I'm running a model with 2 continuous predictors (x1, x2) and 1 continuous outcome variable (y). The results show that both of the slopes are significant, as well as the intercept, with no significant interaction effect. Let's say that my results are something like this:
(intercept): 216.00 x1: -12.00 x2: -8.00
Now, for the sake of interpretability, I've decided to standardize them. So I used the
scale() function, and my model now has this form:
model.s <- lm(scale(y)~scale(x1)*scale(x2))
with these results:
(intercept): -0.0123 # It's not significant anymore x1: -2.3 x2: -1.2
My questions are:
- Why the intercept lost its significance, and if this is normal,
- I have scaled all 3 variables, is anything wrong with that?
- How can I interpret the intercept in the scaled model?
Regarding the last one, my interpretation is that:
- when x1 is at mean(x1) and x2 is at mean(x2), y is 0.0123 SDs away from mean.
- when x1 goes up by 1SD, and x2 is at mean(x2), y decreases by -2.3SDs
- when x2 goes up by 1SD, and x1 is at mean(x1), y decreases by -1.2SDs
With standardized the predictors, but not the outcome variable:
model.s1 <- lm(y~scale(x1)*scale(x2))
The results are somewhat different, it appears that the significance returns to the intercept and the values are altered:
(intercept): 98 x1: -20 x2: -17
My interpretation of these results is:
- when x1 is at mean(x1) and x2 is at mean(x2), y is 98
- when x1 goes up by 1SD, and x2 is at mean(x2), y decreases by -20 units
- when x2 goes up by 1SD, and x1 is at mean(x1), y decreases by -17 units
In other words, I interpret the x1 and x2 in SD terms, while I interpret y in units. Is this interpretation wrong?