Regression coefficients are independent of change of scale and origin.

Regression coefficients are indeed independent of changes in scale and origin, which means that altering the units of measurement or shifting the data does not affect the relationship represented by these coefficients.

Understanding Scale and Origin

Scale refers to the units used to measure a variable, such as converting inches to centimeters. Origin refers to the starting point of the data, like shifting all values up or down by a constant amount.

Impact on Regression Coefficients

• Change of Scale: If you multiply all values of a variable by a constant, the regression coefficients will adjust accordingly, but the underlying relationship remains the same.
• Change of Origin: Adding or subtracting a constant from all values does not alter the slope of the regression line, hence the coefficients stay unchanged.

Why This Matters

This property ensures that the interpretation of the regression coefficients remains consistent, regardless of how the data is scaled or shifted. It allows researchers to focus on the strength and direction of relationships without worrying about the specific units used.