AP Statistics Objectives Ch7
Describe the association
between two quantitative
variables using a scatterplot’s
direction, form, and strength
If the scatterplot’s form is linear,
use correlation to describe its
direction and strength
Vocabulary
Scatterplot
Association
Direction Form Strength
Outlier
Explanatory/Predictor Variable
Response variable
Vocabulary
Correlation
Quantitative Condition
Straight Enough Condition
Outlier Condition
Quick Review of Association
for Categorical Data
Scatterplot
Example
Correlation
Info
Practice
Direction,
Form,
Strength
Vocabulary
Calculator
Skills
Chp 7
Assignment
Chapter 7 Assignment
Pages: 161-166
Problems: #6,12,24,29&30
Scatterplot Example
Scatterplot Example
Chp 7 – Scatterplots, Association, and Correlation
Correlation Facts
Must meet the following conditions in order to
use correlation:
1) Quantitative Condition
– Data must be quantitative.
2) Straight Enough Condition
- Form of scatterplot needs to be fairly linear
3) Outlier condition
- r-value is influenced by outliers
-outliers should be investigated and
regression should be done w/ and w/o outliers
Chp 7 – Scatterplots, Association, and Correlation
More Correlation Facts:
1) It is your responsibility to
check the conditions first
2) -1 ≤ r ≤ 1
3) Sign of the r-value indicates direction
4) r = -1 indicates a perfect negative linear
association
5) r = 1 indicates a perfect positive linear
association
6) r = 0 indicates no linear association
Chp 7 – Scatterplots, Association, and Correlation
More Correlation Facts:
1) It is your responsibility to check the conditions first
2) -1 ≤ r ≤ 1
3) Sign of the r-value indicates direction
4) r = -1 indicates a perfect negative linear association
5) r = 1 indicates a perfect positive linear association
6) r = 0 indicates no linear association
7) Correlation has no units, therefore it is
not affected by rescaling or shifting the data.
8) Correlation treats x and y symmetrically. The
correlation of x with y is the same as the
correlation of y with x.
Chp 7 – Scatterplots, Association, and Correlation
Correlation Non-facts:
The following general categories indicate a quick way
of interpreting a calculated r value:
r-value
Linear Strength
• -0.2 to 00 OR 0.0 to 0.2 None to virtually none
• -0.5 to -0.2 OR 0.2 to 0.5 Weak
• -0.8 to -0.5 OR 0.5 to 0.8 Moderate
• -0.9 to -0.8 OR 0.8 to 0.9 Strong
• -1.0 to -0.9 OR 0.9 to 1.0 Very strong
• Exactly -1 OR Exactly +1 Perfect
NOTE: These are NOT exact values.
Only gauges to help you start.
Describe the association shown
(1)
FORM: CURVED
DIRECTION: NOT APPARENT
STRENGTH: STRONG
(2)
FORM: LINEAR
DIRECTION: POSITIVE
STRENGTH: MODERATE
Describe the association shown
(3)
FORM: LINEAR
DIRECTION: NEGATIVE
STRENGTH: VERY STRONG
(4)
FORM: LINEAR
DIRECTION: NEGATIVE
STRENGTH: WEAK
Describe the association shown
(1) NO ASSOCIATION
FORM: NONE
DIRECTION: NONE
STRENGTH: NONE
(2)
FORM: LINEAR
DIRECTION: POSITIVE
STRENGTH: STRONG
Describe the association shown
(3)
FORM: CURVED
DIRECTION: POSITIVE
STRENGTH: MODERATE
(4)
FORM: LINEAR
DIRECTION: NEGATIVE
STRENGTH: STRONG
Describe the association shown
(3)
FORM: CURVED
DIRECTION: POSITIVE
STRENGTH: MODERATE
(4)
FORM: LINEAR
DIRECTION: NEGATIVE
STRENGTH: STRONG
Chapter 7 Calculator Steps
Naming a List in TI-84
1) STAT
- Edit
- Arrow up to Highlight L1
- Arrow just past L6
2) Type Name of Column
- Name the column “YR”; ENTER
3) Type Name of Next Column
- Arrow Right
- Name the column “TUIT”; ENTER
ENTER DATA
YR
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
TUIT
6546
6996
6996
7350
7500
7978
8377
8710
9110
9411
YR
2000?
