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In this paper we study the interrelationships between two sets of data measured on the same subjects via redundancy analysis. We consider redundancy analysis from an inferential point of view. Under the hypothesis of multinormality, tests of significance are obtained for each successive redundancy component so that only the significant factors are retained for prediction purposes. An example illustrates the method.

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Simple linear regression is extended to multiple linear regression (for multiple predictor variables) and to multivariate linear regression for (multiple response variables). Regression with circular data and/or categorical data is covered. How to select predictors and how to avoid overfitting with techniques such as ridge regression and lasso are followed by quantile regression. The assumption of Gaussian noise or residual is removed in generalized least squares, with applications to optimal fingerprinting in climate change.

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Testing the Significance of the Successive Components in Redundancy Analysis

5 - Linear Regression

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2 results

Testing the Significance of the Successive Components in Redundancy Analysis

5 - Linear Regression

Summary