WARNING:
Due to the mere fact that we are covering chapter 10 before chapters 59, we will have to do a little
creative editing.
You will have to pay close attention to what is being covered in the notes and compare it to that in
the text.
Chapter 10
INTRODUCTION
Chapters 2 & 3 deal with data sets that have only one variable to consider.
Often times we need to know
information about two
variables.
Recall independent and dependent variables from chapter 1.
This is what we are
going to take a peek at in this chapter.
We will deal with
Simple Linear Regression (SLR)
.
In simple linear
regression we are looking at the relationship between a single dependent variable and an independent variable that
are both quantitative.
Linear regression, in general, can have more than one independent variable and a single
dependent variable.
We are not going to look at that.
Also, we will not cover
Multiple Linear Regression
(we
have multiple independent variables, too).
If the data is qualitative, there are other methods of dealing with the
data.
We are not covering those, either.
Regression
, in general, is defined on page 523 of your text as
a statistical
method used to describe the nature of the relationship between variables.
For simple linear regression, we need to look for a couple things:
Two (or more if it is not SLR) variables related
The variables are quantitative
One of the variables must be the independent variable and the other the dependent variable
Each pair of data (dependent and independent variables per person/subject) must be independent of the
other pairs of data.
We look for the data to be positively or negatively correlated.
Once we feel we have these conditions meet, we can then complete SLR to describe the relationship and predict
outcomes.
CORRELATION
SCATTERPLOT
Our first step in determining if the data is correlated is to complete a
scatter plot
. Scatter plots are simply the
graphing of paired data on the xyplane (which is also called the Rectangular Coordinate system, or Cartesion
Plane) .
My paired data will make ordered pairs (x, y).
The independent variable will be my
x
and the dependent
variable will be my
y
.
(Independentx, Dependenty)
Remember
y
depends on
x
.
Each subject will have its own
ordered pair that you will have to plot.
If you have 20 subjects, you have 20 ordered pairs to plot.
To plot the
ordered pairs, you must first draw and label the
x
and
y
axes.
Remember your
y
axis is always the vertical one.
After you draw and label the axes, then plot the ordered pairs.
You have then completed a scatter plot.
Example 1– pg 549
17. Larceny and Vandalism
A criminology student wishes to see if there is a relationship between the number of
larceny crimes and the number of vandalism crimes on college campuses in southwestern Pennsylvania. The data
are shown. Is there a relationship between the two types of crimes?
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 Spring '09
 Coefficient Of Determination, Regression Analysis, regression line

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