Use 10
TUIT
9800
Making a Scatterplot
1) 2nd Y=
2) ENTER to choose ‘Plot1’
3) Choose ‘On’
4) Choose 1st icon for scatterplot
5) 2nd STAT to choose ‘YR’ for ‘Xlist’
6) 2nd
STAT to choose ‘TUIT’ for ‘Ylist’
7) Zoom
9
Find Correlation
1) 2nd CATALOG
2) ENTER ‘D’
3) Arrow down and Choose ‘DiagnosticOn’
4) ENTER twice
5) STAT ‘CALC’ Choose ‘8: LinReg(a+bx)’
6) ‘YR’ , ‘TUIT’ ,
7) VARS
Choose ‘Y-VARS’
ENTER x3
ENTER DATA
YR
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
TUIT
6546
6996
6996
7350
7500
7978
8377
8710
9110
9411
YR
2000?
Use 10
TUIT
9800
What is the resulting
linear regression?
Predicted Tuition =
6477.0 + 323.6(Year)
Would predict 2004 tuition
to be $7771.40.
ENTER DATA
YR
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
TUIT
6546
6996
6996
7350
7500
7978
8377
8710
9110
9411
YR
2000?
Use 10
TUIT
9800
What is the resulting
linear regression?
Predicted Tuition =
6477.0 + 323.6(Year)
Would predict 2004 tuition
to be $7771.40.
Quick Review
Association of two Categorical Variables
1) Use pie chart or segmented bar chart to do visual
comparison
2) Compare the proportions (%)
•
•
If nearly the same - The variables are independent
If not nearly the same – The variables are not
independent
Variables?
Survival & Ticket Class
25.0%
29.8%
16.6%
Association?
Do not appear independent, ticket
class & survival may be associated.
28.6%
35.4%
45.2%
Quick Review
Association of two Categorical Variables
1) Use pie chart or segmented bar chart to do visual
comparison
2) Compare the proportions (%)
•
•
If nearly the same - The variables are independent
If not nearly the same – The variables are not
independent
Variables?
Survival & Ticket Class
25.0%
29.8%
16.6%
Association?
Do not appear independent, ticket
class & survival may be associated.
28.6%
35.4%
45.2%
Chp 7 – Scatterplots, Association, and Correlation
Vocabulary
1. Scatterplot – Graph which shows the relationship
between two quantitative variables
2. Explanatory variable – the quantitative variable
which is plotted on the horizontal axis (aka x-axis) of a
scatterplot. It is used as the “predictor” of the other
variable, but should not be interpreted as the cause
of the other variable.
3. Response variable – the variable which is plotted
on the vertical axis (aka y-axis) of a scatterplot. Be
careful not to interpret the effect of the other.
Chp 7 – Scatterplots, Association, and Correlation
Vocabulary
4.Form – what type of pattern is seen? Is it LINEAR? Is
it CURVED?
5. Direction – If it is POSITIVE, as one variable
increases so does the other. If it is NEGATIVE, as one
variable increases the other decreases
6.Strength – How tight is the scatter around the
underlying form? Is it VERY STRONG? STRONG?
MODERATE? WEAK? Maybe even PERFECT or NONE.
7. Outliers – They need to be identified
Chp 7 – Scatterplots, Association, and Correlation
Vocabulary
8. Correlation – a numerical measure of direction
and strength of a linear association (also referred to
as the r-value)
-----BEFORE using you must meet the
following CONDITIONS:
Chp 7 – Scatterplots, Association, and Correlation
Vocabulary
8. Correlation – a numerical measure of direction
and strength of a linear association (also referred to
as the r-value)
-----BEFORE using you must meet the
following CONDITIONS:
1) Quanitative Variables Condition – both
variables must be quantitative
2) Straight Enough Condition – the form of the
scatterplot must be basically linear, not
curved
3) Outlier Condition – no apparent outliers
exist
Chp 7 – Scatterplots, Association, and Correlation
9. Lurking Variable – A variable other than the
explanatory and response variables recorded that
affects both variables, accounting for the correlation
between the two variables recorded.
Example– The r-value for “average number of
televisions sets per home” for a country and
“average life span” for the country is very high. Does
this mean we should ship tv’s to third world
countries?
The lurking variable here is “average income per
household”. It affects both the number of tv’s and
ability to increase life span through medical care.
Chp 7 – Scatterplots, Association, and Correlation
9. Lurking Variable – A variable other than the
explanatory and response variables recorded that
affects both variables, accounting for the correlation
between the two variables recorded.
Example– The r-value for “average number of
televisions sets per home” for a country and
“average life span” for the country is very high. Does
this mean we should ship tv’s to third world
countries?
The lurking variable here is “average income per
household”. It affects both the number of tv’s and
ability to increase life span through medical care.