Interaction regression models

What is an additive model? A regression model with p-1 predictor variables contains additive effects if the response function can be written as a sum of functions of the predictor variables: For example:

What is an interaction model? Two predictor variables interact when the effect on the response variable of one predictor variable depends on the value of the other.

A two-predictor interaction regression function β 0 = the expected response when X 1 = 0 and X 2 = 0 But now, β 1 and β 2 can no longer be interpreted as the change in the mean response with a unit increase in the predictor variable, while the other predictor variable is held constant at a given value.

If we hold X 2 = x 2 constant: The intercept depends on the value of x 2. The slope coefficient of X 1 depends on the value of x 2.

If we hold X 1 = x 1 constant: The intercept depends on the value of x 1. The slope coefficient of X 2 depends on the value of x 1.

Data analysis example Quality score, y, of a product. Score is number between 0 and 100. Predictor, x 1, is temperature (degrees F) at which product was produced. Predictor, x 2, is pressure (pounds per square inch) at which product was produced. Designed experiment, sample size of n = 27 items.

The regression equation is quality = temp pressure tempsq presssq tp Predictor Coef SE Coef T P Constant temp pressure tempsq presssq tp S = R-Sq = 99.3% R-Sq(adj) = 99.1% Analysis of Variance Source DF SS MS F P Regression Residual Error Total Source DF Seq SS temp pressure tempsq presssq tp

Interaction models in Minitab Use Calc >> Calculator to create interaction predictor variables in worksheet. Use Stat >> Regression >> Regression as always.