Step 1: Examine the relationships between variables on a matrix plot
Use the matrix plot to examine the relationships between two continuous variables. Also, look for outliers in the relationships. Outliers can heavily influence the results for the Pearson correlation coefficient.
Determine whether the relationships are linear, monotonic, or neither. The following are examples of the types of forms that the correlation coefficients describe. The Pearson correlation coefficient is appropriate for linear forms. Spearman's correlation coefficient is appropriate for monotonic forms.
Step 2: Examine the correlation coefficients between variables
Use the Pearson correlation coefficient to examine the strength and direction of the linear relationship between two continuous variables.
The correlation coefficient can range in value from −1 to +1. The larger the absolute value of the coefficient, the stronger the relationship between the variables.
For the Pearson correlation, an absolute value of 1 indicates a perfect linear relationship. A correlation close to 0 indicates no linear relationship between the variables.
The sign of the coefficient indicates the direction of the relationship. If both variables tend to increase or decrease together, the coefficient is positive, and the line that represents the correlation slopes upward. If one variable tends to increase as the other decreases, the coefficient is negative, and the line that represents the correlation slopes downward.
Consider the following points when you interpret the correlation coefficient:
It is never appropriate to conclude that changes in one variable cause changes in another based on correlation alone. Only properly controlled experiments enable you to determine whether a relationship is causal.
The Pearson correlation coefficient is very sensitive to extreme data values. A single value that is very different from the other values in a data set can greatly change the value of the coefficient. You should try to identify the cause of any extreme value. Correct any data entry or measurement errors. Consider removing data values that are associated with abnormal, one-time events (special causes). Then, repeat the analysis.
A low Pearson correlation coefficient does not mean that no relationship exists between the variables. The variables may have a nonlinear relationship.
A positive linear relationship exists between Residence and Age, Employ and Age, and Employ and Residence. The Pearson correlation coefficients for these pairs are:
Residence and Age, 0.838
Employ and Age, 0.848
Employ and Residence, 0.952
These values indicate that there is a moderate positive relationship between the variables.
A negative linear relationship exists for the following pairs, with negative Pearson correlation coefficients:
Debt and Savings , −0.393
Credit cards and Age, −0.130
Credit cards and Savings, −0.410
The relationship between these variables is negative, which indicates that, as debt increases, education and savings decrease, and as the number of credit cards increases, the savings decrease, as well.