Scatter Graphs | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Correlation

What is correlation?

• Correlation is a method used to explain the relationship between two quantities.
• It is often referred to as linear correlation, although the term "linear" is not typically used in exam questions.

Types of Correlation

• Positive correlation: This occurs when one quantity increases as the other quantity increases.
  • For instance, as the temperature rises, the sales of cold drinks tend to increase.
  • Another example is the height of a tree increasing as the tree's age advances.
• Negative correlation: This is observed when one quantity decreases as the other quantity increases.
  • For example, the value of a car typically decreases as the car ages.
  • Similarly, the time spent indoors tends to increase as the number of daylight hours decreases.
• No correlation: This describes a scenario where there is no recognizable relationship between two quantities.
  • For instance, there is no apparent connection between a cricketer's batting average and the cost of a pint of milk.
  • Another example could be the relationship between the time spent playing computer games and the weight of an elephant.

Exceptions and Considerations

• It is important to note that correlations may not always hold true under all circumstances.
• For example, a tree will eventually reach a maximum height, and its growth will cease despite its age increasing.
• Exceptions can also exist within correlated quantities, such as an old sports car that is rare and therefore retains a high value.

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

• Correlation refers solely to whether two quantities are connected by the way their values increase or decrease.
• It does not imply a direct causal relationship between the two quantities in real-life.
• An increase or decrease in one quantity does not necessarily cause a corresponding increase or decrease in the other quantity.
• For example, consider the volume of cheese consumed by a population and the number of marriages in that population.
  • Both could be increasing, but an increase in cheese consumption does not cause people to get married.
• Sometimes, apparent correlations between two quantities may arise due to a third factor, typically time.
• For instance, consider the height of a sunflower and the weight of a puppy.
  • The height of a sunflower doesn't influence the weight of a puppy.
  • Both variables may generally increase over time, leading to a perceived correlation.

Scatter Graphs

What is a scatter graph?

• Scatter graphs help us quickly visualize if there is a relationship (correlation) between two sets of data.
• For instance, a teacher might use scatter graphs to check if there's a connection between grades in math tests and physics tests.
• Scatter plots or scatter diagrams are also terms used interchangeably with scatter graphs.

What do scatter graphs look like?

• Points are plotted for each data pair without joining them.
• Points appear scattered around the diagram.
• The shape of the points indicates the type of correlation being shown.

Examples of Scatter Graphs:

How to Draw a Scatter Graph?

• Plot points usually from a table of values.
• Be cautious about how you plot them, especially when values are very similar.

Line of Best Fit

• If a scatter graph indicates a positive or negative correlation, a line of best fit can be drawn on the graph. This line helps predict one set of data values based on another. For instance, we might predict a student's math grade based on their physics grade.

How to Draw a Line of Best Fit?

• A line of best fit can be sketched by eye and doesn't have to pass through specific points.
• However, in certain scenarios, it may be appropriate for the line to pass through the origin.
  • For instance, when considering the height and weight of a kitten, drawing the line through the origin makes sense.
• Ideally, there should be approximately equal points on each side of the line.
• Additionally, the gaps between the points and the line should be roughly consistent on both sides.