1. Describing Relationships

2. A scatterplot shows the relationship between two quantitative variables.

3. The explanatory variable is graphed on the x axis and the response variable is graphed on the y axis. Each dot represents one “case”

4. CHECK YOUR UNDERSTANDING: Identify the explanatory and response variables in each setting (if applicable)
Julie asks, “Can I predict a state’s mean SAT Math score if I know its mean SAT Critical Reading score?”
Jim wants to know how the mean SAT Math and Critical Reading scores this year in the 50 states are related to each other.
Julie’s case?
Jim’s case?

5. CHECK YOUR UNDERSTANDING: Identify the explanatory and response variables in each setting (if applicable)
How does drinking beer affect the level of alcohol in our blood? The legal limit for driving in all states is 0.08%. In a study, adult volunteers drank different numbers of cans of beer. Thirty minutes later, a police officer measured their blood alcohol levels.

6. CHECK YOUR UNDERSTANDING: Identify the explanatory and response variables in each setting (if applicable)
The National Student Loan Survey provides data on the amount of debt for recent college graduates, their current income, and how stressed they feel about college debt. A sociologist looks at the data with the goal of using amount of debt and income to explain the stress caused by college debt.

7. RECAP: Which is explanatory and which is response
RECAP: Which is explanatory and which is response? (or is there just a relationship)
SATM and SATV
For Jim, Just a relationship
Amount of alcohol consumed and body temperature
Amount of alcohol consumed is explanatory and body temperature is response
Debt /Income and college debt stress
Amount of student loan debt is explanatory and stress is response
YOU TRY- If the two variables were: child’s height at 16 years old and child’s height at 6 years old
Height at age 6 is explanatory and height at age 16 is response

8. Scatterplots and Correlation
Displaying Relationships: Scatterplots
The most useful graph for displaying the relationship between two quantitative variables is a scatterplot.
Scatterplots and Correlation
Definition:
A scatterplot shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point on the graph.
How to Make a Scatterplot
Decide which variable should go on each axis.
Remember, the eXplanatory variable goes on the X- axis!
Label and scale your axes.
Plot individual data values.

9. Scatterplots and Correlation
Displaying Relationships: Scatterplots
Make a scatterplot of the relationship between body weight and pack weight.
Since Body weight is our eXplanatory variable, be sure to place it on the X-axis!
Scatterplots and Correlation
Body weight (lb)
120
187
109
103
131
165
158
116
Backpack weight (lb) 26 30 24 29 35 31 28

10. Describing Relationships: DOFS

11. Scatterplots and Correlation
Interpreting Scatterplots
To interpret a scatterplot, follow the basic strategy of data analysis from Chapters 1 and 2. Look for patterns and important departures from those patterns.
Scatterplots and Correlation
How to Examine a Scatterplot
As in any graph of data, look for the overall pattern and for striking departures from that pattern.
You can describe the overall pattern of a scatterplot by the direction, form, and strength of the relationship.
An important kind of departure is an outlier, an individual value that falls outside the overall pattern of the relationship.

12. So, There are 4 Traits of a Correlation
Form
Direction
Strength
Outliers
Use an acronym …“DOFS” or “FODS” to help you remember!

13. Linear
Quadratic
No Correlation
Cubic
Exponential
FORM

14. Direction Positive Correlation Negative Correlation
Two variables have a positive association when above-average values of one tend to accompany above-average values of the other, and when below-average values also tend to occur together.
Two variables have a negative association when above-average values of one tend to accompany below-average values of the other.

15. Weak ---------------------------> Strong
Strength
Weak > Strong
Determining how weak or strong a correlation actually is can be subjective without a way to measure the strength. Next week we will learn about the correlation coefficient, r, that is used to measure the strength of a correlation.

16. Match the direction and strength to the graph
Correlation
Strong negative Weak Negative No Correlation Weak Positive Strong Positive

17. Match the direction and strength to the graph
Correlation
Strong negative Weak Negative No Correlation Weak Positive Strong Positive

18. Match the direction and strength to the graph
Correlation
Strong negative Weak Negative No Correlation Weak Positive Strong Positive

19. Match the direction and strength to the graph
Correlation
Strong negative Weak Negative No Correlation Weak Positive Strong Positive

20. Match the Correlation Coefficient to the graph
Strong negative Weak Negative No Correlation Weak Positive Strong Positive

21. Data that doesn’t fit in
Outliers
Data that doesn’t fit in

22. EXAMPLE 1 Scatterplots and Correlation
Interpreting Scatterplots
EXAMPLE 1 Scatterplots and Correlation
Outlier
There is one possible outlier, the hiker with the body weight of 187 pounds seems to be carrying relatively less weight than are the other group members.
Strength
Direction
Form
There is a moderately strong, positive, linear relationship between body weight and pack weight.
It appears that lighter students are carrying lighter backpacks.

23. EXAMPLE 2 Scatterplots and Correlation
Interpreting Scatterplots
EXAMPLE 2 Scatterplots and Correlation
Strength
Consider the SAT example from page Interpret the scatterplot.
Direction
Form
There is a moderately strong, negative, curved relationship between the percent of students in a state who take the SAT and the mean SAT math score.
There are two distinct clusters of states and two possible outliers that fall outside the overall pattern.

24. Coding a scatterplot can stress information.

25. Which graph shows a stronger relationship?

27. Describing Distributions
1 Quantitative Variable
Graph using boxplots, stemplots, or histograms
Describe the distributions using SOCS (shape, outliers, center, and spread)
2 Quantitative Variables
Graph using a scatterplot
Describe relationships using DOFS(direction, outliers, form, and strength)