Section 17 Principle of Least Squares: Plot

17.1 Null Model

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

17.2 Regression Model

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

17.3 Prediction

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

17.4 Residual

\[ \large \hat\epsilon_{i} = y_i - \hat y_{i} \]

\[ \large \hat\epsilon_{i} = y_i - \hat\beta_0 + \hat\beta_1x_{1i} + \hat\beta_2x_{2i} \]

17.5 Residual Sum of Squares

\[ \large RSS = \hat\epsilon_{1}^2 + \hat\epsilon_{2}^2 + ... + \hat\epsilon_{n}^2 \]

\[ \large RSS = \sum\limits_{i=1}^{n} \hat\epsilon_{i}^2 \]

17.6 Scatter Plot