General Mathematics Unit 2
Sample learning activity – variation and correlation
Introduction
The task involves varying the location of some points on a scatterplot and observing corresponding
changes in the value of the Pearson r correlation coefficient.
This activity should be carried out with the use of the relevant technology for constructing
scatterplots and calculating correlation coefficients and the equations of regression lines.
Part 1
Construct a set of 20 ordered pairs with integer coordinates randomly selected from within a given
interval of x values and a given interval of y values.
a. Draw a scatterplot of the corresponding points, calculate the correlation, and find the
equation of the corresponding regression line. Plot this line on the same set of axes.
b. Vary the location of some points to produce a close to 0.5 correlation, find the equation of
the corresponding regression line and plot this line on the same set of axes.
c. Vary the location of some points to produce a corresponding weak negative correlation, find
the equation of the corresponding regression line and plot this line on the same set of axes.
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Part 2
Choose a linear function with rule of the form y  ax  b where a and b are integers.
a. Generate a table of twenty (x, y) values, calculate the correlation, and find the equation of
the corresponding regression line.
b. Vary the location of one point and investigate how the correlation and the equation of the
corresponding regression line change. In each case plot the regression line on the same
set of axes as the chosen function.
c. Vary the location of some points to produce a scatterplot with close to zero correlation, find
the equation of the corresponding regression line and plot this line on the same set of axes.
Describe the scatterplot. What interpretation can be given to the equation of the regression
line in this case?
d. Vary the location of some points to produce a scatterplot with a correlation coefficient of
close to -0.4. Find the equation of the corresponding regression line and plot this line on the
same set of axes.
Part 3
Inspect a set of mixed scatterplots for which the correlation of each scatterplot is not known but
can be readily calculated. For each scatterplot estimate the correlation and compare this with the
calculated value.
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Areas of study
The following content from the areas of study is addressed through this learning activity.
Area of study
Topic(s)
Content dot point
Statistics
Investigating relationships
2, 3, 4
between two numerical variables
Outcomes
The following outcomes, key knowledge and key skills are addressed through this task.
Outcome
Key knowledge dot point
Key skill dot point
1
Investigating relationships between
Investigating relationships between
two numerical variables 2, 3, 4
two numerical variables 1, 2, 4
2
1, 2, 4
1, 3, 4
3
2, 3, 5
2, 3, 4, 5, 6, 8, 10
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