Understanding Ordinary Least Squares (OLS) Regression | Built In

Testing Assumptions of Linear Regression in SPSS

Consider the standard simple regression model y=β0 β1 x u under the Gauss-Markov Assumptions SLR.1, SLR.2, SLR.3, SLR.4 and SLR.5. The usual OLS estimators β̂0 and β1 are unbiased for their respective population parameters. Let β̃1 be the estimator of β1 obtained by assuming the intercept is zero (see Section 2-6 ). i. Find E(β̃1) in terms of the xi, β0, and β1. Verify that β̃1 is unbiased for β1 when the population intercept (β0) is zero. Are there other cases where β̃1 is unbiased? ii. Find th