Mean Squared Error Performance of Simple Linear Regression Conditional upon the Outcome of Pretesting the Intercept

Abstract

Following a test of the hypothesis that the intercept of a simple linear regression model is zero, the conditional properties of the fitted model differ from those that obtain in the absence of pretesting and from the unconditional properties in the presence of pretesting. For the estimator of the mean response at a point X ₀, the conditional mean squared error may be better or worse, depending on the magnitude of the pretest hypothesis error and on the outcome of the pretest. The degree to which the conditional mean squared error is better or worse depends on the location of X ₀ relative to , the level of the pretest, and the correlation between the initial least squares estimators of the intercept and slope coefficients.

Key Words:

• Hypothesis test
• Overfitting
• Power
• Underfitting