问如何循环gls()函数，使数据框的每一列回归到一组独立变量上

EN

library(nlme)
#Data
df <- data.frame(a=rnorm(10,1,2),
                 b=rnorm(10,1,5),
                 c=rnorm(10,1,10),
                 d=rnorm(10,1,1),
                 e=rnorm(10,1,8),
                 f=rnorm(10,2,2),
                 g=rnorm(10,1,9),
                 h=rpois(10,0.8))
#Code
index <- which(names(df)!='h')
#List
List <- list()
#Loop 
for(i in index)
{
  #name covariates
  v1 <- names(df[,i,drop=F])
  v2 <- 'h'
  v3 <- as.formula(paste0(v1,'~',v2))
  List[[i]] <- gls(v3,data=df)
  names(List)[i] <- v1
}
List

List
$a
Generalized least squares fit by REML
  Model: v3 
  Data: df 
  Log-restricted-likelihood: -19.74037

Coefficients:
(Intercept)           h 
  1.7981345   0.4395727 

Degrees of freedom: 10 total; 8 residual
Residual standard error: 2.252625 

$b
Generalized least squares fit by REML
  Model: v3 
  Data: df 
  Log-restricted-likelihood: -22.96146

Coefficients:
(Intercept)           h 
   1.562261   -3.610542 

Degrees of freedom: 10 total; 8 residual
Residual standard error: 3.36939 

$c
Generalized least squares fit by REML
  Model: v3 
  Data: df 
  Log-restricted-likelihood: -27.98972

Coefficients:
(Intercept)           h 
  -2.839797    3.759619 

Degrees of freedom: 10 total; 8 residual
Residual standard error: 6.31713 

$d
Generalized least squares fit by REML
  Model: v3 
  Data: df 
  Log-restricted-likelihood: -12.75595

Coefficients:
(Intercept)           h 
  1.0048859   0.7997716 

Degrees of freedom: 10 total; 8 residual
Residual standard error: 0.9408642 

$e
Generalized least squares fit by REML
  Model: v3 
  Data: df 
  Log-restricted-likelihood: -30.02588

Coefficients:
(Intercept)           h 
-0.08323116 -0.11157127 

Degrees of freedom: 10 total; 8 residual
Residual standard error: 8.148097 

$f
Generalized least squares fit by REML
  Model: v3 
  Data: df 
  Log-restricted-likelihood: -19.21926

Coefficients:
(Intercept)           h 
  2.7446886  -0.1064889 

Degrees of freedom: 10 total; 8 residual
Residual standard error: 2.110568 

$g
Generalized least squares fit by REML
  Model: v3 
  Data: df 
  Log-restricted-likelihood: -29.19166

Coefficients:
(Intercept)           h 
   8.483339   -4.746078 

Degrees of freedom: 10 total; 8 residual
Residual standard error: 7.341237 

rg <- names(d)[!names(d) %in% "h"]
setNames(lapply(rg, function(x) 
  lm(reformulate(x, "h"), d)[c("coefficients", "residuals")]), rg)
# $a
# $a$coefficients
# (Intercept)           a 
# -0.1397861   1.5754488 
# 
# $a$residuals
# 1           2           3           4           5           6           7 
# 0.39570210 -1.23447278  1.18733412  1.54241624 -1.48755817  2.11774373 -1.67997168 
# 8           9          10          11          12          13          14 
# 0.73094508  0.86101269  1.73417911  0.51527327 -1.82142311  4.82370202  0.77177476 
# 15          16          17          18          19          20 
# -0.84239625 -1.94642481 -0.16537106 -0.08808104 -4.66894171 -0.74544252 
# 
# 
# $b
# $b$coefficients
# (Intercept)           b 
# 0.5718898   1.5104357 
# 
# $b$residuals
# 1            2            3            4            5            6 
# 2.307058939 -0.145249746  1.307418592 -0.006905091 -4.424897936  1.889070097 
# 7            8            9           10           11           12 
# 0.378266810  2.533283303  2.634312498  1.890371544  1.171424560  0.004782197 
# 13           14           15           16           17           18 
# 0.360489930  0.540625651 -2.526815303  0.937237885 -0.139997905 -3.699625069 
# 19           20 
# -5.578942652  0.568091696 
# 
# 
# $c
# $c$coefficients
# (Intercept)           c 
# 0.163988    1.552544 
# 
# $c$residuals
# 1          2          3          4          5          6          7 
# 1.9319809 -1.8673426  0.2785686  3.3639259  0.9698881  0.9748069  1.6573032 
# 8          9         10         11         12         13         14 
# -1.9639900  4.4070009  0.3136801  1.7674514  2.6942398 -0.1145370 -0.9693461 
# 15         16         17         18         19         20 
# -1.4955686 -1.6776488 -1.9715968 -4.7164340 -4.1706428  0.5882611 
# 
# 
# $d
# $d$coefficients
# (Intercept)            d 
# -0.007487103  1.058906754 
# 
# $d$residuals
# 1          2          3          4          5          6          7 
# 2.8121452 -2.4525667  1.0110283  0.9249691 -0.2128186  0.4389798  0.2134230 
# 8          9         10         11         12         13         14 
# -0.6501655  2.9336712  0.7397345  3.5432953  1.7442696  1.8430766  1.2099507 
# 15         16         17         18         19         20 
# -0.6099311 -1.6920376 -1.5589256 -4.8965761 -7.7081168  2.3665949 

set.seed(42)
d <- setNames(data.frame(matrix(rnorm(20*4), 20, 4)), letters[1:4])
d$h <- with(d, a + b + c + d + rnorm(20))