3.5 Assessing Accuracy of Coefficient Estimates
Y=β0+β1X+ϵ
- RSE = residual standard error
- Estimate of σ
RSE=√RSSn−2 SE(ˆβ0)2=σ2[1n+ˉx2∑ni=1(xi−ˉx)2], SE(ˆβ1)2=σ2∑ni=1(xi−ˉx)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. ✔️