Want to share your content on R-bloggers? click here if you have a blog, or here if you don't. In this exercise, we cover some basics on frequency tables. We also briefly look at chi-square test for independence to find relationships of two variables. Before proceeding, it might be helpful to look over the help pages for the `table`, `summary`, and `margin.table` functions.

Answers to the exercises are available here.

If you obtained a different (correct) answer than those listed on the solutions page, please feel free to post your answer as a comment on that page.

Exercise 1
use the `attach()` command to load the trees dataset in R

Exercise 2
Use the `table()` command with the arguments: trees\$Height and trees\$Volume. This will generate a two-way frequency table. Store this in variable mytable.

Exercise 3
If you are familiar with excel pivot tables, then you will know this function. Use the margin.table( ) function to get the Height frequencies summed over Volume

Exercise 4
Use the `margin.table( )` function to get the Volume frequencies summed over Height.

Exercise 5
Now use the `table()` function again but using all the features of the trees dataset, that includes girth, height and volume. This will print out a multidimensional 3 way frequency table.

Exercise 6
Suppose you have a variable ‘a’ that stores a second sample of heights of trees.
``` a=c(70, 65, 63, 72, 80, 83, 66, 75, 80, 75, 79, 76, 76, 69, 75, 74, 85, 8, 71, 63, 78, 80, 74, 72, 77, 81, 82, 80, 86, 80, 87) ```
Use the cbind() to add the a column to your trees dataset. Store the results back into trees.

Exercise 7
Now create a 2 way frequency table between Height and a as the arguments. Store this table in mytable_2.

Exercise 8

Use the margin.table() function again from Q3 and get Height frequencies summer over a. What differences do you observe from the results of Q3.

Exercise 9
Chi Square test for independance:
a)Print the results of the summary() function on mytable. Note the Chi Square test for independance results and P value
b)Print the results of the summary() function on mytable_2. Note the Chi Square test for independance results and P value.

Exercise 10
What did the chi square test for independance help you to see?