1. Quantitative Structure Activity Relationships (QSAR) -- 1.1. Introduction -- 1.2. Modification of Substances -- 1.3. Physico-Chemical Descriptors -- 1.4. Biological Descriptors -- 1.5. Prediction Model -- 1.6. The Development of an Insecticide: an Example -- 2. Linear Multivariate Prediction -- 2.1. Introduction -- 2.2. Multivariate Prediction -- 2.3. Prediction Criteria -- 2.4. Exploratory Graphical Methods -- 2.5. Method and Variable Selection -- 2.6. Assessment of the Goodness of Prediction of the Selected Model -- 3. Heuristic Multivariate Prediction Methods -- 3.1. Introduction -- 3.2. Principal Component Regression -- 3.3. Partial Least Squares -- 3.4. Dimension Selection -- 3.5. Example -- 4. Classical Analysis of Reduced Rank Regression -- 4.1. Introduction -- 4.2. QSAR: Biological Responses -- 4.3. Reduced Rank Regression Models -- 4.4. Extensions of the Standard Reduced Rank Regression Model -- 4.5. Prediction Criteria for the Rank Selection of Reduced Rank Regression Models -- 4.6. Variable Selection for Reduced Rank Regression Models -- 5. Bayesian Analysis of Reduced Rank Regression -- 5.1. Introduction -- 5.2. The Reduced Rank Regression Model -- 5.3. Markov Chain Monte Carlo Methods -- 5.4. Example -- 6. Case Studies -- 6.1. ®Voltaren: An Anti-Inflammatory Drug -- 6.2. Development of a Herbicide -- 7. Discussion -- A.1 Introduction -- A.2 Multivariate Regression MR -- A.3 Principal Component Analysis PCA -- A.4 Partial Least Squares PLS -- A.5 Canonical Correlation Analysis CCA -- A.6 Reduced Rank Regression with Diagonal Error Covariance Matrix RRR -- A.7 Redundancy Analysis RDA -- A.8 Software -- A.9 Matrix Algebra Definitions -- A.10 Multivariate Distributions -- References -- Main Notations and Abbreviations.