Section 19 Simple Linear Regression: Model

19.1 Blood pressure data

19.1.1 Null Model

\[ \large SBP \sim mean(SBP) \]

19.1.2 Regression Model

\[ \large SBP \sim mean(SBP) + BMI \]

Note: The above model formula indicates mean(SBP) when BMI=0

19.2 Statistical Model

19.2.1 Null Model

SBP = overall mean + sampling variability

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

19.2.2 Regression Model

SBP = overall mean + coefficient*BMI + sampling variability

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

19.3 Scatter Plot