Chapter 14
Describing Relationships: Scatterplots and Correlation
In this chapter
•
Identifying correlation graphically
•
Quantifying a linear correlation
•
“Causal” research
Identifying correlation graphically
Correlation
– an association or relationship between two variables
Scatterplot
or
Scatter diagram
– displays the relationship between two quantitative
variables
•
X axis – (independent variable or explanatory variable)
•
Y axis – (dependent variable or response variable)
The relationship is like in algebra when dealing with functions. In statistics, you must
always decide which variable is X and Y based on which variable is dependent. The
difference between what is done in algebra and in this class comes from the definition of
a function; each X will have exactly one Y. That is not the case when dealing with data.
Commonly you will give two individuals the same X and get different values for Y.
Example
Suppose you have two variables, dosage of drug and reduction in blood pressure. Which
one should be your X and which one should by your Y? In this case reduction in blood
pressure is the Y variable because the reduction in blood pressure would be dependent on
the dosage of the drug. Therefore, the dosage of the drug is X, your independent variable.
Below is some sample data for this situation.
X = Dosage of Drug
Y = Reduction in Blood Pressure
100
10
200
18
300
32
400
44
500
56
In order to graph this data, you simply plot the points on the xyplane. Remember that we
are looking for a relationship or pattern in the data. The graph for this data follows:
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Dosage of Drug and Reduction in Blood Pressure
500
400
300
200
100
60
50
40
30
20
10
X
Y
Notice in the above graph there is a pattern in the data. As the dosage of the drug
increases, the reduction in blood pressure also increases. We will now look at the specific
patterns you need to be able to identify.
Perfect positive linear correlation
– We will focus on linear patterns in this class. For
the graph below, all the points are exactly on a line with a positive slope. We only say
perfect if all the points are exactly on a given function. Positive is used because the line
has a positive slope. It is important you use these exact terms.
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 Fall '10
 Bradley,W
 Statistics, Correlation, Causality, Correlation and dependence, Pearson productmoment correlation coefficient, Covariance and correlation, 20 30 40, Spearman's rank correlation coefficient

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