F-test, critical value, and the decision rule

In the previous examples, we saw the F-value for the performance of the whole model. Now, let's look at the F-distribution. Assume that x₁ and x₂ are two independent random variables with the Chi-Square distribution with df₁ and df₂ degrees of freedom, respectively. The ratio of x₁/df₁ divided by x₂/df₂ would follow an F-distribution:

An R program to draw a graph for the F distribution with (10, 2) degrees of freedom is shown here:

> d1<-4 
> d2<-2 
> n<-100 
> x = seq(0, 5, length = n) 
> plot(x, df(x = x, df1 = d1, df2 = d2),type='l') 

The related plot is shown here:

The following R program shows the critical value for a given α of 0.1 and (1, 2) degrees of freedom:

> alpha<-0.1
> d1<-1
> d2<-1
> qf(1-alpha,df1=d1,df2=d2)
[1] 39.86346

The following Python program...