1. Interaction regression models

2. 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:

4. 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.

5. 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.

6. 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.

7. 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.

10. 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.

12. The regression equation is quality = - 5128 + 31.1 temp + 140 pressure - 0.133 tempsq - 1.14 presssq - 0.145 tp Predictor Coef SE Coef T P Constant -5127.9 110.3 -46.49 0.000 temp 31.096 1.344 23.13 0.000 pressure 139.747 3.140 44.50 0.000 tempsq -0.133389 0.006853 -19.46 0.000 presssq -1.14422 0.02741 -41.74 0.000 tp -0.145500 0.009692 -15.01 0.000 S = 1.679 R-Sq = 99.3% R-Sq(adj) = 99.1% Analysis of Variance Source DF SS MS F P Regression 5 8402.3 1680.5 596.32 0.000 Residual Error 21 59.2 2.8 Total 26 8461.4 Source DF Seq SS temp 1 1510.7 pressure 1 279.3 tempsq 1 1067.6 presssq 1 4909.7 tp 1 635.1

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