Download Powerpoint 3.1 B

AP Statistics Section 3.1B
Correlation
A scatterplot displays the direction,
form and the strength of the
relationship between two
quantitative variables.
Linear relations are particularly
important because a straight line is
a simple pattern that is quite
common.
We say a linear relation is strong if
the points lie close to a straight
line
and weak if
they are widely scattered about
the line.
Relying on our eyes to try to judge
the strength of a linear relationship
is very subjective. We will be
determining a numerical summary
called the __________.
correlation
The correlation ( r ) measures the
direction and the strength of the
linear relationship between two
quantitative variables.
The formula for correlation of variables x and y
for n individuals is:
1 n  Xi  X

r

n  1 i1  sX
 Yi  Y 


 s 
 Y 
where Xi and Yi are values
for the first individual , X 2
and Y2 the second individual ,
etc.
TI 83/84: Put data into 2 lists, say L1 and L2
STAT CALC 8:LinReg(a+bx) L1, L2 ENTER
Note: If r does not appear,2nd 0 (Catalog)
Scroll down to “Diagnostic On”
Press ENTER twice
Find r for the data on sparrowhawk
colonies from section 3.1 A
r  .7485
Important facts to remember when
interpreting correlation:
1. Correlation makes no distinction
between __________
explanatory and
________
response variables.
2. r does not change when we
change the unit of measurement
of x or y or both.
3. Positive r indicates a ________
positive
association between the variables
and negative r indicates a
________
negative association.
4. The correlation r is always
between ___
 1 and ___.
1 Values of r
near 0 indicate a very _____
weak
relationship.
Example 1: Match the scatterplots
below with their corresponding
correlation r
6
4
2
1
3
5
Cautions to keep in mind:
1. Correlation requires both
variables be quantitative.
2. Correlation does not describe
curved relationships between
variables, no matter how strong.
3. Like the mean and standard
deviation, the correlation is NOT
resistant to outliers.
What effect does adding an outlier
have on r and why?
r will move closer to zero, because with the outlier
the points do not lie as close to a straight line as they
would without the outlier.
4. Correlation is not a complete
summary of two-variable data.
Ideally , give the mean and
standard deviations of both x and y
along with the correlation.