Ch 4 – Describing the Relation between Two Variables
Definition
:
When the values of two variables are measured for each member of a population or
sample, the resulting data is called bivariate
.
When both variables are quantitative, we may represent the data set as a set of ordered pairs of
numbers, (x, y).
The variable x is called the input (or independent) variable
; the variable y is called the
response (or dependent) variable
.
We may examine the relationship between the two variables
graphically using a scatter diagram, or scatterplot
.
Example
:
The following data set for a sample of 6 randomly middleage to elderly patients consists of
x = age of patient, and y = measured value of systolic blood pressure of patient.
We expect that as
people age, their blood pressure will increase.
We will examine the relationship between the two
variables.
Age, x
Systolic Blood Pressure, y
43
128
48
120
56
135
61
143
67
141
70
152
To construct a scatterplot of the data using the TI83:
1)
Choose
STAT
,
EDIT
.
Name one column Age; name the other column SBP.
2)
Enter the data into the two columns.
3)
Choose
WINDOW
.
Set
Xmin
to be slightly smaller than the smallest value of x.
In this case, we
set
Xmin
= 40.
Set
Xmax
to be slightly larger than the largest value of x.
In this case, we set
Xmax
= 72.
Set Ymin to be slightly smaller than the smallest value of y; in this case,
Ymin
= 118.
Set
Ymax
to be slightly larger than the largest value of y; in this case,
Ymax
= 155.
Set
Xscl
= 1, and
Yscl
= 1.
4)
Choose
2
nd
,
STAT PLOT
.
Turn
Plot 1 On
.
For
Type
, choose the first type, scatterplot.
For
Xlist
,
enter the name of the x variable; for
Ylist
, enter the name of the y variable.
5)
Hit the
GRAPH
key.
In this example, we see an increasing, linear trend relationship between age and systolic blood
pressure, as expected.
If we want to see the coordinates of the data points, we use the
TRACE
key.
Linear Correlation
The purpose of linear correlation analysis is to measure the strength of the linear relationship between
x and y.
Note
:
If the relationship between the two does not appear to be linear, then linear correlation analysis
should not be done.
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Types of relationships:
1)
If there is an increasing linear trend relationship, so that larger values of x tend to be associated
with larger values of y, then we say that there is a positive correlation between x and y.
There may be
a strong positive linear trend relationship, if the data points cluster closely around a straight line; or a
weak positive linear trend relationship, if the data points are not all close to a straight line.
2)
If there is a decreasing linear trend relationship, so that larger values of x tend to be associated with
smaller values of y, then we say that there is a negative correlation between x and y.
There may be a
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 Fall '10
 Staff
 Statistics, Regression Analysis, Correlation and dependence, Pearson productmoment correlation coefficient, systolic blood pressure

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