Correlation part 1
Relationship between variables...
We are covering...
Idea of correlation
Plotting scatter diagrams
Describing the pattern of points
Drawing line of best fit and using the LOBF to make
predictions
Finding the difference between interpolation and
extrapolation
Activity 1: Read the following slides...
Look for holes in the arguments
Can you state what the fallacies might be?
Are they valid and false?
Or just invalid?
Children brought up in homes with more household appliances tend
to perform better in school. Therefore, household appliances
improve intelligence.
Underlying variable fallacy
Teens involved in violent crimes tend to play violent video
games. Therefore, playing violent video games causes teenagers to
get involved in criminal behaviour.
http://btr.michaelkwan.com/2009/01/10/correlation-does-not-imply-causation/
Reverse implication fallacy
Correlation does not imply causation...
...but the existence of a correlation can flag something worth
investigating...
Taller people might be heavier than shorter people, but you will
have to allow for body shape
Taller people might be heavier than shorter people, but you will
have to allow for body shape
Scatter diagrams can show you the relationship between
variables...
Have you spotted it?This thing is UPSIDE DOWN. The height axis
is goes the wrong way!
Scatter diagram
Another chart X Y plot in MS Excel
The student data set handout...
Forearm and handspan
Serge Rachmaninov could play a left hand chord of C E-Flat G C
G
Activity 2: plot scatter diagram
Plot your own scatter diagram of the hand span and forearm
data
What scale are you going to use?
Where will you start and finish the axes?
Compare your scatter diagram with someone else. Does the pattern
of crosses look about the same?
Describing the pattern
Words and ellipses
Strong
Positive
Correlation
No correlation, little relationship
Moderate
Negative
Correlation
Homework Q1
Plot a scatter diagram of Handspan vs Shoe Size from this data
set
Describe the pattern using the vocabulary developed on the last
slide
Do you think that the relationship between shoe size and hand
span might be stronger than the relationship between hand span and
fore arm length? What basis have you for your opinion?
Line of best fit
Only for medium to strong correlations...
1. Follows trend of points
1. Follows trend of points
2. Roughly equal numbers of points above and below line
1. Follows trend of points
2. Roughly equal numbers of points above and below line
3. Does not (necessarily) pass through any given point
1. Follows trend of points
2. Roughly equal numbers of points above and below line
3. Does not (necessarily) pass through any given point
4. Nothing special about outer points or axes origin!
Too shallow
Too Steep
Lines of best fit will pivot around the point which represents
the mean of the X and the mean of the Y variables.
Using LOBF to make predictions
Drawing lines on the graph
Y
X
Y
X
Y
X
Y
X
Predicting a value of the X variable from the Y value
Y
X
Y
X
Y
X
Predicting a value of the Y variable from the X value
Activity 3: Draw LOBF
Take your plot of the forearm and handspan length and draw a
line of best fit on the graph
Compare your LOBF with someone else. Is yours shallow or steep
or somewhere in the middle?
Use your graph to predict the forearm length of someone with a
hand span of 20.5 cm
Use your graph to predict the hand span of someone whose forearm
is 48cm long
How do the results compare with others? Which prediction varies
more?
Interpolation and extrapolation
Safe data processing
Y
X
The LOBF has been drawn beyond the range of the data
Y
X
Y
X
Could be a small part of a curve and the curve could go either
way...
Y
X
Y
X
Interpolation- Predictions within the range of the data points
safe...
Y
X
Y
X
Y
X
Y
X
Y
X
Extrapolation- Predictions outside the range of the data points
unsafe... very large errors possible
Homework Q2
Draw a LOBF on your shoe size and hand span scatter diagram
Use your LOBF to predict the hand span of someone with a shoe
size of 7
Use the LOBF to predict the shoe size of someone with a hand
span of 24.5 cm
Which prediction is the most reliable. Write a sentence to two
explaining your answer
Scatter diagram of forearm length and handspan widthHandspan
(cm)Forearm (cm)Column F
12450
22245
32147
42042
518.540
618.542
717.539
82146.4
922.543.8
1018.741
112040.5
122248
1317.137.8
1419.741.6
1517.243
Scatter diagram of forearm length and handspan widthHandspan
(cm)Forearm (cm)Column F
12450
22245
32147
42042
518.540
618.542
717.539
82146.4
922.543.8
1018.741
112040.5
122248
1317.137.8
1419.741.6
1517.243
