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 “ryx”

• This value must be tested for significance in order to determine if developing a single regression model is merited.

• The null (Ho) hypothesis assumes that ryx \= 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 rxy 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.