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11.5 - Alternative: Standardize the Variables.11.4 - Interpretation of the Principal Components.11.2 - How do we find the coefficients?.11.1 - Principal Component Analysis (PCA) Procedure.Lesson 11: Principal Components Analysis (PCA).10.5 - Estimating Misclassification Probabilities.10.1 - Bayes Rule and Classification Problem.9.6 - Step 3: Test for the main effects of treatments.9.5 - Step 2: Test for treatment by time interactions.9.3 - Some Criticisms about the Split-ANOVA Approach.8.10 - Two-way MANOVA Additive Model and Assumptions.8.9 - Randomized Block Design: Two-way MANOVA.8.7 - Constructing Orthogonal Contrasts.8.4 - Example: Pottery Data - Checking Model Assumptions.8.2 - The Multivariate Approach: One-way Multivariate Analysis of Variance (One-way MANOVA).8.1 - The Univariate Approach: Analysis of Variance (ANOVA).

Lesson 8: Multivariate Analysis of Variance (MANOVA).

7.2.8 - Simultaneous (1 - α) x 100% Confidence Intervals.

7.2.7 - Testing for Equality of Mean Vectors when \(Σ_1 ≠ Σ_2\).

7.2.6 - Model Assumptions and Diagnostics Assumptions.

7.2.4 - Bonferroni Corrected (1 - α) x 100% Confidence Intervals.

7.2.2 - Upon Which Variable do the Swiss Bank Notes Differ? - Two Sample Mean Problem.

7.2.1 - Profile Analysis for One Sample Hotelling's T-Square.

7.1.15 - The Two-Sample Hotelling's T-Square Test Statistic.

7.1.12 - Two-Sample Hotelling's T-Square.

7.1.11 - Question 2: Matching Perceptions.

7.1.8 - Multivariate Paired Hotelling's T-Square.

7.1.7 - Question 1: The Univariate Case.

7.1.4 - Example: Women’s Survey Data and Associated Confidence Intervals.

7.1.1 - An Application of One-Sample Hotelling’s T-Square.

Lesson 7: Inferences Regarding Multivariate Population Mean.

6.2 - Example: Wechsler Adult Intelligence Scale.

Lesson 6: Multivariate Conditional Distribution and Partial Correlation.

5.2 - Interval Estimate of Population Mean.

5.1 - Distribution of Sample Mean Vector.

Lesson 5: Sample Mean Vector and Sample Correlation and Related Inference Problems.

4.7 - Example: Wechsler Adult Intelligence Scale.

4.6 - Geometry of the Multivariate Normal Distribution.

4.4 - Multivariate Normality and Outliers.

4.3 - Exponent of Multivariate Normal Distribution.

Lesson 4: Multivariate Normal Distribution.

Lesson 3: Graphical Display of Multivariate Data.

Lesson 2: Linear Combinations of Random Variables.

1.5 - Additional Measures of Dispersion.

Lesson 1: Measures of Central Tendency, Dispersion and Association.

The \((1 - α) \times 100%\) prediction ellipse above is centered on the population means \(\mu_\)

The geometry of the multivariate normal distribution can be investigated by considering the orientation, and shape of the prediction ellipse as depicted in the following diagram: