Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004 AND Mathematical Studies Standard Level Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman Oxford University Press, 2012

Correlation Definition: Correlation - a mutual relationship or connection between two or more things. (google.com) When two set of data appear to be connected (i.e. when one set of data is dependent on the other) there are a various methods we can use to test this correlation: – Scatter Diagram – Line of Best Fit – Pearson’s Correlation Coefficient – Line of Regression

Correlation Vocabulary Bivariate data – data with two variables. Scatter Diagram – a graph that shows the relationship between two variables. Independent Variable – plotted on the horizontal axis. Dependent Variable – plotted on the vertical axis.

Types of Correlation In a positive correlation the dependent variable increases as the independent variable increases. In a negative correlation the dependent variable decreases as the independent variable increases. When the points are scattered randomly across the diagram there is no correlation.

Describing Correlation 1)Look for a direction: positive correlation negative correlation no correlation

Describing Correlation 2)Describe strength:

Describing Correlation 2)Describe strength:

3)Determine if the Trend is Linear: These points do not follow a linear trend. Describing Correlation

At a tournament, athletes throw a discus. The age and distance thrown are recorded for each athlete: Do you think the distance an athlete can throw is related to the person’s age? What happens to the distance thrown as the age of the athlete increases? Example How could you graph the data to more clearly see the relationship between the variables?

The discus throwing data: Be sure to put the: – independent variable along the horizontal axis – dependent variable along the vertical axis. Example

The manager of a recreation park thought that the number of visitors to the park was dependent on the temperature. There is a strong positive correlation between temperature and number of visitors to the park. Practice He kept a record of the temperature and the number of visitors over a two-week period. Plot these points on a scatter diagram and comment on the type of correlation. T(C) #V

A mathematical studies student wanted to check if there was a correlation between the predicted height of daisies and their actual height. There is a moderate positive correlation between predicted height and actual height. Practice Plot these points on a scatter diagram and comment on the type of correlation. P(cm) A(cm)