1. Bivariate Data
Response Variable: measures the outcome of a study (aka Dependent Variable)
Explanatory Variable: helps explain or influences the change in the response variable (aka Independent Variable)
Not every bivariate data has a response and explanatory variable. Sometimes you are simply exploring a relationship between the variables.

2. OR Just exploring relationship?
Which is response and which is explanatory?
OR Just exploring relationship?
- The amount of time spent studying for a stats exam and the grade on the exam.
- Inches of rainfall in the growing season and the yield of corn in bushels per acre.
- A student’s grade in statistics and their grade in Spanish.
- A family’s income and the years of education of the eldest child
Classifying one variable as explanatory and the other as response DOES NOT imply CAUSATION.
There may also be other variables lurking in the background that are influencing the relationship.

3. Scatterplot
a graph that displays the relationship between bivariate, quantitative data.
Each point represents an individual from the data.
When interpreting a scatterplot, you must look at both the overall pattern of the points as well as points that deviated from the pattern.

4. Interpreting Scatterplots
a) direction
Positive Association Negative Association
b) form – curvature and clusters
c) strength – how closely the points follow a clear form
d) outliers – individual deviations from the overall pattern

5. If it is important to differentiate the bivariate data by individuals, a categorical component can be added to the scatterplot by using different colors or symbols

6. Scatterplot on the calculator
Place the explanatory data in L1
Place the response data is L2
2nd Y= button (Stat Plot)
Choose the scatterplot….1st graph
X list = L1
Y List = L2
Zoom 9

7. We need a numerical method to determine the correlation.
Correlation: the direction and strength of a linear relationship between bivariate, quantitative variables
Eyes are not always a good judge of this…
We need a numerical method to
determine the correlation.

8. Correlation (symbolized as r) is calculated by the following formula:
Where zx is the z-score of the explanatory variable and zy is the z-score of the corresponding response variable

9. Correlation on the calculator
Be sure Diagnostic is turned on…
Go to Catalog and scroll down to Diagnostic On, hit enter
Place the explanatory data in L1
Place the response data is L2
Go to STAT  CALC  #8 and hit enter
the r value will be in that list of values

10. It does not matter which is x and y for the formula
If you change the units of measure on either or both variables, the correlation will NOT change
For any correlation,
If r > 0, there is a positive association
If r < 0, there is a negative association
Correlation describes LINEAR relationships ONLY (not curved)
Correlation (r) is affected by outliers and is NOT a complete summary of bivariate data

11. The closer the correlation coefficient is to either 1 or -1, the more linear the scatterplot with appear.