# Controlling variables for interaction effects

I'm trying to understand what adding a 3rd covariate to a regression model does to the overall effects on interaction effects. I'll be using the mtcars dataset in R for this.

I'm using the variables vs (Engine: 0 = V-shaped, 1 = straight) and am (Transmission: 0 = automatic, 1 = manual) to predict mpg Miles per gallon. I want to also see what the effect of including another variable disp Displacement has on the overall interaction effects.

So I run the code here to see what the model is like without the disp covariate.

data(mtcars)
mtcars

model_no_covariates=lm(mpg ~ vs * am, data=mtcars)
summary(model_no_covariates)


Here is the output of that model

            Estimate Std. Error t value Pr(>|t|)
(Intercept)   15.050      1.002  15.017 6.34e-15 ***
vs             5.693      1.651   3.448   0.0018 **
am             4.700      1.736   2.708   0.0114 *
vs:am          2.929      2.541   1.153   0.2589


Now I run a model with the covariate

model_covariates1=lm(mpg ~ vs * am + disp, data=mtcars)
summary(model_covariates1)


Here is the ouput of that model

             Estimate Std. Error t value Pr(>|t|)
(Intercept) 25.830194   3.141938   8.221 7.93e-09 ***
vs           0.191405   2.076056   0.092  0.92722
am           0.136115   1.941240   0.070  0.94462
disp        -0.030145   0.008465  -3.561  0.00139 **
vs:am        4.920696   2.206541   2.230  0.03425 *


I see things have changed, but what exactly does the covariate change in the interaction effect here? What is the interpretation of how disp affects the interaction? Explanations with plots and visualizations are very much appreciated as I'm trying to understand how to better explore these effects myself with plots, but I'm unsure where to start

Edit: instead of just providing estimates from interaction effects I included the full model output