Terminology:

Measurement or Quantitative Variables:
variables that involve measurement or
counting: e.g. number of pages in a book (count), number of students in class
(count), height (measured), weight (measured), exam score (measured).

Deterministic Relationship:
One variable is directly related to another.
For
example, if we know your height in inches we can easily convert the height to
centimeters by multiplying by 2.54

Statistical Relationship:
a relationship where a natural variability exists.
Consider the first exam scores and mean quiz score.
Although there is a
relationship between the performance on both of these variables, students having
the same mean quiz average did not achieve the same exam score.
For instance, 4
students have a quiz average of 92.22 but had the following exam scores: 73.3,
86.7, 86.7, and 96.7

Linear Relationship and Regression:
if there exists a statistical relationship
where one measurement variable reacts in a linear manner with a change in the
second measurement variable then we can employ what is called in statistics
regression methods
to explore and explain this linear relationship.
For instance,
if we can show that a linear relationship exists between mean quiz scores and
exam scores then we can use regression methods to explain and predict one
variable based on the other.

Response, Outcome, Dependent variable versus Explanatory, Independent,
Predictor variable:
in regression the response or outcome or dependent variable
is the variable we are interested in predicting or explaining using a second
variable called the explanatory or independent or predictor variable.
E.g. we want
to predict exam scores (response/outcome) based on mean quiz scores
(predictor/explanatory); explain the variation in weight (response/outcome) using
height (predictor/explanatory)
Determining Linear Relationship

Scatterplot:
this is a plot of points for the combinations of the observations of the
response and predictor variables putting the response on the Y or vertical axis and
the predictor on the X or horizontal axis.

For the scatterplot below what can you see?
i. Does the plot indicate any relationship?
ii. If yes, is it linear?
iii. If linear what direction?
 From this plot you can see that there appears to be a linear relationship that is positive.
That is, as Quiz Average increases so does Exam score.
A negative relationship evolves
when as the predictor variable increases the response decreases. (e.g. consider driving
speed and travel time: the faster you drive (i.e. speed increases) travel time decreases.
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 Fall '08
 SEIFRIEDTHOMASJ
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