Question

Consider a regression study involving a dependent variable y, a quantitative independent variable $x_1$, and a categorical independent variable with five levels (i.e., five possible value outcomes). Write a multiple regression equation relating $x_1$ and the categorical variable to y. HINT: Remember to use dummy variable(s). $\circ E(y) = \beta_0 + \beta_1x_1 + (\beta_2 + \beta_3 + \beta_4 + \beta_5 + \beta_6)x_2$ $\circ E(y) = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_3 + \beta_4x_4 + \beta_5x_5$ $\circ E(y) = \beta_0 + \beta_1x_1 + \beta_2x_2$ $\circ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_3 + \beta_4x_4 + \beta_5x_5 + \epsilon$ $\circ E(y) = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_3 + \beta_4x_4$ $\circ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_3 + \beta_4x_4 + \epsilon$

          Consider a regression study involving a dependent variable y, a quantitative independent variable $x_1$, and a categorical independent variable with five levels (i.e., five possible value outcomes).
Write a multiple regression equation relating $x_1$ and the categorical variable to y.
HINT: Remember to use dummy variable(s).
$\circ E(y) = \beta_0 + \beta_1x_1 + (\beta_2 + \beta_3 + \beta_4 + \beta_5 + \beta_6)x_2$
$\circ E(y) = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_3 + \beta_4x_4 + \beta_5x_5$
$\circ E(y) = \beta_0 + \beta_1x_1 + \beta_2x_2$
$\circ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_3 + \beta_4x_4 + \beta_5x_5 + \epsilon$
$\circ E(y) = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_3 + \beta_4x_4$
$\circ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_3 + \beta_4x_4 + \epsilon$

Consider a regression study involving a dependent variable y, a quantitative independent variable x1, and a categorical independent variable with five levels (i.e., five possible value outcomes).
Write a multiple regression equation relating x1 and the categorical variable to y.
HINT: Remember to use dummy variable(s).
∘ E(y) = β0 + β1x1 + (β2 + β3 + β4 + β5 + β6)x2
∘ E(y) = β0 + β1x1 + β2x2 + β3x3 + β4x4 + β5x5
∘ E(y) = β0 + β1x1 + β2x2
∘ y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + β5x5 + ϵ
∘ E(y) = β0 + β1x1 + β2x2 + β3x3 + β4x4
∘ y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ϵ

Added by Charles M.

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