Unit 3 - The Coefficient of Determination

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Edit   Delete - Last Modified By: BJO at 18/03/2015 10:41:55 PM

Pearson's correlation coefficient can be calculated using the following:

 

 Look at the first bracketed term in the summation (the S bit)  Have you seen this before?

Yep, it's a z-score!

So, the "Pearson's Product-Moment Correlation Coefficient" can be described as the following:

"The sum of all of the z-scores of each point in the independent data set, multiplied by the z-score of the corresponding data point in the dependent data, averaged by dividing by the number of points minus one"

Good stuff!

 

Edit   Delete - Last Modified By: BJO at 19/03/2015 11:35:22 AM

It's important that you can describe what the coefficient of determination is: a lot of VCE exam questions will require you to do this for example, in Heffernan practice exam for 2012, there is a question regarding women's age of leaving school (dependent variable) and their mother's age of leaving school (independent variable):

" 1. Find the coefficient of determination for this data set. Express your answer correct to 4 decimal places.

2. Interpret the coefficient of determination found in part i. in terms of the variables age and mother’s age."

Let's say the coefficient of determination (r2) is 0.75.  What is the correct answer for 2. above?

To see the answer, drag and hold below:

It would be something like "75% of the variation in women's age of leaving school (dependent variable) can be explained by the variation in the age that their mothers left school (independent variable)".

Answer is in here ^

Edit   Delete - Last Modified By: BJO at 19/03/2015 9:30:55 AM

Check out these.

 

Edit   Delete - Last Modified By: BJO at 19/03/2015 11:40:20 AM

Here it is in MathSpeak:  COD = r * r,  or COD = r2

Is COD always positive? Why?  r is not!

Why do you need to know this?
You will see questions in past, and maybe the current exam, that will ask you to calculate the COD.  Other questions will ask you to "describe" it.

You need to be able to write that "the <percentage> variation in the <dependent variable> is due to the variation in the <independent variable>" - we'll do this in class if necessary.

Carrying on from what we did in the in the Pearson's Correlation Coefficient Learning Bite:
a) please calculate the value of the COD for the data set that you analysed.
b). Describe/Make a statement/Comment on this value.

When you have done a), b), above, please show your teacher.

For extra practice, please do Exercises 2G: Some/All