What is the X on Y Regression Line?
In statistics, regression lines are used to model the relationship between two variables and make predictions. You are probably familiar with the y on x regression line, which predicts values of from known values of . But what if you want to go the other way , predicting from a known value of ? That's exactly what the x on y regression line does.
X on Y Regression Line: Also called the inverse regression line, this is the line of best fit that minimises the horizontal distances from the data points to the line. It is used to predict the value of (the independent variable) for a given value of (the dependent variable).
The key distinction is the direction of prediction:
- Y on X: given a value of , predict
- X on Y: given a value of , predict
Think of it like a temperature converter. The y on x line converts Celsius → Fahrenheit. The x on y line runs the process in reverse: given a Fahrenheit reading, what was the original Celsius value? Both lines pass through the mean point , but they are tilted differently.