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Article Review: An Introduction to Regression Analysis by Alan O. Sykes

Article Review: An Introduction to Regression Analysis by Alan O. Sykes


In his working paper titled An Introduction to Regression Analysis, Alan O. Sykes presents an in-depth introduction of regression analysis, its application in economics, law, medicine and other fields and its significance in proving evidence for many economic and legal issues. The author uses several illustrations to provide an insight into the applicability of this statistical tool.

Methodology Summary

The author uses illustrations from econometrics to show how regression analysis can be applied in problem solving. For example, in the case of demand for oranges, he suggests building a model taking only price simplification. To respond to the criticism of oversimplification, we can say that it is better to get started and build a simplified model than a more complex model. This idea is expressed by the authors in his examples. According to the author, an economic model based on the observation can be tested.

Understanding of the Issues in the Article

The author describes the classification of regression like multiple regression and linear regression. In practice, the regression line is often sought as a linear function which is represented by the following representation. This best approximates the desired curve. This is done using the least squares method when minimizing the sum of squared deviations of the actually observed  from the estimated  (referring to evaluation using the straight line that claims to represent the unknown regression dependence):

In the above, M represents the sample size. This approach is based on the known fact that the terms appearing in the above sum is a minimum value for the case when .

To solve the problem of regression analysis by least squares method, the author has introduced the concept of residual function:

The condition of minimum residual function:

The resulting system assumeslinear equations with  unknown. In this ...
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