find a straight line trend by least square method
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Fig 2.8 Straight-line trend
The straight-line trend is represented by the equation: Yt= a +bX, where Yt are the trend vales, a is the Y intercept or the value of Y when X = 0, b represents the slope of line or the amount by which Y variable will change if X is increased or decreased by one unit, and X variable is the time period.
In order to determine the value of the constants ‘a’ and ‘b’, following two equations, called normal equations, are to be solved.
∑X = Na + b∑X
∑XY = a∑X + b∑X2 , where N is the number of time periods.
While fitting the trend line by the method of least squares three things are always specified:
Which year was selected as origin?What is unit of time represented by X, i.e. whether X represents 1 month ½ month, ½ year or 1 year?In what kind of units is Y being measured?
The straight-line trend is represented by the equation: Yt= a +bX, where Yt are the trend vales, a is the Y intercept or the value of Y when X = 0, b represents the slope of line or the amount by which Y variable will change if X is increased or decreased by one unit, and X variable is the time period.
In order to determine the value of the constants ‘a’ and ‘b’, following two equations, called normal equations, are to be solved.
∑X = Na + b∑X
∑XY = a∑X + b∑X2 , where N is the number of time periods.
While fitting the trend line by the method of least squares three things are always specified:
Which year was selected as origin?What is unit of time represented by X, i.e. whether X represents 1 month ½ month, ½ year or 1 year?In what kind of units is Y being measured?
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