Running a linear regression in R, Python, Julia, and Octave

The following code block shows how to run such a one-factor linear regression in R:

> set.seed(12345)
> x<-1:100
> a<-4
> beta<-5
> errorTerm<-rnorm(100)
> y<-a+beta*x+errorTerm
> lm(y~x)

The first line of set.seed(12345) guarantees that different users will get the same random numbers when the same seed() is applied, that is, 12345 in this case. The R function rnorm(n) is used to generate n random numbers from a standard normal distribution. Also, the two letters of the lm() function stand for linear model. The result is shown here:

Call: lm(formula = y ~ x)
Coefficients: 
(Intercept) x 
4.114 5.003

The estimated intercept is 4.11, while the estimated slope is 5.00. To get more information about the function, we can use the summary() function, shown in the following code:

> summary(lm(y...