Students' perceptions of science ability. The American Educational Research Journal (Fall 1998) published a study of students' perceptions of their science ability in hands-on classrooms. A first-order, main effects model that was used to predict ability perception (y) included the following independent variables:

Control Variables

x₁ = Prior science attitude score

x₂ = Science ability test score

x₃ = 1 if boy, 0 if girl

x₄ = 1 if classroom 1 student, 0 if not

x₅ = 1 if classroom 3 student, 0 if not

x₆ = 1 if classroom 4 student, 0 if not

x₇ = 1 if classroom 5 student, 0 if not

x₈ = 1 if classroom 6 student, 0 if not

Performance Behaviors

x₉ = Active-leading behavior score

x₁₀ = Passive-assisting behavior score

x₁₁ = Active-manipulating behavior score

(a) Hypothesize the equation of the first-order, main effects model for E(y).

(b) The researchers also considered a model that included all possible interactions between the control variables and the performance behavior variables. Write the equation for this model for E(y)

(c) The researchers determined that the interaction terms in the model, part b, were not significant, and therefore used the model, part a, to make inferences. Explain the best way to conduct this test for interaction. Give the null hypothesis of the test.