So for example, if one is examining the relationship between income and education, r will have the same value regardless if one uses dollars or yen or marks or pesos. For this reason it is called a standardized measure. Correlation is intimately tied to the notion of regression . It thus provides an explanation of the variation in a dependent variable. The mathematical relationship thus tells us in addition how much error or indeterminacy exists in the X-Y relationship.
Ordinary regression assumes the function is linear or can be made linear.
In particular, a Y score equals 2 plus 2 times a value of X plus an error. Another way of saying this is that one wants to reduce the error so that the predicted values of Y will be as close to the observed values as possible. The graph of the data point that fit a linear relationship is a straight line. Notice it is a straight line. As X increases by 1, Y increases by 2.