Question: Consider a regression study involving a dependent variable y , a quantitative independent variable x 1 , and a categorical independent variable x 2 with
Consider a regression study involving a dependent variabley, a quantitative independent variablex1,
and a categorical independent variablex2with two levels (level 1 and level 2). (Usex2= 0 for level 1 andx2= 1 for level 2.)
(a)
what is the multiple regression equation relatingx1
and the categorical variable toy.
- E(y) =0+1x1+2x2
- E(y) =0+1x1
- E(y) =0+1x1+2
- y=0+1x1+2x2
(b)
What is the expected value ofycorresponding to level 1 of the categorical variable?
E(y| level 1)
=
(c)
What is the expected value ofycorresponding to level 2 of the categorical variable?
E(y| level 2)
=
(d)
Interpret the parameters in your regression equation.
- 1represents the difference in the expected value ofyfor level 1 and level 2.2is the change inE(y) for a 1 unit change inx1holdingx2constant.
- 1is the change inE(y) for a 1 unit change inx1holdingx2constant.2represents the difference in the expected value ofyfor level 1 and level 2.
- 1is the change inE(y) for a 1 unit change inx2holdingx1constant.2represents the difference in the expected value ofyfor level 1 and level 2.
- 1represents the difference in the expected value ofyfor level 1 and level 2.2is the change inE(y) for a 1 unit change inx1.
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