Extra Sum of Squares Principle (ESSP) is a statistical technique used to determine how much of an observed effect is due to a particular independent variable. It is commonly used in linear regression and analysis of variance (ANOVA) and can be used to compare the relative effectiveness of different independent variables. The main idea behind the ESSP is to compare the sum of squares of two models to determine which model explains a larger portion of the observed effect.
The ESSP is based on the concept that the total sum of squares of a regression model can be divided into two parts: the sum of squares due to the independent variable (SSI) and the sum of squares due to the error (SSE). The ESSP then uses the ratio of the two sums of squares to determine which variable is more effective in explaining the observed effect. Specifically, the SSI is compared to the SSE, and if the SSI is greater than the SSE, then the independent variable is more effective in explaining the observed effect.
The ESSP can be applied to both linear regression and ANOVA. In linear regression, the ESSP can be used to compare the relative effectiveness of different independent variables. For example, if two independent variables are used in a linear regression model, the ESSP can be used to determine which variable explains a larger portion of the observed effect. In ANOVA, the ESSP can be used to determine which independent variable is most effective in explaining the variation in the dependent variable.
The ESSP is an important tool for statistical analysis and can be used to compare the relative effectiveness of different independent variables. It is a useful technique for linear regression and ANOVA, as it can help determine which independent variable is most effective in explaining the observed effect.
References
Cramer, E. S. (2003). Applied linear regression models (4th ed.). Boston, MA: Irwin/McGraw-Hill.
Fernandez, C., & Ley, C. (2010). Introduction to linear regression analysis (5th ed.). Hoboken, NJ: John Wiley & Sons.
Thompson, B. (2011). Analysis of variance (ANOVA) and extra sum of squares principle (ESSP). Retrieved from https://stats.stackexchange.com/questions/3235/anova-and-extra-sum-of-squares-principle-essp