Method Of Moving averages Secular Trend Time series
The Method of least Squares Curve fitting
The Technique of obtaining the mathematical curve by the principle of least squares is known as curve fitting
Two Types of trends are there
Linear Trend is one which gives the straight line when Plotted the values on a graph paper
If we are getting non-linear curves like parabola,exponential curve,logistic curve We can say it is a non-linear Trend.
We can fit the curve by Principle of least Squares
“The sum of the squares of the deviations between the observed values and the trend values is least”
Lines of Best Fit
If we are drawing a straight line by the method of curve fitting based on the principle of least squares ,such line we can say line of best fit
Equation of least squares
y = a + bx where y is the value for dependent Variable
a and b are constants
For finding a and b we will apply the method of least Squares
How can we find the value of a and b
Let E be the sum of the squares of deviations of all the original values.
E=( y – (a + bx))²
By the method of calculus ,partial differential coefficients of E with respect to a and b are zero.Thus we will get two normal Equations
y=na +b x
xy= a x +b x²
Solve these two Equations we will get a and b
Substituting these values in the equation y=a+bx we get the trend Equation Substitute the various values in the trend Equation
Question No 1
The following are the annual Profits in 1000s of Rs in a textiles Business
Year 1998 1999 2000 2001 2002 2003 2004
Profit in 60 72 75 65 80 85 95 Thousands a.Using the method of least squares fit a straight line. b.Also Make an estimate profit in 2005 c.Estimate the trend Values for all the years? d.Compute short term Fluctuations? e.Plot the given values and trend values on a graph?
The Trend Eqn is y=76 + 4.86xIn the year 2005 x=4 then y=76+(4.86*4)=95.44
Therefore the profit for the year 2005 will be 95.44 thousand Rs.