Population Regression Line: Unbiased Estimation & Hypothesis Testing of β1 - Prof. Brett D, Study notes of Data Analysis & Statistical Methods

Download Population Regression Line: Unbiased Estimation & Hypothesis Testing of β1 - Prof. Brett D and more Study notes Data Analysis & Statistical Methods in PDF only on Docsity! 18 November Inferences about the shape of the population regression line b1 is a point estimate for β1 b1 is a statistic, so it has a sampling distribution Sampling distribution for b1 μb1 = β1 b1 is an unbiased estimator of β1 σ b1 = σ √Sxx Where Sxx is s.d. of x b1 ~ N (μb1 , σb1 x ) σ not usually known, so we estimate Sb1 = Se √Sxx = standard error of coefficient Thus, we know b1−β1 Sb1 = b1−β1 Se √S xx ~ tn – 2 CIs for β1 CI = b1± tn−1 crit Se √Sxx = b1 ± tn−1 crit Sb1 Hypothesis Tests for β1 We can test