The secular trend is measured by the method of the free-hand curve in the following steps:
- Take the time periods along $x$-axis by taking appropriate scaling
- Plot the points for observed values of the $Y$ variable as the dependent variable against the given time periods
- Join these plotted points by line segments to get a historigram
- Draw a free hand smooth curve (or a straight line) through the histogram
In this method we draw the given times series data on graph paper, then we draw a free hand trend line through the plotted graph according to the trend of the graph. Then we read trend values from this free-hand trend line.
It is generally preferred to use a curve instead of a straight line to show the secular trend.
- The free-hand curve method is a simple, easy, and quick method for measuring secular trends.
- A well-fitted trend line (or curve) gives a close approximation to the trend based on a mathematical model.
- It is a rough and crude method.
- It is greatly affected by personal bias as different persons may fit different trends to the same data.
The estimates are not reliable due to personal bias.
Question: The following time series shows the number of road accidents in Punjab for the year 1972 to 1978.
|No. of Accidents||2493||2638||2699||3038||3745||4079||4688|
- Obtain the historigram showing the number of road accidents and a free hand trend line by drawing a straight line
- Find the trend values for this time series