Transcript stats_3_2

Reminder
Remember that both mean and standard
deviation are not resistant measures so
you want to take that into account when
calculating the correlation r.
 Review practice quiz for 3.2 quiz

AP Statistics, Section 3.2, Part 1
1
Warm Up
Select two quantitative variables for the
class and create a scatter plot to see if
there is an association.
OR
 Ladies

 Collect
the height in inches and shoes size
from the ladies and create a scatter plot.

Gentlemen
 Collect
the height in inches and shoes size
from the gentlemen and create a scatter plot.
Section 3.2
AP Statistics
Correlation


Is there a “correlation”
between a baseball
team’s “earned run
average” and the number
of wins?
Is the association strong
or weak?
Is the association
positively associated or
negatively associated?
Wins

2003 ERA vs Wins
ERA
Quality of
pitching
AP Statistics, Section 3.2, Part 1
4
Calculating Correlation


The calculation of
correlation is based
on mean and
standard deviation.
Remember that both
mean and standard
deviation are not
resistant measures.
 xi  x   yi  y 
1
r


 

n  1  sx   s y 
AP Statistics, Section 3.2, Part 1
5
Reminder

Remember that both mean and standard
deviation are not resistant measures so
you want to take that into account when
calculating the correlation r.
AP Statistics, Section 3.2, Part 1
6
Calculating Correlation
The formula
for calculating
 What does the
z-values.

Both z-values
are negative.
Their product
is positive.
contents of the
parenthesis look like?
What happens when
 xi  x
1
r


the values are both
n  1  sx
from the lower half of
Both z-values
the population? From
are positive.
the upper half?
  yi  y 

 
  sy 
Their product
is positive.
AP Statistics, Section 3.2, Part 1
7
Calculating Correlation

What happens when
one value is from the
lower half of the
population but other
value is from the
upper half?
 xi  x   yi  y 
1
r


 

n  1  sx   s y 
One z-value is positive
and the other is
negative. Their product
is negative.
AP Statistics, Section 3.2, Part 1
8
Using the TI-83 to calculate r

You must have
“DiagnosticOn” from
the “Catalog”
AP Statistics, Section 3.2, Part 1
9
Using the TI-83 to calculate r

Run LinReg(ax+b)
with the explantory
variable as the first
list, and the response
variable as the
second list
AP Statistics, Section 3.2, Part 1
10
Example
shoe size vs. height
STATCALC8:LinReg(a+bx)L1,L2
AP Statistics, Section 3.2, Part 1
11
Using the TI-83 to calculate r

The results are the
slope and vertical
intercept of the
regression equation
(more on that later)
and values of r and r2.
(More on r2 later.)
AP Statistics, Section 3.2, Part 1
12
On AP Exam
1.
Interpret the slope
 ERA
is the number of runs given up per
game by the pitcher
 For every run my team gives up, the team
losses 15games
2.
3.
Interpret the intercept
Interpret r
AP Statistics, Section 3.2, Part 1
13
Facts about correlation
Both variables need to be quantitative
 Because the data values are standardized,
it does not matter what units the variables
are in
 The value of r is unitless.

AP Statistics, Section 3.2, Part 1
14
Facts about correlation





The value of r will always be between -1 and 1.
Values closer to -1 reflect strong negative linear
association.
Values closer to +1 reflect strong positive linear
association.
Values close to 0 reflect no linear association.
Correlation does not measure the strength of
non-linear relationships
AP Statistics, Section 3.2, Part 1
15
Interpreting r
If the -1<r<-.75, the association is called
“strong negative” linear association
 If the -.75<r<-.25, the association is called
“moderate negative” linear association
 If the -.25<r<0, the association is called
“weak negative” linear association
 And r=0, no correlation!

AP Statistics, Section 3.2, Part 1
16
Interpreting r
If the 0<r<.25, the association is called
“weak positive” linear association
 If the .25<r<.75, the association is called
“moderate positive” linear association
 If the .75<r<1, the association is called
“strong positive” linear association

AP Statistics, Section 3.2, Part 1
17
Facts about correlation
Correlation is blind to the relationship
between explanatory and response
variables.
 Even though you may get a r value close
to -1 or 1, you may not say that
explanatory variable causes the
response variable. We will talk about this
in detail in the second semester.

AP Statistics, Section 3.2, Part 1
18
AP Statistics, Section 3.2, Part 1
19
Assignment
Exercises 3.25,3.26, 3.27,3.31,3.36,3.37
 Chapter 3.2 practice quiz for quiz on

AP Statistics, Section 3.2, Part 1
20