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1
Chapter 7
(Scatterplots, Association, Correlation)
In chapters 79 we will be considering relationships/associations between
two quantitative variables
measured
on the same set of individuals.
Similar to 1variable data, we should begin by graphing the data and then look for overall patterns or deviations
in the data.
Scatterplots are used to plot 2variable data.
Both variables must be quantitative variables (can be measured numerically)
A scatterplot is simply a plotting of data points with one variable graphed on the horizontal axis (xaxis) and the
other variable graphed on the vertical axis (yaxis).
Graphing data via a scatterplot allows us to see the overall
pattern of the data, along with identifying any striking deviations from the pattern (outliers).
The key features to look for in a scatterplot are Form, Direction, Strength, and Outliers.
Form – Is the association between the variables linear, curved, or other?
Direction – Is the association positive or negative?
A positive association
:
As one variable increases, the other variable also increases in value
A negative association
:
As one variable increases, the other variable decreases in value
Strength – How much scatter is present? (a measure of how closely the points follow a clear form)
Outliers – Points that lie outside the overall pattern of the data. (important to identify & research outliers)
Clusters/SubGroups – When there are distinct groupings of some data points
(separate the data into different groups and draw separate scatterplots for each cluster)
When using scatterplots to show the relationship between two variables, we must distinguish between the
explanatory (predictor)
variable and the
response
variable.
The explanatory variable explains (predicts)
changes in the response variable.
In other words, the response variable responds to changes in the explanatory
variable.
In algebra, we called the explanatory
variable the independent
variable, and the response
variable is
the dependent
variable.
(see pages 169170)
In a scatterplot, the explanatory variable is graphed on the horizontal axis (xaxis) and the response variable is
graphed on the vertical axis (yaxis).
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Activity 1:
The following table describes the ACT scores (from high school) and their undergraduate GPA (out of 4.00) for
15 randomly selected graduates receiving a bachelor’s degree from a major university last year.
ACT
22
21
18
27
24
26
19
21
28
20
22
19
23
24
29
GPA
2.85
3.08
2.30
3.46
2.75
3.18
2.41
2.75
3.58
2.47
2.70
2.34
2.63
2.90
3.23
A. Which is the explanatory variable and which is the response variable?
Explanatory Variable:
Response Variable:
B. Use your calculator to make a scatterplot of this sample data.
Click on STAT/EDIT & enter the given data into two lists.
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 Spring '08
 Ripol
 Statistics, Correlation

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