Cochran’s Theorem in Statistics: From Univariate to Multivariate Analysis

Cochran’s Theorem in Statistics: From Univariate to Multivariate Analysis

🔎 Introduction Cochran’s theorem is a cornerstone in statistical theory. It explains when quadratic forms of normal variables follow...

When Does a Quadratic Form Follow a Chi-Square Distribution?

When Does a Quadratic Form Follow a Chi-Square Distribution?

🔎 Motivation Quadratic forms arise in many statistical methods: Sample variance (measuring spread) Regression & ANOVA (part...

Multiple measurement, or observation, as row or column vector

Multiple measurement, or observation, as row or column vector

A multiple measurement or observation may be expressed as \[x=[\begin{matrix} 4 & 2 & 0.6 \\ \end{matrix}]\] referring to the p...

What is Multivariate Analysis?

What is Multivariate Analysis?

When researchers conduct a survey or experiment there are often many variables of interest. Multivariate analysis is a branch of stat...

What is singular and Non-singular?

What is singular and Non-singular?

If a matrix A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLx...

Canonical Correlation

Canonical Correlation

What is canonical Correlation? Canonical correlation analysis is a multivariate statistical model that facilitates the study of line...

Mean Vector and Covariance Matrix

Mean Vector and Covariance Matrix

The first step in analyzing multivariate data is computing the mean vector and the variance covariance matrix. Example: Sample data matr...