Explore the fundamental concepts and advanced applications of correlation in statistics through this comprehensive 2.5-hour tutorial. Delve into the properties and geometrical interpretation of Pearson's correlation coefficient, and master the intricacies of partial correlation across multiple scenarios. Examine multiple correlation, semipartial correlation, and various rank correlation methods including Spearman's and Kendall's Tau. Investigate the correlation of bivariate discrete distributions and the relationship between variate values and corresponding ranks. Learn to perform power and sample size calculations for multiple correlation coefficients using R, and understand the eigenvalue inequality for correlation matrices. Gain practical insights and theoretical knowledge to enhance your statistical analysis skills.