Ch 4 – Describing the Relation between Two Variables
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
The following data set for a sample of 6 randomly middle-age 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
Systolic Blood Pressure, y
To construct a scatterplot of the data using the TI-83:
Name one column Age; name the other column SBP.
Enter the data into the two columns.
to be slightly smaller than the smallest value of x.
In this case, we
to be slightly larger than the largest value of x.
In this case, we set
Set Ymin to be slightly smaller than the smallest value of y; in this case,
to be slightly larger than the largest value of y; in this case,
= 1, and
Plot 1 On
, choose the first type, scatterplot.
enter the name of the x variable; for
, enter the name of the y variable.
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
The purpose of linear correlation analysis is to measure the strength of the linear relationship between
x and y.
If the relationship between the two does not appear to be linear, then linear correlation analysis
should not be done.