Method

This is also known as straight line method.  This method is most commonly used in research to estimate the trend of time series data, as it is mathematically designed to satisfy two conditions.  They are: 

1) Sum of (Y + YC ) = 0, and 

2) Sum of (Y + YC )2 = least

The straight line method gives a line of best fit on the given data.  The straight line which can satisfy the above conditions and make use of regression equation, is given by: 

YC = a + bx

Where, ‘YC represents the trend value of the time series variable y, ‘a’ and ‘b’ are constant values of which ‘a’ is the trend value at the point of origin and ‘b’ is the amount by which the trend value changes per unit of time, and ‘x’ is the unit of time (value of the independent variable). 


Important Key Notes


Cyclical Variations: A type of variation in time series, in which the values of variables vary up and down around the secular trend line.


Irregular Variations: A type of element of a time series, refers to such variations in business activity which do not repeat according to a definite pattern and the values of variables are completely unpredictable.


Seasonal Variation: Pattern of change in a time series within a year and the same changes tend to be repeated from year to year.


Secular Trend: A type of variation in a time series, the long-term tendency of a time series to grow or decline over a period of time.


Time Series: is a data on any variable accumulated at  regular time intervals.

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