**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:
- Verify a relationship between dependent variable Y and independent variable X.
- Identify the mathematical form of the relationship (ex. linear, exponential)
- 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.

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