Regression model ($f_{\beta }(y\mid x)$)

A regression model specifies features of the conditional distribution of a response given predictor covariates, often a conditional mean or a full parametric density. Linear regression specifies a linear conditional mean; logistic regression specifies a logit-linear conditional probability for a binary response. The conditional comparison represented by a coefficient depends on which covariates are included.

A statistical interaction means that the effect of one predictor depends on another on the chosen response scale. In a linear regression, an interaction term ${\beta }_{3}XZ$ changes the slope in $X$ to ${\beta }_1+{\beta }_{3}Z$. Whether interaction is present depends on the comparison scale; additive effects and multiplicative effects use different null contrasts. Comparing subgroup effects requires an interaction contrast, rather than contrasting their separate significance labels.

Analysis of one factor's effect at a specified level of another factor, for example a cue-congruence difference separately at each delay. The interaction compares those effects directly. One significant simple-effect test and one nonsignificant simple-effect test do not themselves establish an interaction; compare the estimates with the appropriate uncertainty and multiple testing treatment.

An interaction plot displays response means against levels of one factor, with separate lines for levels of another and optional panels for further factors. In an additive linear regression, the difference between two lines is constant across the horizontal factor, so the population-mean lines are parallel. Changing line separations or crossings show a statistical interaction on that response scale. Sample means may be nonparallel through noise, so the plot describes the effect pattern rather than replacing a formal hypothesis test.

An interaction term lets the effect of one predictor depend on another. Inthe slope with respect to $X$ is ${\beta }_1+{\beta }_{3}Z$.

A two-factor interaction means that changing one factor has a different effect at different levels of another. For a two-level factorial design, its sign column is $x_i{x}_j$, and four times its coefficient is the corresponding difference of differences. It can be confounded with other factorial contrasts in a fractional factorial design.

A coefficient multiplying an interaction term controls its strength relative to the chosen field normalization. Its engineering dimension determines whether it is dimensionless, relevant or irrelevant. A renormalized coupling constant constant is specified at a renormalization scale; its change with that scale is described by the renormalization-group beta function.

A hierarchical statistical model that contains an interaction term retains its associated lower-order effects. For two categorical predictors this means keeping both main effects when keeping their interaction. A nonsignificant averaged main effect may coexist with large opposite effects in different groups. Dropping its lower-order term while retaining the interaction can make the model depend on arbitrary factor coding.