Total sum of squares | EPFL Graph Search

Are you an EPFL student looking for a semester project?

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

In statistical data analysis the total sum of squares (TSS or SST) is a quantity that appears as part of a standard way of presenting results of such analyses. For a set of observations, , it is defined as the sum over all squared differences between the observations and their overall mean .: For wide classes of linear models, the total sum of squares equals the explained sum of squares plus the residual sum of squares. For proof of this in the multivariate OLS case, see partitioning in the general OLS model. In analysis of variance (ANOVA) the total sum of squares is the sum of the so-called "within-samples" sum of squares and "between-samples" sum of squares, i.e., partitioning of the sum of squares. In multivariate analysis of variance (MANOVA) the following equation applies where T is the total sum of squares and products (SSP) matrix, W is the within-samples SSP matrix and B is the between-samples SSP matrix. Similar terminology may also be used in linear discriminant analysis, where W and B are respectively referred to as the within-groups and between-groups SSP matrices.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (8)

Related lectures (32)

Partition of sums of squares

The partition of sums of squares is a concept that permeates much of inferential statistics and descriptive statistics. More properly, it is the partitioning of sums of squared deviations or errors. Mathematically, the sum of squared deviations is an unscaled, or unadjusted measure of dispersion (also called variability). When scaled for the number of degrees of freedom, it estimates the variance, or spread of the observations about their mean value.

Total sum of squares

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Linear Regression: Simple EE-209: Elements of statistics for data science

Introduces simple linear regression, properties of residuals, variance decomposition, and the coefficient of determination in the context of Okun's law.

Distribution Estimation COM-406: Foundations of Data Science

Covers the estimation of distributions using various methods such as minimum loss and expectation.

Multilinear Regression: Design Optimization ENG-606: EU EIT Urban Mobility 3-day seminar

Explores multilinear regression, design optimization, ANOVA, model fit, and experimental design.