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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It

3.9 Bivariate HOME | Achievement Objectives | Overview | Data sets & Variable Types | Introduction | Scatter plots | Excel | iNZight | Correlation Coefficient & Linear Model | The effect of Groups & Unusual Values | Predictions | Causality | Non-Linear Models | Discussion & Conclusion | Report Writing

The effect of Unusual Values & Groups on 'r'

8

How Groups can effect 'r'

Groups can cause a relationship to be stronger, weaker, or have little effect. Investigate the influence of groups.

If there are groupings in your data that behave differently then consider fitting a different linear regression line for each grouping to test the influence of the group.

 

Starter 4

Effects of Groups
Class notes, Class notes
Class site

Booklet pg12

 

 

How Unusual Values can effect 'r'

The relative position of an Unusual Value han have a huge effect on the 'relationship'

Investigate the affect of Unusual Value and the robustness of the model.
Simulation, move the unusual value, (allow macros)

They may increase the strength of any relationship
They may reduce the strength of any relationship
They may have no influence on the strength of any relationship

Remember the CONTEXT!!!!

A good approach to modeling bivarate data is to complete the analysis including unusual values, and also analyse the data without unusual values. A comparison of the two models can be done, and a discussion of the significance, nature and appropriateness of the unusual values can be made.

Effects of Unusual Values
Class notes, Class notes

web links McDonalds outlier

The Effect of Unusual Values http://illuminations.nctm.org

Guessing http://istics.net

Class Exemplar:
Hawai'i Island Chain: Data csv, Information page |
Google Doc write up

Class Exemplar:
American New Cars 1993
Data csv, Information pdf |
Google Doc write up

Booklet pg9, 10, 11

 

The effect of Groups

Overlapping Groups

Groups causing a Stronger 'Relationship'

Groups causing a Weaker 'Relationship'

 

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The effect of Unusual Values

 

Activity:
Construct a scatterplot for the data set.
Calculate the correlation coefficient for the scatterplot.
Identify the unusual value and discuss its significance for the scatterplot.
Construct a second scatterplot with the unusual value removed
Calculate the correlation coefficient again
How has the correlation coefficient changed? What do you notice?

 

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