Tilde operator is used to define the relationship between dependent variable and independent variables in a statistical model formula. The variable on the left-hand side of tilde operator is the dependent variable and the variable(s) on the right-hand side of tilde operator is/are called the independent variable(s). So, tilde operator helps to define that dependent variable depends on the independent variable(s) that are on the right-hand side of tilde operator.
> Regression_Model <- lm(y~ x1 + x2 + x3)
Here, the object Regression_Model stores the formula for linear regression model created by using function lm and y is the dependent variable and x1, x2, and x3 are independent variables.
This model can be created by using a dot (.) if we want to include all the independent variables but for this purpose, we should have all the variables stored in a data frame.
> Regression_Data <- data.frame(x1, x2, x3, y) > Regression_Model_New < - lm(y~ . , data = Regression_Data)
This will have the same output as the previous model, but we cannot use tilde with dot if we want to create a model with few variables.
Suppose you want to create a new model with x1 and x3 only then it can be done as follows −
> Regression_Model_New1 <- lm(y~ x1 + x3, data = Regression_Data)
But we cannot do it using dot with tilde as −
> Regression_Model_New2_Incorrect <- lm(y~ . + x3, data = Regression_Data)