Simple Linear Correlation
Simple --- Two Variables (X & Y)
Linear --- Straight Line ( Y = mX + b )
Correlation --- Mathematical Relationship
Assumptions:
1. Both X and Y are random variables.
2. Data pairs (X, Y) are Bivariate Normal Distributions.
For any fixed value of X, the Y values are normally distributed.
For any fixed value of Y, the X values are normally distributed.
Properties of r:
1. The value of r is a measure of linear relationship only.
2. -1 < r < +1
For r = -1, perfect negative correlation.
For r = +1, perfect positive correlation.
If r = 0, then zero linear correlation.
Common Errors:
1. Significant linear correlation does NOT provide proof of Cause & Effect.
2. Lack of significant LINEAR correlation does not imply there is no other mathematical relationship.
3. Tests for correlation should not based on rates or averages.
4. Do not use the regression equation for predicting if there is no significant correlation.
5. When using the regression equation for predicting, stay within the range of the X variable.
6. A regression equation based on old data is not necessarily valid for current situations.
7. A regression equation based on current data is not necessarily valid for future situations.
8. Do not use the regression equation to make predictions about a population that is different from the
population from which the sample data were drawn.