omparing Two Quantitative Variables
Submitted by gfj100 on Fri, 10/30/2009  09:39
As we did when considering only one variable, we begin with a graphical display.
A
scatterplot
is the most useful display technique for comparing two quantitative variables. We
plot on the yaxis the variable we consider the
response
variable and on the xaxis we place
the
explanatory or predictor
variable.
How do we determine which variable is which? In general, the explanatory variable attempts to
explain, or predict, the observed outcome. The response variable measures the outcome of a
study. One may even consider exploring whether one variable
causes
the variation in another
variable – for example, a popular research study is that taller people are more likely to receive
higher salaries. In this case, Height would be the explanatory variable used to explain the
variation in the response variable Salaries.
In summarizing the relationship between two quantitative variables, we need to consider:
1.
Association/Direction (i.e. positive or negative)
2.
Form (i.e. linear or nonlinear)
3.
Strength (weak, moderate, strong)
Example
We will refer to the Exam Data set, (
Final.MTW
or
Final.XLS
), that consists of random sample
of 50 students who took Stat200 last semester. The data consists of their semester average on
mastery quizzes and their score on the final exam. We construct a scatterplot showing the
relationship between Quiz Average (explanatory or predictor variable) and Final (response
variable). Thus, we are studying whether student performance on the mastery quizzes explains
the variation in their final exam score. That is, can mastery quiz performance be considered a
predictor of final exam score? We create this graph using either Minitab or SPSS:
•
Using Minitab
•
Using SPSS
1.
Opening the Exam Data set.
2.
From the menu bar select Graph > Scatterplot > Simple
3.
In the text box under Y Variables enter Final and under X Variables enter Quiz Average
4.
Click OK
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View Full DocumentAssociation/Direction and Form
We can interpret from either graph that there is a
positive association
between Quiz Average
and Final: low values of quiz average are accompanied by lower final scores and the same for
higher quiz and final scores. If this relationship were reversed, high quizzes with low finals, then
the graph would have displayed a
negative association
. That is, the points in the graph would
have decreased going from right to left.
The scatterplot can also be used to provide a description of the
form
. From this example we can
see that the relationship is linear. That is, there does not appear to be a change in the direction in
the relationship.
Strength
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 Spring '11
 AndyRegards
 Linear Regression, Regression Analysis, quiz average

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