Linear Regression loop for each independent variable individually against dependent

This will do it for you.

lapply( mtcars[,-1], function(x) summary(lm(mtcars$mpg ~ x)) )

A data.frame object is a list with some other features so this will go through each column of mtcars excluding the first one and perform the regressions. If you save the resulting list in something like L then you can access each one easily by just using the same name or number as the column in the original data.frame. So L$cyl gives the regression summary for mpg on cyl.

A data.table version of Johns solution

library(data.table)
Fits <- 
    data.table(mtcars)[, 
              .(MyFits = lapply(.SD, function(x) summary(lm(mpg ~ x)))), 
              .SDcols = -1]

Some explanations of the code

• data.table will convert mtcars to a data.table object
• .SD is also a data.table object which contains the columns one wants to operate on
• .SDcols = -1 tells .SD not to use first column (as we don't want to fit lm(mpg ~ mpg)
• lapply just runs the model over all the columns in .SD (except the one we skipped) and returns objects of class list

Fit will a be list of summaries, you can inspect them using

Fits$MyFits

But you can also operate on them, for example, applying coef function on each fit

Fits[, lapply(MyFits, coef)]

Or getting the r.squered

Fits[, lapply(MyFits, `[[`, "r.squared")]

Hi try something like that :

models <- lapply(paste("mpg", names(mtcars)[-1], sep = "~"), formula)
res.models <- lapply(models, FUN = function(x) {summary(lm(formula = x, data = mtcars))})
names(res.models) <- paste("mpg", names(mtcars)[-1], sep = "~")
res.models[["mpg~disp"]]


# Call:
# lm(formula = x, data = mtcars)

# Residuals:
#     Min      1Q  Median      3Q     Max 
# -4.8922 -2.2022 -0.9631  1.6272  7.2305 

# Coefficients:
#              Estimate Std. Error t value Pr(>|t|)    
# (Intercept) 29.599855   1.229720  24.070  < 2e-16 ***
# disp        -0.041215   0.004712  -8.747 9.38e-10 ***
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# Residual standard error: 3.251 on 30 degrees of freedom
# Multiple R-squared:  0.7183,  Adjusted R-squared:  0.709 
# F-statistic: 76.51 on 1 and 30 DF,  p-value: 9.38e-10