Simple linear regression is not a misnomer–– it is an uncomplicated technique for predicting a continuous outcome variable, Y, on the basis of just one predictor variable, X. As detailed in previous exercises, a number of assumptions are made so that we can model the relationship between X and Y as a linear function. Using our advertising dataset, we could model the relationship between the amount spent on podcast advertising in a month and the number of respective products eventually sold as follows:

$Y = beta_0 + beta_1*X + error$

Where…

Y: represents the dollar value of products sold

X: represents the amount spent on respective product podcast ads

Beta_0: is the intercept, or the number of products sold when no money has been spent on podcasts

Beta_1: is the coefficient, or the slope, of the line representing the relationship

Error: represents the random variation in the relationship between the two variables

To build this model in R, using the standard lm() package, we use the formula notation of Y ~ X:

model <- lm(sales ~ podcast, data = train)

But wait! Before building this model, we need to split our data into test and training sets For the development of this simple model, we’ll use a standard 60/40 split of our data; where 60% is used to train the model, and 40% is used to test the model’s accuracy and generalizability. We can randomly assign data points to test or training using base R’s sample() method and list indexing functionality

# specify 60/40 split
sample <- sample(c(TRUE, FALSE), nrow(advertising), replace = T, prob = c(0.6,0.4))
# subset data points into train and test sets
train <- advertising[sample, ]
test <- advertising[!sample, ]