Coefficients and Datasets 2

How scaling input variables affects OLS coefficient estimates

This is an easy statistics question that tests your understanding of how ordinary least squares (OLS) responds to simple data transformations. It is commonly asked in interviews to confirm that a candidate understands the mechanics of linear regression and can reason through the algebra without getting lost in notation.

The question asks you to predict how the fitted coefficients change when all values of the independent variable are scaled by a constant factor. Solving it requires only the definition of the OLS estimator and a clear head about how the covariance and variance terms rescale. The key insight is recognizing that the regression line must still fit the data, and working through what that constraint means for each coefficient separately.

• OLS estimator formula and its dependence on covariance and variance
• Behavior of covariance under scaling of one variable
• Behavior of variance under scaling
• Interpretation of the intercept and slope in the context of transformed data