Scatterplots, Association, and Correlation

1. Scatterplots, Association, and Correlation Ch. 7

2. Scatterplot • When to use: Number of variables: 2 Data type: quantitative data Purpose: investigate the relationship between variables x-axis is the explanatory variable y-axis is the response variable

3. Relationship Association Correlation The underlying form of the association between two variables is linear • The variables are somehow (statistically )linked

4. Describing the Relationship • Direction – positive or negative • Form – linear, curved, something else • Strength – strong (little scatter), moderate (some scatter), weak (much scatter) • Unusual features – outliers, clumps, etc.

5. (Potential) Outliers • A point that lies away from the rest of the data • There is no rule for determining outliers • Can have a large impact on the analysis • Make no relationship look strong • Make a strong relationship look weak • Do the analysis with and without outliers

6. Correlation Conditions Quantitative Variables Condition Both variables must be quantitative variables Straight Enough Condition The form of the scatterplot must be straight enough that a linear relationship makes sense Outlier Condition Report the correlation with the outlier and without the outlier

7. Correlation Coefficient • The strength of a linear relationship is given by the correlation coefficient Don’t compute it by hand

8. Correlation Properties • Always between -1 and +1 • The sign of the correlation coefficient gives the direction of the association • The correlation of x with y is the same as the correlation of y with x • Unitless • Not affected by changes in center or scale of the variables • Measures the strength of a linear relationship • Sensitive to outliers