Inverse regression

Inverse regression is a statistical technique where we reverse the traditional relationship between variables. Instead of predicting a response variable from explanatory variables, it predicts the explanatory variables based on the response. For example, if normally we estimate temperature from altitude, inverse regression might analyze how altitude varies when temperature is known. This approach is useful when the focus is on understanding the distribution of predictors given outcomes, especially when the predictor variables are more variable or error-prone than the response. It helps improve estimation accuracy and provides insights into the relationship structure from a different perspective.