We investigate the extent to which it may be possible to carry out a regression analysis using graphics alone, an idea that we refer to as graphical regression. The limitations of this idea are explored. It is shown that graphical regression is theoretically possible with essentially no constraints on the conditional distribution of the response given the predictors, but with some conditions on marginal distribution of the predictors. Dimension reduction subspaces and added variable plots play a central role in the development. The possibility of useful methodology is explored through two examples.
- Added variable plots
- Dimension reduction subspaces
- Graphical regression
- Three-dimensional scatterplots
- conditional independence