1. Chapter 4 - Scatterplots and Correlation
Dealing with several variables within a group vs. the same variable for different groups.
Response Variable: measures the outcome of a study.
Explanatory Variable: attempts to explain the observed outcomes.
ex: Body Temp vs. Alcohol (Mice)
ex: Predicting SAT Math if you know SAT Verbal

2. WARNING! WARNING! EXPLANATORY VARIABLES DO NOT NECESSARILY CAUSE CHANGES IN RESPONSE VARIABLES!!!

3. (2.1 cont’d)
Scatter Plot: The most effective way to display the relationship between two quantitative variables measured on the same individuals.
Horizontal Axis (x) = explanatory variable (if there is one)
Vertical Axis (y) = response variable (if there is one)
If there is no exp/resp distinction, it can be plotted either way…

5. Interpreting Scatter Plots
Look for overall pattern
Direction / Form / Strength
Direction = “Positive” or “Negative “ Association:
Positive Association: Above average values of one variable tend to accompany above average values of the other variable.
Negative Association: Above average values of one variable tend to accompany below average values of the other variable.
Form - can be linear / curved / clustered
Strength
Stronger = less scatter - closer to a straight line…
Weaker = more scatter, not as linear…

6. Direction = Positive
Direction = Positive
Form = Linear
Form = Scattered
Strength = Fairly Strong
Strength = Weak

7. Direction = Negative
Form = Scattered
Strength = Weak

8. Direction = Negative
Form = Curved / Clustered
Strength = Weak

9. Calculator Steps for Scatter plot
ex 2.5 pg 99:
1) Enter data into list 1 & 2 2)
2nd Y= 3)
Enter 4)
Select Type
Set Xlist / Frequency

10. Calculator Steps for Scatter plot (cont’d)
5) Turn On
6) Set Window to match Data
Window
7) Graph

11. Adding categorical variables to scatter plots
Use different colors or symbols to indicate a categorical variable or duplicate values…

12. Cell Minutes per Week vs. GPA
Seniors
4.0
Juniors + + + +
Soph + + + + + + +
3.0
Duplicate + + + + + + + + + + +
2.0 + +
1.0 25 50 75
100
125
150
175
200
225
250

13. **Same Data – Different Scales**
Correlation
Correlation = a numerical measure of how strong a linear relationship is.
Visually, correlation is hard to judge. Our eyes can be fooled by white space around a scatterplot and the plotting scales.
**Same Data – Different Scales**
ex:

14. ex: Correlation between height and weight – height is x / weight is y….
… of the standardized heights
… and the standardized weights
Formula:
…for each measurement
n - 1
… is an average
… of the products
Correlation variable
… of the sum

15. Step 1) Insert Data into lists
Calculator Procedure
Step 1) Insert Data into lists
ex: Fossil Data
Step 2) Run Stat Calc LinReg
** Set DiagnosticOn**
(one time step)

16. Correlation Facts
Correlation (r) always falls between -1 and 1.
The closer to 0 r is, the weaker the relationship.
Positive r = positive association / negative r = negative association.
Because r uses standardized values, r has no units.
Correlation measures the strength of only LINEAR relationships. It cannot be used to describe curved relationships no matter how strong they are.

17. WARNING! WARNING! CORRELATION IS STRONGLY AFFECTED BY OUTLIERS!!
WARNING! WARNING! CORRELATION IS NOT A
COMPLETE DESCRIPTION OF
2-VARIABLE DATA!!

18. The image above shows scatterplots of Anscombe's quartet, a set of four different pairs of variables created by Francis Anscombe. The four y variables have the same mean (7.5), standard deviation (4.12) and correlation (0.81)