R: How to convert a string to a list variable in for loop?

Here's an approach using lapply and split which will return a list with one element per chick and each chick-element in the list is itself a list with three components: the model, model summary and residuals.

res <- lapply(split(ChickWeight, paste0("Chick", ChickWeight$Chick)), function(x) {
  Fit <- lm(x$Time ~ x$weight)
  list(
    Regr = Fit,
    Sum = summary(Fit),
    Residual = residuals(Fit)
  )
})

Now, to look at the results, e.g. for "Chick1" you can do:

> res$Chick1
$Regr

Call:
lm(formula = x$Time ~ x$weight)

Coefficients:
(Intercept)     x$weight  
     -2.487        0.120  


$Sum

Call:
lm(formula = x$Time ~ x$weight)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.5545 -1.1895  0.2818  1.3340  1.7635 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -2.486826   0.980399  -2.537   0.0295 *  
x$weight     0.120031   0.007868  15.255 2.97e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.507 on 10 degrees of freedom
Multiple R-squared:  0.9588,    Adjusted R-squared:  0.9547 
F-statistic: 232.7 on 1 and 10 DF,  p-value: 2.974e-08


$Residual
          1           2           3           4           5           6           7 
-2.55448776 -1.63476925 -0.59501946  0.80482416  1.36444885  1.32391715  1.76351056 
          8           9          10          11          12 
 1.48291632  0.60216569 -0.03852238 -1.39939812 -1.11958577 

Or, if you want to get only the residuals of chick1, you can do:

> res$Chick1$Residual
          1           2           3           4           5           6           7 
-2.55448776 -1.63476925 -0.59501946  0.80482416  1.36444885  1.32391715  1.76351056 
          8           9          10          11          12 
 1.48291632  0.60216569 -0.03852238 -1.39939812 -1.11958577 

Edit after comment:

I never work with assign so I won't suggest any use of it here either but if you want to use a for loop, you could do it like this (or somehow similar):

chicks <- unique(ChickWeight$Chick)
res <- vector("list", length = length(chicks))

for(i in chicks) {
  DataSub <- ChickWeight[ChickWeight$Chick == i, ]
  Fit <- lm(DataSub$Time ~ DataSub$weight)
  res[[i]] <- list(
    Regr = Fit,
    Sum = summary(Fit),
    Residual = residuals(Fit)
  )
}