Editing Design matrix (section)

===Simple linear regression===
This section gives an example of [[simple linear regression]]—that is, regression with only a single explanatory variable—with seven observations.
The seven data points are {''y''<sub>''i''</sub>, ''x''<sub>''i''</sub>}, for ''i''&nbsp;=&nbsp;1,&nbsp;2, …, 7. The simple linear regression model is
: <math> y_i = \beta_0 + \beta_1 x_i +\varepsilon_i, \,</math>
where <math> \beta_0 </math> is the ''y''-intercept and <math>\beta_1</math> is the slope of the regression line. This model can be represented in matrix form as
:<math>
\begin{bmatrix}y_1 \\ y_2 \\ y_3 \\ y_4 \\ y_5 \\ y_6 \\ y_7 \end{bmatrix}
= 
\begin{bmatrix}1 & x_1  \\1 & x_2  \\1 & x_3  \\1 & x_4  \\1 & x_5  \\1 & x_6 \\ 1 & x_7  \end{bmatrix}
\begin{bmatrix} \beta_0 \\ \beta_1  \end{bmatrix}
+
\begin{bmatrix} \varepsilon_1 \\ \varepsilon_2 \\ \varepsilon_3 \\
\varepsilon_4 \\ \varepsilon_5 \\ \varepsilon_6 \\ \varepsilon_7 \end{bmatrix}
</math>
where the first column of 1s in the design matrix allows estimation of the ''y''-intercept while the second column contains the ''x''-values associated with the corresponding ''y''-values. The matrix whose columns are 1's and ''x'''s in this example is the design matrix.