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The correlation
coefficient measures the degree or amount of the relationship between two
variables. The correlation coefficient is often represented by the symbol r.
If the points for the observations appear to be scattered randomly
in the scatterplot, then there is no relationship and the correlation coefficient
equals zero. When this page loads, the graph below shows an example of a random
scatter of points with a correlation of zero.
Shortly we will learn how to calculate the correlation coefficient. For now,
use the interactive graph below to see how the scatterplot looks for different
values of the correlation coefficient r.
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Move the slider to increase and decrease the relationship between the two
variables.
Click on the "Switch Sign" button to jump between positive and negative
relationships of the same strength.
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If the scores on the two variables tend to go up together, there is a
positive relationship between the two variables. In positive
relationships, if the score on one of the variables is high, the corresponding score
on the other variable tends to be high also. For example, height and weight of
people have a positive relationship: taller people generally are heavier than shorter
people and heavier people are generally taller than lighter people. When the
relationship is positive, the correlation coefficient has a positive sign.
If the scores on the two variables tend to go in opposite directions, there is a
negative relationship between the two variables. In negative
relationships, if the score on one of the variables is high, the corresponding
score on the other variable tends to be low. For example, speed of doing a task
and the accuracy with which the task is done have a negative relationship. At
high speeds, accuracy tends to be lower than for low speeds and accuracy tends to
be higher when speeds are low. When the relationship is negative, the correlation
coefficient has a negative sign.
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