AP Statistics Section 3.1BCorrelation
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
and weak if
the points lie close to a straight line
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:
Y
in
i X
i
s
YY
s
XX
nr
11
1
etc.
,individual second theY and
X ,individualfirst for the
valuesare Y and X where
2
2
ii
TI 83/84: Put data into 2 lists, say STAT CALC 8:LinReg(a+bx) ENTER
Note: If r does not appear,2nd 0 (Catalog) Scroll down to “Diagnostic On”Press ENTER twice
21,LL21 and LL
Find r for the data on sparrowhawk colonies from section 3.1 A
7485.r
Important facts to remember when interpreting correlation:
1. Correlation makes no distinction between __________ and
________ variables.explanatory
response
2. r does not change when we change the unit of measurement
of x or y or both.
3. Positive r indicates a ________ association between the variables
and negative r indicates a ________ association.
positive
negative
4. The correlation r is always between ___ and ___. Values of r
near 0 indicate a very _____ relationship.
1 1weak
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?
outlier. he without twould
they as linestraight a toclose as lienot do points the
outlier with thebecause zero, closer to move r will
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.