## Code

```
# Allow only 1 d.f. for three of the predictors
<-
prostate transform(prostate,
ekg.norm = 1*(ekg %in% c("normal","benign")),
rxn = as.numeric(rx),
pfn = as.numeric(pf))
# Force pfn, rxn to be linear because of difficulty of placing
# knots with so many ties in the data
# Note: all incomplete cases are deleted (inefficient)
<- redun(~ stage + I(rxn) + age + wt + I(pfn) + hx +
r + dbp + ekg.norm + hg + sz + sg + ap + bm,
sbp r2=.3, type='adjusted', data=prostate)
r
```

```
Redundancy Analysis
~stage + I(rxn) + age + wt + I(pfn) + hx + sbp + dbp + ekg.norm +
hg + sz + sg + ap + bm
n: 483 p: 14 nk: 3
Number of NAs: 19
Frequencies of Missing Values Due to Each Variable
stage I(rxn) age wt I(pfn) hx sbp dbp
0 0 1 2 0 0 0 0
ekg.norm hg sz sg ap bm
0 0 5 11 0 0
Transformation of target variables forced to be linear
R-squared cutoff: 0.3 Type: adjusted
R^2 with which each variable can be predicted from all other variables:
stage I(rxn) age wt I(pfn) hx sbp dbp
0.658 0.000 0.073 0.111 0.156 0.062 0.452 0.417
ekg.norm hg sz sg ap bm
0.055 0.146 0.192 0.540 0.147 0.391
Rendundant variables:
stage sbp bm sg
Predicted from variables:
I(rxn) age wt I(pfn) hx dbp ekg.norm hg sz ap
Variable Deleted R^2 R^2 after later deletions
1 stage 0.658 0.658 0.646 0.494
2 sbp 0.452 0.453 0.455
3 bm 0.374 0.367
4 sg 0.342
```

## Code

`r2describe(r$scores, nvmax=4) # show strongest predictors of each variable`

```
Strongest Predictors of Each Variable With Cumulative R^2
stage
sg (0.51) + bm (0.57) + ap (0.572) + ekg.norm (0.573)
I(rxn)
sbp (0.009) + bm (0.015) + hg (0.023) + wt (0.026)
age
hx (0.027) + ekg.norm (0.044) + hg (0.052) + bm (0.061)
wt
hg (0.068) + dbp (0.107) + bm (0.117) + sbp (0.124)
I(pfn)
ap (0.099) + bm (0.138) + hg (0.148) + sbp (0.157)
hx
ekg.norm (0.039) + sg (0.059) + age (0.075) + sbp (0.083)
sbp
dbp (0.399) + age (0.419) + I(pfn) (0.427) + ekg.norm (0.433)
dbp
sbp (0.399) + age (0.416) + hg (0.425) + wt (0.43)
ekg.norm
hx (0.039) + age (0.055) + sbp (0.069) + bm (0.077)
hg
bm (0.087) + wt (0.132) + I(pfn) (0.141) + I(rxn) (0.15)
sz
sg (0.143) + bm (0.157) + sbp (0.161) + dbp (0.165)
sg
stage (0.51) + sz (0.546) + hx (0.551) + ekg.norm (0.553)
ap
I(pfn) (0.099) + bm (0.15) + stage (0.155) + sbp (0.159)
bm
stage (0.254) + I(pfn) (0.299) + hg (0.33) + ap (0.348)
```