Dummy Variable/Examples/Regression Equation

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Example of Dummy Variable

Consider the regression equation with the two explanatory variables $x_1$ and $x_2$:

$y = \beta_0 + \beta_1 x_1 + \beta_2 x_2$

It is sometimes more convenient to write it as:

$y = \beta_0 x_0 + \beta_1 x_1 + \beta_2 x_2$

where in this context $x_0$ is a dummy variable which always takes the value $1$.

Hence, if we also want to consider the regression model where $\beta_0 = 0$, this can be accommodated by setting the dummy variable $x_0$ equal to $0$.