Scatter Graphs (OCR GCSE Maths)

What is correlation?

• Correlation is a way of describing the way two quantities are related to each other
  • You may see this referred to as linear correlation
  • The word linear will not appear in an exam question
• Correlation can be one of three types
  • Positive correlation
    • This is where one quantity increases as the other quantity increases
    • Examples
      As the temperature increases, the sales of cold drinks increase
      As the age of a tree increases, its height increases
  • Negative correlation
    • This is where one quantity decreases as the other quantity increases
    • Examples
      The age of a car and its value
      The amount of daylight hours and the time spent indoors
  • No correlation
    • This is where there is no apparent relationship between the two quantities
    • Examples
      The batting average of a cricketer and the cost of a pint of milk
      The amount of time spent playing computer games and the weight of an elephant
• Note in some cases, a correlation might not be true all the time
  • For example, a tree will reach an age where it is fully grown and it's height no longer increase
• There could also be exceptions to quantities that have correlation
  • For example, an old, but rare, sports car may be worth a lot of money

What does the phrase "correlation doesn't mean causation" mean?

• Correlation only refers to whether two quantities are linked by the way their values increase or decrease
• It does not necessarily mean they are linked in real-life
  • One quantity increasing or decreasing does not cause the other quantity to increase or decrease
  • e.g. the volume of cheese eaten by a population and the number of marriages in that population
    • both could be increasing but an increase in the volume of cheese eaten does not cause people to get married
• It could be that the two quantities are not linked in real-life but can appear linked due to a third quantity - usually time
  • e.g. the height of a sunflower and the weight of a puppy
    
    • the height of a sunflower does not cause the weight of a puppy to change!
    • but both generally increase with time

What is a scatter graph?

• Scatter graphs are used to quickly see if there is a connection (correlation) between two pieces of data
  • For example a teacher may want to see if there is a link between grades in mathematics tests and grades in physics tests
• You may also come across scatter plots or scatter diagrams
  • these are the same as scatter graphs

What do scatter graphs look like?

• For each data pair, points are plotted
  • they are not joined up!
  • points are 'scattered' around the diagram
• The general shape the points form indicate the type of correlation they are showing

How do I draw a scatter graph?

• This is simply a matter of plotting points - usually from a table of values
  • be very careful which way round you are plotting them
  • this is particularly important when values are very similar

What is a line of best fit?

• If a scatter graph suggests there is a positive or negative correlation
  • a line of best fit can be drawn on the scatter graph
    • this can then be used to predict one data value from the other
      e.g. we can use the physics grade for a student to predict their maths grade

How do I draw a line of best fit?

• A line of best fit can be drawn by eye
  • it does not have to pass through any particular point(s)
    • however, in some cases it would make sense that it is drawn through the origin
      e.g. the height and weight of a kitten
  • there should roughly be as many points on one side of the line as the other
  • the spaces between the points and the line should roughly be the same on either side

How do I use a line of best fit?

• The line of best fit can be used to predict the value of one variable from the other variable
  • Predictions should only be made for values that are within the range of the given data
  • Making a prediction within the range of the given data is called interpolation
  • Making a prediction outside of the range of the given data is called extrapolation and is much less reliable
  • The prediction will be more reliable if the number of data values in the original sample set is bigger