Added variable plot: meaning of x axis "adjusted whole model"

I used plotAdded function to visualize the multilinear regression model, but I don't understand the meaning of the x-axis "adjusted whole model". What is the calculation to obtain x-axis values?

Thanks

Answer 1

[Vishesh]

• plotAdded(mdl) creates an added variable plot for the whole model mdl except the constant (intercept) term.
• Let us say we were just modelling y as a function of x. It would be easy to visualize the model by plotting y against x (using a scatterplot for example) then plotting the model as a straight line.
• Now let us say we have multiple predictors, we can not just use a simple scatter plot anymore because we have a large number of predictors. We might think that we could scatter y against each of the predictors (let us call them x_i). This is certainly a good thing to do anyway, before modelling, which can be done using plotmatrix.
• However, the disadvantage of this is that the x_i are usually not independent, and what we really want to see is the effect of moving each individual x_i on the response y.
• Now let us move to the actual plot. This is an attempt to understand the effect of x_i on y, controlling for the other predictors.
• The steps to create the plot are the following:

(a) Regress x_i against all the other predictors

(b) Regress y against all predictors except x_i

(c) Scatter the residuals from (b) (y-axis) against the residuals from (a) (x-axis). This is the plot that

we see and what "adjusted" means, essentially just means "without x_i"