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The strength of a linear relationship may also be measured using the CORRELATION COEFFICIENT, r.
• The correlation coefficient is a number between -1 and 1.
• A positive sign indicates that y increases as x increases, a negative sign indicates that y decreases as x increases.
• The closer r is to zero the weaker the relationship.
• If r is 1 or -1, there is perfect correlation, that is, the points lie in one single line.
• r has no units
This table gives a ‘rule of thumb’ for how a relationship with a particular value of r may be described.
In summary:
What does the value of r tell us?
r measures how close the points in a scatter plot come to lying in a straight line.
It is a numerical measure of the scatter and therefore of the strength of a linear relationship.
The sign on r indicates the direction of the linear association.
The precision of a prediction depends on the strength of the relationship.
r is only used for linear relationships.
CAUTION
Use correlation only if you have two quantitative variables
Use correlation only if the relationship is linear.
Beware of outliers (see later)
Example Investigation - Body Fat Percentage
Example Investigation - Body Fat Percentage
Written Report - (so far)
Written Report - (so far)
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