3.5 Assessing Accuracy of Coefficient Estimates

Y=β0+β1X+ϵ

  • RSE = residual standard error
  • Estimate of σ

RSE=RSSn2 SE(ˆβ0)2=σ2[1n+ˉx2ni=1(xiˉx)2],  SE(ˆβ1)2=σ2ni=1(xiˉx)2

  • 95% confidence interval: a range of values such that with 95% probability, the range will contain the true unknown value of the parameter
    • If we take repeated samples and construct the confidence interval for each sample, 95% of the intervals will contain the true unknown value of the parameter

ˆβ1±2  SE(ˆβ1) ˆβ0±2  SE(ˆβ0) Learning Objectives:

  • Estimate the standard error of regression coefficients. ✔️