Editing Design matrix (section)

===Multiple regression===
This section contains an example of [[Linear Regression|multiple regression]] with two covariates (explanatory variables): ''w'' and ''x''.
Again suppose that the data consist of seven observations, and that for each observed value to be predicted (<math>y_i</math>), values ''w''<sub>''i''</sub> and ''x''<sub>''i''</sub> of the two covariates are also observed. The model to be considered is
:<math> y_i = \beta_0 + \beta_1 w_i + \beta_2 x_i + \varepsilon_i </math>
This model can be written in matrix terms as
:<math>
\begin{bmatrix}y_1 \\ y_2 \\ y_3 \\ y_4 \\ y_5 \\ y_6 \\ y_7 \end{bmatrix} = 
\begin{bmatrix} 1 & w_1 & x_1  \\1 & w_2 & x_2  \\1 & w_3 & x_3  \\1 & w_4 & x_4  \\1 & w_5 & x_5  \\1 & w_6 & x_6 \\ 1& w_7  & x_7  \end{bmatrix}
\begin{bmatrix} \beta_0 \\ \beta_1 \\ \beta_2  \end{bmatrix}
+
\begin{bmatrix} \varepsilon_1 \\ \varepsilon_2 \\ \varepsilon_3 \\
\varepsilon_4 \\ \varepsilon_5 \\ \varepsilon_6 \\ \varepsilon_7 \end{bmatrix}
</math>

Here the 7×3 matrix on the right side is the design matrix.