R presents various ways to carry out linear regressions. The most natural way is to use the lm() function, the R build-in OLS estimator. In this post I will present you how to use lm() and run OLS on the following model

The lm() function requires you to specify the model and to indicate the object containing the data. You have to specify the model in lm() the following way

where and are replaced with the variables names.

The model would look the following way when specified in R. I assume that the data is stored in a data frame named df.

## use R build-in OLS estimaor (lm())
reg <- lm(y ~ x1 + x2 + x3, data=df)
summary(reg)

Furthermore, R offers several additional function in order to evaluate the regression output. Some of these post-regression functions are listed below

# several other useful functions
coefficients(reg) # show coefficients
anova(reg) # show anova table
vcov(reg) # show covariance matrix for model parameters
confint(reg, level=0.95) # CIs for model parameters
regted(reg) # show fitted values
residuals(reg) # show residuals
influence(reg) # show diagnostics

Finally, the lm() function is a complete wrapper around the OLS estimator in R. It provides little inside of the calculations carried out in the background. In the following post I rebuild the OLS estimator from scratch using R.  I go through every single step of the calculations and provide estimates of the coefficients, standard errors and p-values. Finally, I incorporate the presented code into a function and show that the function returns the same results as lm(). The manually constructed function can be found here.