Advanced Linear Regression Analysis

The course provides you with advanced methods to analyse your data. You learn to study the effects of subdividing your data into subgroups and to see the importance of different covariance structures in data. You will be trained to detect special features in data, like internal trend, gaps in data, tendency for grouping or non-linearity in data.


1. New horizon in mathematical modelling
2. The modelling clock
3. The H-principle and algorithms
4. Decompositions in linear models
5. Prediction in linear models
6. Weighing schemes
7. Ridge regression
8. Plots of latent structure
9. Model stationarity
10. Classification variables
11. Four aspects of modelling
12. Comparison of methods
13. Three data blocks
14. Sample subset selection
15. Multiple vs single latent structure
16. Robustness in linear models
17. Bootstrapping. Confidence intervals
18. Important/special response values
21. Presentation of results

1. Introduction and background

13. Subset selection*

2. Notation*

14. Case study*

3. Datasets*

15. Procedures and industrial data

4. Analysis of industrial data*

16. Comparison of methods

5. Scaling of data*

17. Path modeling

6. Orthogonal decompositions

18. Weighing procedures

7. H-principle of mathematical modeling

19. Multi-way data analysis

8. Algorithms associated with the H-principle

20. Non-linear modeling

9. Prediction variance

21. Ridge Regression (RR)*

10. Mean squared error

22. Linear dynamic models*

11. Measures of fit and precision

23. Mixed linear models*

12. Dimension of models*

24. Summary*