Scatterplot

 Used to determine relationship between two continuous variables.
 One variable plotted on xaxis, another on yaxis.
 Positive Correlation: Higher xvalues correspond to higher yvalues.
 Negative Correlation: Higher xvalues correspond to lower yvalues.
 Examples:
 Body weight and BMI
 Height and Pressure etc.
Scatterplot Matrix
Linear vs Nonlinear Relationship
Variables changing proportionately in response to each other show linear relationship. Linear relationship is an abstract concept it depends what can be called linear and what can’t in a given context. A linear relationship may exist locally with a non linear relationship globally.
Summary Tables
Method for understanding the relationship between two variables when at least one the variables is discrete.
Example: Summary information about ages of active psychologists by demographics.
Ages  (1) Total Active Psychologists  Active Psychologists by Gender  Active Psychologists by Race/Ethnicity  

(2) Female  (3) Male  (4) Asian  (5) Black/ African American  (6) Hispanic  (7) White  
Mean  50.5  47.9  55.1  46.5  47.9  46.4  51.1 
Median  51  48  57  43  46  44  53 
Std. Dev.  12.5  12.4  11.4  13.3  10.3  11.2  12.6 
Discrete Variable(s): Demography: (1), (2), (3), (4), (5), (6), (7)
Continuous Variable: Age
 CrossTabulation Tables/ Crosstabs/ Contingency Tables
 Method for summarizing two categorical variables
 In practice, continuous variables may be at times summarized as categorical variables.
 Example: Age could be divided into categories as young, adult and senior citizen, etc. Income could be divided into categories as poor, middle class, upper middle class, wealthy, etc.
 Correlation Coefficient
 A quantification of the linear relationship between two variables
 Ranges from 1 to +1
 Used for variables on an interval or ratio scale
\(
r_{xy}\) = \( \frac{\sum_{i=1}^{i=n}\left({x_i\,\,\bar{x}}\right)\left({y_i\,\,\bar{y}}\right)}{\left(n\,\,1\right)s_{x}s_{y}}
\) = \(
\frac{\sum{\left( {x_i\,\,\bar{x}} \right)}\left( {y_i\,\,\bar{y}} \right)}{\sqrt{\sum\left({x_i\,\,\bar{x}}\right)^2\sum\left({y_i\,\,\bar{y}}\right)^2}}
\)
NOTE: Correlation coefficient does not capture nonlinear relationships. Many nonlinear relationships might exist which are not captured (\(r\) = 0) by correlation coefficient.