Figure TB 11-3
$$Y _ { i } = \beta _ { 0 } + \beta _ { 1 } z _ { 1 i } + \beta _ { 2 } z _ { 2 i } + \beta _ { 3 } z _ { 1 i } z _ { 2 i } + e _ { i }$$
-In the accompanying formula,β3 represents the____.
A)intercept coefficient
B)residual coefficient
C)interaction of factors 1 and 2
D)mean difference for factor 3

Question

​Figure TB 11-3
 $$Y _ { i } = \beta _ { 0 } + \beta _ { 1 } z _ { 1 i } + \beta _ { 2 } z _ { 2 i } + \beta _ { 3 } z _ { 1 i } z _ { 2 i } + e _ { i }$$
-In the accompanying formula,β3 represents the____.
A)intercept coefficient
B)residual coefficient
C)interaction of factors 1 and 2
D)mean difference for factor 3

Quizplus · Accepted Answer

β3 represents the interaction coefficient between factors 1 and 2. It measures the extent to which the effect of factor 1 on the response variable depends on the level of factor 2 and vice versa.

​Figure TB 11-3 Yi=β0+β1z1i+β2z2i+β3z1iz2i+eiY _ { i } = \beta _ { 0 } + \beta _ { 1 } z _ { 1 i } + \beta _ { 2 } z _ { 2 i } + \beta _ { 3 } z _ { 1 i } z _ { 2 i } + e _ { i }Yi​=β0​+β1​z1i​+β2​z2i​+β3​z1i​z2i​+ei​

Figure TB 11-3 $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } z _ { 1 i } + \beta _ { 2 } z _ { 2 i } + \beta _ { 3 } z _ { 1 i } z _ { 2 i } + e _ { i }$