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)
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)
=0
+1
x1
+2
x2
(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.
Step by Step Solution
There are 3 Steps involved in it
Get step-by-step solutions from verified subject matter experts
Study Help