Sum of Squares Definition
In regression analysis, sum of squares refers to a statistical method of analyzing how data series are generated and how they disperse. The goal of the analysis is to uncover how the data points or series are alloted a fitting function. Variation is another term that describes the sum of squares.
To calculate sum of squares, the formula below will be used;
Sum of squares=i=0∑n (Xi −X)2
In the above formula,
Xi =The ith item in the set
X=The mean of all items in the set
(Xi −X)=The deviation of each item from the mean
(The above formula is applicable for a set X of n items.)
A Little More on What is the Sum of Squares
Statistically, sum of squares evaluate how data series are dispersed and how they deviate from the mean. This analysis is important in the calculation of mean for a set of data points. Also, sum of squares tells us the extent of variation that has occurred to a set of measurement. The variation of data series is helpful in knowing how the values of data points fit into the available regression model.
While mean is defined as the average of a set of numbers, variation refers to a spread between individual values and the mean. Sum of squares is an important method of analysis that enable analysts find out the variation between data points as well as how each data point is fitted into a function before the points are summed up.
Also, the relationship between two variables be it a linear relationship or otherwise is determined through sum of squares. A variation between two variables that is unexplainable is known as residual sum of squares.
Here are some vital things to know about sum of Squares;
- In regression analysis, sum of squares is an analysis technique used in measuring the dispersion of data points.
- The sum of squares examine the deviation of data series from mean.
- When the sum of squares is high, it indicates that there is a huge variability within the data points, while a low sum of squares mean that there isn’t much variation between data points and the mean value.
Limitations of Using the Sum of Squares
Sum of squares might be difficult to analyze or interpret when additional data points are included in the set, this is a limitation because when this happens the sum of squares expands significantly. Oftentimes, sum of squares cannot be used in making decisions on investment. Analysts and investors are required to make detailed findings and various data analysis to know the degree of variability of an asset.
Sum of squares is important when using variance and standard deviation as measurements of variation. Also, the linear least squares method and non-linear least squares method of regression analysis make use of sum of squares.