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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

Scatterplots

4

Scatterplots

What is a scatter plot?
When investigating bivariate data making a scatter plot is the first step.

BEFORE you add any lines or curves to the scatter plot make a visual interpretation...in context

Is the association linear looking or not?
“There looks to be a linear association between .... and .... (or not)

If there looks like a linear association then you con preceded with applying a linear model.
(If there is no obvious association you should reconsider your variables)

What can we describe from a of scatter plot?
Describe the Trend. (Linear or non-Linear)
Describe the Association. (Positive or Negative)
Describe the Strength. (Weak, Moderate, Strong)
Describe the Groups or clusters (possible reasons or causes)
Describe the Unusual Values (any worth noting)
Describe the Scatter (Even or changing)

If the scatterplot indicates a linear model is appropriate then we can proceed.

Discuss what you see in your scatterplots
"from the scatterplot it appears that as (blah) increases then (blah) tends to increase also. Am I surprised by this? Why am I surprised or not by this (in context)

"i would expect that measurements of (blah) and (blah) are in proportion"

Investigate the effect of other variables or groups

Starter 2

Class notes, Class notes
Class site

Ex 13.01 p???

AIS  p99

Booklet pg2 (describe scatter plot & variable types, and research question.
Pg3, 4, 5

p44, p46 Ex 'A'

(Java app) Build your own scatter plot You can add points to the plot and move points around. See the effects on the least squares fitted line (the plotted line and its equation) and the correlation coefficient. (link to www.ruf.rice.edu)

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

What do I look for in scatterplots?

Trend

Do you see:  a linear trend…

 

or  a non-linear trend?

Association

Do you see: a positive association

as one variable gets bigger, so does the other


or  a negative association?

as one variable gets bigger, the other gets smaller

Strength

little scatter (Strong)

lots of scatter (Weak)

Groups

Do you see any groupings?

Unusual Values

Do you see any Unusual values


Is the unusual value an error or just different?
Do NOT remove it unless it is an error

Scatter

Do you see: constant scatter…  

roughly the same amount of scatter as you look across the plot

 

or non-constant scatter?

the scatter looks like a “fan” or “funnel”

 

 

Mean January Air Temperatures
for 30 New Zealand Locations

Average Age New Zealanders are First Married

 

 

 

% of population who are Internet Users vs
GDP per capita for 202 Countries

 

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