Application of Least Square Method

Posted: August 26th, 2021

Week 8: Application of Least Square Method

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Application of Least Square Method

In this discussion, the aim is to examine the application of the least square method. It is a mathematical method or concept for regression analysis used in determining a line of best fit for a given dataset(Hansen, Pereyra & Scherer, 2013). The technique helps achieve a visual output that demonstrates a relationship between different data points. Every point in data shows a particular relationship between the unknown dependent and independent variables. In this case, the method serves to inform on the rationale for drawing a line of best fit across the data points. For instance, using a linear least square method, the aim is always to attain a straight line that minimizes aggregate errors of the squares(Hansen, Pereyra & Scherer, 2013; Vinzi, 2010). Thus, the method has full application in different disciplines for understanding the behavior of data. The usual fields the method is applied include engineering, medical, statistics, finance, business, and economics, among others.

Practically, the least square method is applied in finance discipline, particularly for analyzing the stock returns of a company. Here, the purpose is to help the analyst test thedependence of stock returns on index returns. Therefore, this is achieved by plotting all stock returns using excel or other analytical software charts(Vinzi, 2010). In this case, index returns are regarded as independent variables, while stock returns are considered dependent variables. Once the line of best fit is attained, the analyst can explain the dependence in the stock variables using coefficients. Specifically, the line of best fit yields an equation that helps understand relationships existing between the data points(Vinzi, 2010). Besides, the least square measures the lowest level of dispersion in the data point. Hence, the method is applied since it is the smallest variance. 

References

Hansen, P., Pereyra, V. & Scherer, G. (2013). Least squares data fitting with applications. Baltimore, Md: Johns Hopkins University Press.

Vinzi, V. (2010). Handbook of partial least squares: concepts, methods, and applications. Berlin-New York: Springer.