Question

13. Please describe what a main effect examines in factorial ANOVA, and describe what an interaction effect examines in factorial ANOVA. (1 point – .5 point main effect, .5 point interaction effect)

A main effect...

An interaction effect...

In factorial ANOVA, an F ratio is computed for each main effect and for each interaction effect. For example, if we have two factors –factor A and factor B--this gives us three F ratios. We would have an F ratio for the main effect of factor A, for the main effect of factor B, and for the interaction between A X B. How many F ratios would we get if we had three factors –A, B, and C—and we tested all main effects, all possible 2-way interactions, and the 3-way interaction? (1 point)

You would have...

Please write out the basic (i.e., single-predictor) regression equation (1 point)

Ŷ =

If the unstandardized regression coefficient (the slope of y on x) in a basic, single-predictor regression was found to be b_yx = -0.40, what is the interpretation of “b_yx = -0.40”? (1 point)

If the regression constant (the y intercept) in a basic, single-predictor regression was found to be a = .80, what is the interpretation of “a = .80”? (1 point)

Answer 1

Main effect: In factorial ANOVA analysis main effect examine the effect of each independent variable on the dependent variable. For each individual variable, F ratio is calculated to test the significance on the independent variable in factorial ANOVA analysis.

Interaction Effect:In factorial ANOVA analysis interaction effect examine the effect of interaction of independent variable on the dependent variable. Similarly, for each interaction between two variable, F ratio is calculated to test the significance of the interaction in factorial ANOVA analysis. An interaction is present if the two independent variable are not independent such that an interaction also affect the dependent variable.

For three factor A, B and C,

All the two and three way interactions are, AB, AC, BC and ABC

The basic regression equation with one predictor variable is,

Where, a is the intercept of linear equation and b is the slope of the equation.

Interpretation of b₁=-0.40,

For each unit increase in predictor variable x, the dependent variable will decrease by 0.40.

Interpretation of a=-0.80,

If the predictor variable = 0, the expected mean of dependent variable y will be 0.80

y=a + ba