OLS Regression in R - r

Question

I am really struggling with the following problem set using R
.
I want to simulate a data set with one dependent and 20 independent variables that are normally i.i.d.. Each variable should have 100 observations. (I managed to do this part)
(Now the part I am struggling with):
My plan is to conduct automated regressions for all possible combinations of up to 5 regressor using an own coded regression function that simulates the output of summary(lm) that uses a vector y and a matrix or vector x as input (so my.lm(y,x)). And then bringing the results in a suitable data structure.
I would be thankful for every hint!

Answer 1

I doubt the soundness of what you are trying to do but here it goes.
I will make up a dataset, since you have not posted one.
my.lm <- function(x, y, n = 5){
f <- function(inx){
inx_cols <- Combn[inx, ]
inx_cols <- inx_cols[inx_cols != 0]
X <- as.data.frame(x[, inx_cols])
names(X) <- paste0("X", inx_cols)
X <- cbind(X, y)
name_y <- names(X)[length(names(X))]
fmla <- as.formula(paste(name_y, ".", sep = "~"))
tryCatch(lm(fmla, data = X), error = function(e) e)
}
nc_x <- ncol(x)
nr <- sum(choose(nc_x, seq_len(n)))
Combn <- matrix(0, nrow = nr, ncol = n)
first <- 1
for(i in seq_len(n)){
last <- first + choose(nc_x, i) - 1
Combn[first:last, seq_len(i)] <- t(combn(nc_x, i))
first <- last + 1
}
apply(Combn, 1, f)
}
set.seed(6876)
regr <- replicate(20, rnorm(100))
coefs <- sample(-5:5, 20, TRUE)
resp <- regr %*% coefs + rnorm(100)
lm_list <- my.lm(regr, resp)
length(lm_list)
#[1] 21699
So the function above produced as many objects as expected.
Before continuing, let's see how many are errors (singular matrix, for instance).
err_list <- lapply(lm_list, function(x){
if(inherits(x, "error")) x else NULL
})
err_list <- err_list[!sapply(err_list, is.null)]
length(err_list)
#[1] 0
No errors.
So get the summaries of the objects of class "lm".
good_list <- lapply(lm_list, function(x){
if(inherits(x, "lm")) x else NULL
})
good_list <- good_list[!sapply(good_list, is.null)]
smry_list <- lapply(good_list, summary)
smry_list[[1]]
#
#Call:
# lm(formula = fmla, data = X)
#Residuals:
# Min 1Q Median 3Q Max
#-34.654 -9.487 -1.985 9.486 50.213
#Coefficients:
# Estimate Std. Error t value Pr(>|t|)
#(Intercept) 0.6449 1.5237 0.423 0.673
#X1 -7.3969 1.5074 -4.907 3.68e-06 ***
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
#Residual standard error: 15.02 on 98 degrees of freedom
#Multiple R-squared: 0.1972, Adjusted R-squared: 0.189
#F-statistic: 24.08 on 1 and 98 DF, p-value: 3.684e-06