Looping regression over increasing sample sizes in R - r

Question

I am trying to store the coefficients & SEs of a linear regression in R. The regression starts with a sample size of 10 and needs to add 1 for each loop up to 1000. I have generated random variables (using rnorm), created variables to store the values in and can get the code to store the first regression, but it stops after 1 loop (sample size 10). What am I missing in my code here? Thank you for your help.
matrix_coef <-NULL
df <- data.frame(yi, x1, x2)
for (i in 10:1000) {
lm(df)
matrix_coef <- summary(lm(df))
b0[i]<- coef(matrix_coef)[1:1, 1:1]
bx1[i] <- coef(matrix_coef)[2:2, 1:1 ]
bx2[i] <- coef(matrix_coef)[3:3, 1:1]
sd0[i] <- coef(matrix_coef)[1:1, 2:2]
sdx1[i] <- coef(matrix_coef)[2:2, 2:2]
sdx2[i] <- coef(matrix_coef)[3:3, 2:2]
}

Answer 1

You've got a few issues:
Inside the loop, df doesn't change, you're always fitting lm to the full data. You need to use i to change the data that the model trains on. Something like lm(df[1:i, ]), perhaps (assuming your full data has 1000 rows and you want the iterations to fit the first 10, then 11, then 12, ... 1000 rows, rather than, say, resampling each time)
The line lm(df) by itself fits a model, but you don't do store the results and your next line summary(lm(df)) fits the exact same model again.
You initialize the wrong object. matrix_coef <- NULL essentially does nothing. The line matrix_coef <- summary(lm(df)) inside your loop will have no problem creating the matrix_coef object. (And we can save a bunch of typing by defining it as coef(summary(lm(df))) and not typing coef() on all the subsequent lines.) However, the objects that you index should be initialized, and preferably to the correct length.
1:1 is the same as 1. 2:2 is the same as 2, etc.
Addressing all of these gives us this:
set.seed(47)
n <- 15 ## small n for demonstration purposes
df <- data.frame(yi = rnorm(n), x1 = rnorm(n), x2 = rnorm(n))
b0 <- numeric(n)
bx1 <- numeric(n)
bx2 <- numeric(n)
sd0 <- numeric(n)
sdx1 <- numeric(n)
sdx2 <- numeric(n)
for (i in 10:n) {
matrix_coef <- coef(summary(lm(df[1:i, ])))
b0[i] <- matrix_coef[1, 1]
bx1[i] <- matrix_coef[2, 1]
bx2[i] <- matrix_coef[3, 1]
sd0[i] <- matrix_coef[1, 2]
sdx1[i] <- matrix_coef[2, 2]
sdx2[i] <- matrix_coef[3, 2]
}
b0
# [1] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
# [9] 0.00000000 -0.17267676 -0.17490218 -0.08251370 -0.04048010 -0.04976162 -0.03881043
sdx2
# [1] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4888940
# [11] 0.4470402 0.4569932 0.4724890 0.4669553 0.4323498