Quants: Correlation Analysis

Correlation

• Correlation is math-speak for relationships.  Is there a relationship between the change in the value of one variable and the change in value of another?
• Correlation and simple regression can help you:
1. Verify a relationship between dependent variable Y and independent variable X.
2. Identify the mathematical form of the relationship (ex. linear, exponential)
3. Determine the value of the y-intercept and the slope of the coefficient.

Correlation Coefficient

• Correlation Coefficient = a range between -1 and 1
• Determines the direction (positive or negative) and strength of the relationship (a value of zero indicates no relationship) between two variables.
• Commonly expressed as “r_yx”
• This value must be tested for significance in order to determine if developing a single regression model is merited.
• The null (H_o) hypothesis assumes that r_yx = 0 and no relationship exists.
• Look at diagrams for a Student’s t-distribution to visualize your null hypothesis’ fail to reject and rejection ranges.
• If you believe that you have found a relationship, then your hope is that the null will be rejected and the correlation coefficient is not equal to zero.

Limits of Correlation Analysis

• The correlation coefficient assumes that the relationship is liner, but many relationships between two variables are non-linear.
• If the data sample contains outlier observations, then r_xy can be distorted.
• The analyst may discover a high correlation when no real relationship exists (the relationship is spurious).
• Data mining for relationships is not preferred to holding an actual theoretical basis for testing to identify potentially significant correlations.