Repeatedly Running Linear Models on Different Response Variables

I was recently asked by a coworker if there was an easy way to run multiple linear regression models on columns in a dataset. Basically, there were 4 predictor variables and then 199 columns of response variables, with each column being output from a sensor.

This is what I came up with (shown here with only 3 sensor response columns)

# Load packages
library(readr)

dataset <- read_csv("model-data.csv")  # read in data

sensors <- names(dataset[5:7]) # Get list of sensor column names

fit.list <- list() # Initialize the fit output list.

for(sensor in 1:length(sensors)) {
  y <- sensors[sensor]
  lm.formula <- as.formula(paste(y, "F1+F2+F3+F4", sep="~"))
  fit <- lm(lm.formula, data=dataset)
  fit.list[[y]] <- fit
}

fit.list

## $S1
## 
## Call:
## lm(formula = lm.formula, data = dataset)
## 
## Coefficients:
## (Intercept)           F1           F2           F3           F4  
##   2033.5685      -3.2984       2.3454       0.6821      -1.4307  
## 
## 
## $S2
## 
## Call:
## lm(formula = lm.formula, data = dataset)
## 
## Coefficients:
## (Intercept)           F1           F2           F3           F4  
##    2024.733        4.331       -1.898        2.837       -1.902  
## 
## 
## $S3
## 
## Call:
## lm(formula = lm.formula, data = dataset)
## 
## Coefficients:
## (Intercept)           F1           F2           F3           F4  
##    2055.860        2.403       -2.897       -4.088       -1.809

If you have any ideas on how this could be improved, please let me know.