1. Chapter 14 STA 200 Summer I 2011

2. Scatter Plots A scatter plot is a graph that shows the relationship between two quantitative variables measured on the same individuals. One variable is on the x-axis, while the other is on the y-axis.

3. Scatter Plots (cont.) If the two variables we’re dealing with are an explanatory variable and a response variable, the explanatory variable belongs on the x-axis (and the response variable belongs on the y- axis). Each individual is represented by a point in the scatter plot.

4. Things to Look For in a Scatter Plot Direction Form Strength Outliers

5. Direction A scatter plot exhibits positive association when large values of one variable tend to correspond with large values of the other variable (positive slope). A scatter plot exhibits negative association when large values of one variable tend to correspond with small values of the other variable (negative slope).

6. Form/Strength Form: The different forms a scatter plot can have include linear (straight-line) relationships and curved relationships. Scatter plots may also contain clusters of points. Strength: The strength of a relationship exhibited in a scatter plot is determined by how closely the points follow a clear form.

7. Example 1 Direction: Form: Strength: Outliers:

8. Example 2 – Direction: – Form: – Strength: – Outliers:

9. Measuring Strength The two scatter plots above contain the same data points. Both of them show a positive straight-line relationship. However, because of the differences in scaling, the relationship appears stronger in the graph on the right than it does in the graph on the left.

10. Correlation

11. Understanding Correlation

12. Understanding Correlation (cont.) The correlation doesn’t change when the units of measurement change. – This happens because it’s calculated from standard scores, which have no units of measurement. Correlation ignores the distinction between explanatory and response variables.

13. Understanding Correlation (cont.) Correlation only measures the strength of linear association between two variables. Since the mean and standard deviation are affected by outliers, so is the correlation.

14. Understanding Correlation (cont.)