fit a straight line trend by the method of least square to the following data and estimate sales for 2018 year 2009 to 2016 and profits 80,90,92,83,94,99,92,104
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During Time Series analysis we come across with variables, many of them are dependent upon others. It is often required to find a relationship between two or more variables. Least Square is the method for finding the best fit of a set of data points. It minimizes the sum of the residuals of points from the plotted curve. It gives the trend line of best fit to a time series data. This method is most widely used in time series analysis. Let us discuss the Method of Least Squares in detail.
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Components of Time Series
Calculation of Trend By Moving Average Method
Method of Least Squares
Each point on the fitted curve represents the relationship between a known independent variable and an unknown dependent variable.
In general, the least squares method uses a straight line in order to fit through the given points which are known as the method of linear or ordinary least squares. This line is termed as the line of best fit from which the sum of squares of the distances from the points is minimized.
Equations with certain parameters usually represent the results in this method. The method of least squares actually defines the solution for the minimization of the sum of squares of deviations or the errors in the result of each equation.
The least squares method is used mostly for data fitting. The best fit result minimizes the sum of squared errors or residuals which are said to be the differences between the observed or experimental value and corresponding fitted value given in the model. There are two basic kinds of the least squares methods – ordinary or linear least squares and nonlinear least squares.