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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?