1. Scatterplots, Association and Correlation
Chapter 7
Scatterplots, Association and Correlation

2. Examining Relationships
Relationship between 2 quantitative variables.
Ex. ___________________________________

3. Two Types of Variables ________________________ Example
Measures an outcome of a study
Used to explain the response variable.
Example
_____________________= Response variable.
_____________________= Explanatory variable.

4. Two Types of Variables
If there is a time factor, explanatory variable usually comes first.
Example
__________________________________________
Sometimes, no true response or explanatory variables.
Ex. _______________________________

5. NOT Looking at Causation.
Does not mean that
changes in _______________ variable
_____________
changes in _______________ variable.

6. Graphing Two Quant. Variables - Scatterplot
Explanatory variable: __________________
Response variable: ___________________

7. Ex. Degree Days vs. Gas Usage
Response = Amount of gas usage in a home
Explanatory = Degree Days
Measure of temperature for month
High Temperature means low Degree Days.

8. Ex. – Degree Days vs. Gas Usage
Month Degree Gas Month Degree Gas
Nov July
Dec Aug
Jan Sept
Feb Oct
March Nov
April Dec
May Jan
June Feb
Plot this by hand first, then show them splus graph.

10. Interpreting Scatterplots.
Overall Pattern
Form
Direction
Strength
Deviations from the Pattern
Outliers.

11. Interpreting Scatterplots
Form
Is the plot linear? Is the plot curved? Is there a distinct pattern in the plot?
Strength
Does the plot follow the form very closely? Or is there a lot of variation?

12. Interpreting Scatterplots
Direction
Is the plot increasing? Is the plot decreasing?
Positively Associated
Above (below) average in one variable tends to be associated with above (below) average in another variable.
Negatively Associated
Above (below) average in one variable tends to be associated with below (above) average in another variable.

13. Ex. – Degree Days vs. Gas Usage
Form – ___________________
Strength – ____________________
Direction –__________________________
Outliers? – _____________

15. % Taking SAT vs. Average Score
Form – _____________________________
___________________________________
Strength – __________________________
Direction – __________________________
Outliers – ______________

16. Correlation Measures strength of ________________
relationship between two quantitative variables.

17. What is r?
Change axes of plot to

20. Example Degree Days vs. Gas Usage
Percent taking SAT vs. Average Verbal Score.

21. Properties of r r has no units, just a number.
For ____________ association between two ____________________ variables ONLY.
Affected by _____________.

22. Properties of r r ranges in value from –1 to 1.
________ indicates a straight increasing line.
________ indicates a straight decreasing line.
________ indicates no _________ relationship.
As r moves away from 0, the linear relationship between variables gets ___________.
Changing the scale of x or y will not change the value of r.
Do graphs on board. (r = -1, r = -0.5, r = 0, r = 0.5, r = 1)

23. Calculating r.
Femur (x)
Humerus (y)

24. Calculating r.

25. Calculating r.

26. Examples Degree Days vs. Gas Usage
% Taking SAT vs. Average Verbal Score