Dimension reduction and graphical exploration in regression including survival analysis.

Area of Science:

• Statistics
• Data Visualization
• Regression Analysis

Background:

• Exploratory and diagnostic stages of regression analysis can be challenging.
• Traditional methods may not fully leverage modern computational capabilities.
• Dimension reduction and visualization techniques offer potential improvements.

Purpose of the Study:

• To discuss recent advances in dimension reduction and visualization for regression analysis.
• To present selected methodologies and their applications.
• To highlight the integration of these methods within the Arc computer program.

Main Methods:

• Expository discussion of selected dimension reduction techniques.
• Application of these techniques to regression diagnostics.
• Demonstration of survival regression with censoring using new methods.

Main Results:

• Selected dimension reduction and visualization methods significantly enhance regression analysis.
• New results are presented for survival regressions with censoring.
• All discussed methodologies are implemented in the Arc software.

Conclusions:

• Advanced dimension reduction and visualization tools greatly facilitate regression analysis.
• The Arc program provides a unified platform for these modern statistical methods.
• The integration of graphics and regression methods improves data exploration and diagnostics.