Suppose I have the following data
x<-rnorm(100,1,10000)
y<-rnorm(100,1,10000)+2*x+x^2
If I use the lm function as follows:
model1<-lm(y~x+x^2)
The R does not understand that it is to put between the independent variables the term x squared. It simply ignores the term and regresses the model as the code below:
model2<-lm(y~x)
Use model1 <- lm(y ~ x + I(x^2)) .
The problem is that characters like + , - , * , and ^ have specific meanings inside a formula; the I function causes its expression ( x^2 ) to be interpreted literally as potentiation.
Another way to do regression is to use the poly
x<-rnorm(100,1,10000)
y<-rnorm(100,1,10000)+2*x+x^2
model1<-lm(y~poly(x,degree=2,raw=T))
Whenever you want to use a function of some variable, you can use the function I() .
x<-rnorm(100,1,100)
y<-rnorm(100,0,10)+2*x+x^2
mod <- lm(y~x+I(x^2))
The advantage of using I() in relation to creating a new variable with x^2 values is that you do not need to specify x^2 values to perform projections, just enter x .
predict(mod, data.frame(x=1:3))
1 2 3
2.211883 7.209663 14.207509