1. Definition and components Correlation vs. Association
Scatterplots
Chapter 7
Definition and components
Describing
Correlation
Correlation vs. Association

2. I. Scatterplots
A graph that plots the relationship between two quantitative variables.
Used to see if a relationship exists between the two variables.

3. I. Scatterplots Explanatory Variable – x- value Response Variable
Predictor
Input
Independent
Response Variable
Y-value
Output
Dependent

4. II. Creating a Scatterplot
Enter all x-variables in L1, and all y-variables in L2.
Turn on Statplot and go to
Use ZoomStat to obtain graph.
Use Trace to get specific points
Scale and label axes.
I:\Math Department\TI-84-Emulator\Wabbitemu.exe

5. Does fast driving waste fuel?
Speed (km/h)
Fuel used (L/100km) 10
21.00 90
7.57 20
13.00
100
8.27 30
10.00
110
9.03 40
8.00
120
9.87 50
7.00
130
10.79 60
5.90
140
11.77 70
6.30
150
12.83 80
6.95

6. Make scatterplot in calculator.
Transfer information onto your paper, make sure to add labels and scale for x & y-axis.

7. A score of 100 is considered to be average.
Now try on your own.
Either by hand or in the calculator, create a scatterplot of the data on Age at First Word vs. Gesell Score.
A score of 100 is considered to be average.

8. III. Describing Scatterplots
Direction
Positive
Negative
Form
Linear
Exp. Curve
Quadratic curve
none

9. III. Describing Scatterplots
Strength
Strong
Weak
Unusual Features
Outliers
Change in form or strength.

10. Example 2
Describe the following Scatterplots (direction, form, strength, unusual features)

11. Describe the scatterplot you made in the fuel efficiency example.

12. Now try on your own.
Now describe the relationship between Age at First Word vs. Gesell Score on your worksheet.

13. IV. Correlation coefficient
Measures the strength of the linear association between two quantitative variables.
In order to use this number, the data must meet the following conditions.
Quantitative Variables Condition
Straight Enough Condition
Outlier Condition (calculate with & without outlier)

15. IV. Correlation Coefficient
To calculate correlation:
Enter data into L1 & L2
Go to Catalog (2nd ,0) and choose DiagnosticsON.
STAT, CALC, LinReg(ax+b).
The correlation number is the last entry r=
Calculate the correlation coefficient of your speed vs fuel example.
Is it appropriate to use correlation for this example? Why or Why not?

16. IV. Correlation Coefficient
Correlation gives strength and direction.
Closer to -1 indicates perfect Negative linear association.
Closer to +1 indicates perfect Positive linear association.
Closer to 0 indicates NO Linear association.

17. Then answer question # 4 on the worksheet.
Now try on your own.
Calculate the correlation coefficient for the relationship between Age at First Word vs. Gesell Score on your worksheet.
Then answer question # 4 on the worksheet.

18. Now try on your own.
Calculate the correlation coefficient for the relationship between Age at First Word vs. Gesell Score on your worksheet.

19. Pick up SEC Football Worksheet.
This is due at the end of the class.

20. What do you think the correlation coefficients are for the following?

21. IV. Correlation Coefficient
Has no units, based on z-scores
Are unaffected by changes in center or scale.
Can be greatly affected by outliers.

22. V. Correlation vs Association
Indicates that there is a relationship between the two variables (any form).
Measures the strength of a LINEAR association.
Get out a whiteboard and marker

23. Examples
Sketch what you think the scatterplot would look like, then describe the association.
Drug dose vs. degree of pain relief.
Calories consumed and weight loss.
Hours of sleep and score on a test.
Shoe size and grade point average
Age of car and money spent on repairs

24. What’s wrong with these statements?
There is a high correlation between the gender of American workers and their income.
We found a high correlation (r=1.09) between students’ ratings of faculty teaching and ratings made by other faculty members.
The correlation between planting rate and yield of corn was found to be r= 0.23 bushel