Transcript 7.1 Correlation?

Statistical Reasoning
for everyday life
Intro to Probability and
Statistics
Mr. Spering – Room 113
7.1 Correlation?
 Correlation…
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Correlation exists between two variables when higher
values of one variable consistently go with higher values
of another or when higher values of one variable
consistently go with lower values of another.
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Examples:
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Height and weight
Demand and price
Practice time and skill
Smoking and lung cancer
High cholesterol and heart disease
Etcetera, etcetera, etc.
7.1 Correlation?
Scatter Plots…Scatter Plot is a graph in which
each point corresponds to the values of two
variables…
…To be more specific, a scatter plot, scatter diagram or scatter
graph is a chart that uses Cartesian coordinates to display
values for two variables. The data is displayed as a collection of
points, each having one coordinate on the horizontal axis and
one on the vertical axis. A scatter plot does not specify
dependent or independent variables. Either type of variable can
be plotted on either axis. Scatter plots represent the association
(not causation) between two variables.
7.1 Correlation?
•Positive Correlation…
Both variables tend to increase (or decrease) together.
7.1 Correlation?
•Negative Correlation…
Two variables tend to change in opposite directions,
with one increasing while the other decreases.
Example:
7.1 Correlation?
Height and eye
color
•No Correlation…
There is no apparent relationship between the two
variables.
7.1 Correlation?
•Nonlinear relationship…
The two variables are related, but the relationship
results in a scatter plot that does not follow a straightline pattern.
7.1 Correlation?
•Correlation
Coefficient…
Coefficient represented by
the letter, r, measures the
strength of a correlation.
[TI-84 plus → STAT;
TESTS; LinRegTTest…
and LinRegTInt…scroll
down, look for r-value]
INTERPOLATING???
7.1 Correlation?
• Properties of the Correlation Coefficient, r.
1. The value of r is always between -1 and 1. That is
-1 ≤ r ≤ 1.
2. A positive correlation has a positive correlation if a scatter
diagram’s points lie closer to a rising straight line. They will
have an r-value closer to 1. A perfect positive correlation has a
coefficient of 1.
3. A negative correlation has a negative correlation if a scatter
diagram’s points lie closer to a descending straight line. They
will have an r-value closer to -1. A perfect negative correlation
has a coefficient of -1.
4. If there is no correlation, the points do not follow any ascending
or descending straight lines, and the r value is close to 0.
7.1 Correlation?
• Properties of the Correlation Coefficient, r.
LETS PLAY?!?!?!?!?!?
http://argyll.epsb.ca/jreed/math9/strand4/scatterPlot.htm
7.1 Correlation?
• Properties of the Correlation Coefficient, r.
• Calculating the correlation coefficient…
r
n   ( xy )  ( x)  ( y )
n  ( x 2 )  ( x) 2  n  ( y 2 )  ( y ) 2
Don’t get confused or mad, there
are no secrets in mathematics!
7.1 Correlation?
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HOMEWORK:
pg 295 # 1-17 all, # 23