Correlation Session

54
Correlation part 1 Relationship between variables...

description

Scatter diagrams, strong and weak correlation, positive and negative correlation, lines of best fit, extrapolation and interpolation. Aimed at UK level 2 students on Access and GCSE Maths courses.

Transcript of Correlation Session

Page 1: Correlation Session

Correlation part 1

Relationship between variables...

Page 2: Correlation Session

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

Page 3: Correlation Session

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?

Page 4: Correlation Session

“Children brought up in homes with more household appliances tend to perform better in school. Therefore, household appliances improve intelligence.”

Page 5: Correlation Session

“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/

Page 6: Correlation Session

Correlation does not imply causation...

Page 7: Correlation Session

...but the existence of a correlation can flag something worth investigating...

Page 8: Correlation Session

Taller people might be heavier than shorter people, but you will have to allow for body shape

Page 9: Correlation Session

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...

Page 10: Correlation Session

Scatter diagram

Another chart – X Y plot in MS Excel

Page 11: Correlation Session

The student data set handout...

Page 12: Correlation Session

Forearm and handspan

Page 13: Correlation Session

16 17 18 19 20 21 22 23 24 2535

37

39

41

43

45

47

49

51

Scatter diagram of forearm length and handspan width

Handspan (cm)

Fo

rea

rm (

cm)

Page 14: Correlation Session

16 17 18 19 20 21 22 23 24 2535

37

39

41

43

45

47

49

51

Scatter diagram of forearm length and handspan width

Handspan (cm)

Fo

rea

rm (

cm)

Page 15: Correlation Session

Serge Rachmaninov could play a left hand chord of C E-Flat G C G

Page 16: Correlation Session

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?

Page 17: Correlation Session

Describing the pattern

Words and ellipses

Page 18: Correlation Session
Page 19: Correlation Session
Page 20: Correlation Session

StrongPositiveCorrelation

No correlation, little relationship

ModerateNegativeCorrelation

Page 21: Correlation Session

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?

Page 22: Correlation Session

Line of best fit

Only for medium to strong correlations...

Page 23: Correlation Session
Page 24: Correlation Session
Page 25: Correlation Session

1. Follows trend of points

Page 26: Correlation Session

1. Follows trend of points

2. Roughly equal numbers of points above and below line

Page 27: Correlation Session

1. Follows trend of points

2. Roughly equal numbers of points above and below line

3. Does not (necessarily) pass through any given point

Page 28: Correlation Session

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!

Page 29: Correlation Session
Page 30: Correlation Session
Page 31: Correlation Session

Too shallow

Page 32: Correlation Session

Too Steep

Page 33: Correlation Session

Lines of best fit will pivot around the point which represents the mean of the X and the mean of the Y variables.

Page 34: Correlation Session

Using LOBF to make predictions

Drawing lines on the graph

Page 35: Correlation Session

Y

X

Page 36: Correlation Session

Y

X

Page 37: Correlation Session

Y

X

Page 38: Correlation Session

Y

X

Predicting a value of the X variable from the Y value

Page 39: Correlation Session

Y

X

Page 40: Correlation Session

Y

X

Page 41: Correlation Session

Y

X

Predicting a value of the Y variable from the X value

Page 42: Correlation Session

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?

Page 43: Correlation Session

Interpolation and extrapolation

Safe data processing

Page 44: Correlation Session

Y

X

The LOBF has been drawn beyond the range of the data

Page 45: Correlation Session

Y

X

Page 46: Correlation Session

Y

X

Could be a small part of a curve – and the curve could go either way...

Page 47: Correlation Session

Y

X

Page 48: Correlation Session

Y

X

Interpolation- Predictions within the range of the data points safe...

Page 49: Correlation Session

Y

X

Page 50: Correlation Session

Y

X

Page 51: Correlation Session

Y

X

Page 52: Correlation Session

Y

X

Page 53: Correlation Session

Y

X

Extrapolation- Predictions outside the range of the data points unsafe... very large errors possible

Page 54: Correlation Session

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 7½

● 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