What is the difference between regression to correlation? What is ordinal regression?

Answer 1

Regression attempts to model one variable as a function of one or more explanatory variables, such as trying to predict annual income based on years of education (I made this example up):

Predicted Income = 35,000 + 3,400 * Years of Education

Correlation, on the other hand, attempts to measure the strength of the relationship between two variables. Given two variables, correlation "grades" the strength of the relationship between them. There are several measures of correlation, but the most common returns larger absolute values for stronger relationships, and lower absolute values for weaker ones.

Data is called "ordinal" when it has order, but distance between distinct values has no meaning (or is unknown). A typical example would be rank data: We know that first place is "greater than" second place, but not by how much. Ordinal regression is simply regression which attempts to predict ordinal values.

Answer 2

Regression is a process where y is considered an observational response to a independent variable x. Correlation treats both x and y as independent.