Linear Independence: Covariance and Statistical Dependence

This lecture covers the concept of covariance as a measure of linear independence between variables, exploring how it is used to estimate the degree of linear independence. It also delves into statistical dependence, examining how multiple responses vary with each other and discussing the conditional distribution of variables. The lecture further discusses the relationship between education and fertility, showcasing a scatter plot analysis and exploring the likelihood of finding specific combinations of values. Additionally, it presents a methodology for hypothesis testing and comparison statistics for continuous outcomes, including t-tests, ANOVA, non-parametric statistics, and correlation coefficients.