Scatter plots are similar to line graphs in that they
use horizontal and vertical axes to plot data points.
However, they have a very specific purpose. Scatter
plots show how much one variable is affected by another.
The relationship between two variables is called their
correlation .
Scatter plots usually consist of a large body of data.
The closer the data points come when plotted to making
a straight line, the higher the correlation between the
two variables, or the stronger the relationship.
If the data points make a straight line going from the
origin out to high x- and y-values, then the variables
are said to have a positive correlation . If
the line goes from a high-value on the y-axis down to
a high-value on the x-axis, the variables have a
negative correlation .
A perfect positive correlation is given the value of 1.
A perfect negative correlation is given the value of -1.
If there is absolutely no correlation present the value
given is 0. The closer the number is to 1 or -1, the
stronger the correlation, or the stronger the relationship
between the variables. The closer the number is to
0, the weaker the correlation. So something that seems
to kind of correlate in a positive direction might have
a value of 0.67, whereas something with an extremely weak
negative correlation might have the value -.21.
An example of a situation where you might find a perfect positive
correlation, as we have in the graph on the left above, would be
when you compare the total amount of money spent on tickets at
the movie theater with the number of people who go. This means
that every time that "x" number of people go, "y" amount of money
is spent on tickets without variation.
An example of a situation where you might find a perfect negative
correlation, as in the graph on the right above, would be if you
were comparing the speed at which a car is going to the amount of
time it takes to reach a destination. As the speed increases, the
amount of time decreases.
On the other hand, a situation where you might find a strong but not
perfect positive correlation would be if you examined the number of
hours students spent studying for an exam versus the grade received.
This won't be a perfect correlation because two people could spend the
same amount of time studying and get different grades. But in general
the rule will hold true that as the amount of time studying increases
so does the grade received.
Let's take a look at some examples. The graphs that were shown
above each had a perfect correlation, so their values were 1 and
-1. The graphs below obviously do not have perfect correlations.
Which graph would have a correlation of 0? What about 0.7? -0.7? 0.3?
-0.3?
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