Scatter Graphs & Correlation (Cambridge International IGCSE Mathematics)

Correlation

What is correlation?

• Correlation describes how two quantities are related to each other

• Positive correlation is when one quantity increases and the other quantity increases

  • For example, as temperature increases, sales of cold drinks increase

• Negative correlation is when one quantity decreases while the other quantity increases

  • For example, the value of a car decreases as its age increases

• No (zero) correlation is where there is no apparent relationship

  • For example, the masses of snails and scores in an exam

What does the phrase "correlation does not imply causation" mean?

• If two quantities correlate, it does not mean that the first causes the second

• For example, each day you record the height of a sunflower and the weight of a puppy

  • As the height of the sunflower increases, the weight of the puppy increases

    • This is a positive correlation

  • But you cannot claim that:

    • If you want your puppy to weigh more, make your sunflower taller!
    • Sunflowers grow better when puppies are heavier!

  • Both quantities may be increasing due to another reason

    • In this case,time

Scatter Graphs

What are scatter graphs?

• Scatter graphs (or scatter diagrams) are used to plot pairs of data

  • For example, students' Maths grades against their Physics grades

• The vertical and horizontal axes represent the two quantities being measured

• Points are plotted as crosses, ×

  • They are not joined up

• The general shape formed by the points shows the type of correlation

  • Positive correlation goes from bottom left to top right

    • A positive gradient

  • Negative correlation goes from top left to bottom right

    • A negative gradient

  • No (zero) correlation looks like a cloud of points

• Correlations can be weak or strong

  • The stronger the correlation, the closer to a straight line the data points lie