Section 29 Estimates: Confidence Intervals

29.1 Estimates: Effects

\[ \large fm \leftarrow lm(SBP \sim BMI, \space data=BP) \]

\[ \large summary(fm) \]

\[ \large confint(fm) \]

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	36.2037	1.4801	24.4601	0
BMI	2.6323	0.0590	44.5940	0

	2.5 %	97.5 %
(Intercept)	33.2956	39.1117
BMI	2.5163	2.7483

29.2 Explanation

Statistical Model

\[ \large y_{i} = \beta_0 + \beta_1 x_{i} + \epsilon_{i} \]

95% Confidence Interval

\[ \large CI_{0.95}(\hat \beta_1) = \left[ \hat\beta_1 \pm t_{0.025, df_{residual}} * SE(\hat\beta_1) \right]\]

95% Confidence Interval

\[ \large CI_{0.95}(\hat \beta_0) = \left[ \hat\beta_0 \pm t_{0.025, df_{residual}} * SE(\hat\beta_0) \right]\]