Generate density plot of the F-distribution

The test statistic associated with ANOVA is the F-test (or F-ratio). Recall that when carrying out a t-test, you computed an observed t-value, then compared that with a critical value derived from the relevant t-distribution. That t-distribution came from a family of t-distributions, each of which was defined entirely by its degrees of freedom.

ANOVA uses the same principle, but instead an observed F-value is computed and compared to the relevant F-distribution. That F-distribution comes from a family of F-distributions, each of which is defined by two numbers (i.e. degrees of freedom), which we'll refer to as df1 and df2. The F-distribution has a different shape than the t-distribution and in this exercise, you'll generate a few density plots of the F-distribution to help visualize this.

Use the seq() function to create a variable x containing 200 numbers between 0 and 2. See ?seq if you need help with this.
Use df() to evaluate the densities for seven different t-distributions at these values of x. The t-distributions should have the following degrees of freedom (df1,df2): (1,1), (3,1), (6,1), (3,3), (6,3), (3,6) and (6,6). For example, dt(x, 5, 5) would evaluate the t-distribution with degrees of freedom (5,5) at all 200 values of x.
Create line plots of these densities, using different colors for each. Use plot() to create the first (with argument type = "l" for "line"), then use lines() to create the rest, so that the lines get added to the original plot instead of overwriting it.
Add a legend to the topright corner of your plot with the title "F distributions". In the script, you only have to fill in the first two arguments: "topright" and title = "___".

Exercise

Generate density plot of the F-distribution

Instructions