How do you interpret interaction terms in multiple regression analysis?
Instruction: Describe how to include and interpret interaction terms in a multiple regression model.
Updated
Official answer
For a linear model E[Y|X,Z] = b0 + b1X + b2Z + b3XZ, the slope with respect to X is b1 + b3Z. The coefficient b1 is the slope when Z equals zero, not an overall slope that applies at every Z.
For example, if b1 = 2 and b3 = -0.5, the slope for X is 2 at Z=0, 1 at Z=2 and 0 at Z=4. A negative interaction means the X slope decreases as Z increases under this coding; it is not a universal statement that the variables are harmful together.
Keep the lower-order terms unless the model has a justified constraint. Centering can make the zero point more meaningful, but it does not remove the underlying interaction. Report predicted outcomes or conditional slopes with uncertainty at values supported by the data.
In logistic regression, a product-term coefficient concerns the log-odds scale; probability-scale interactions require examining predicted probabilities. An observational interaction is an association unless the study design and assumptions support a causal interpretation.