Section 16 Multiple Linear Regression: Model


16.1 Blood pressure data


16.1.1 Null Model

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


16.1.2 Regression Model

\[ \large SBP \sim Intercept + BMI + Age \]

Note: Intercept incorporates mean SBP when BMI and Age equals to zero.


16.2 Statistical Model


16.2.1 Null Model

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


16.2.2 Regression Model

\[ \large y_{i} = a + \beta_1 x_{1i} + \beta_2 x_{2i} + \epsilon_{i} \]


16.3 Prediction

\[ \large \hat y_{i} = \hat\beta_0 + \hat\beta_1x_{1i} + \hat\beta_2x_{2i} \]


16.4 Scatter Plot