r - How to calculate "terms" from predict-function manually when regression has an interaction term -

does know how predict-function calculates terms when there interaction term in regression model? know how solve terms when regression has no interaction terms in when add 1 cant solve manually anymore. here example data , see how calculate values manually. thanks! -aleksi

set.seed(2)   <- c(4,3,2,5,3) # first make data   b <- c(2,1,4,3,5)   e <- rnorm(5)   y= 0.6*a+e   data <- data.frame(a,b,y)   model1 <- lm(y~a*b,data=data) # regression   predict(model1,type='terms',data) # terms   #this gives result:                  b        a:b 1  0.04870807 -0.3649011  0.2049069 2 -0.03247205 -0.7298021  0.7740928 3 -0.11365216  0.3649011  0.2049069 4  0.12988818  0.0000000 -0.5919534 5 -0.03247205  0.7298021 -0.5919534 attr(,"constant") [1] 1.973031 

your model technically y ~ b0 + b1*a + b2*a*b + e. calculating a done multiplying independent variable coefficient , centering result. example, terms a be

cf <- coef(model1)  scale(a * cf[2], scale = false)              [,1] [1,]  0.04870807 [2,] -0.03247205 [3,] -0.11365216 [4,]  0.12988818 [5,] -0.03247205 

which matches output above.

and since interaction term nothing else multiplying independent variables, translates to

scale(a * b * cf[4], scale = false)            [,1] [1,]  0.2049069 [2,]  0.7740928 [3,]  0.2049069 [4,] -0.5919534 [5,] -0.5919534