The meaning of an explanatory variable in computing accuracy of a prediction model (migrated to CrossValidated)

I am following the predictive modeling example found here, chapter 10.

This piece of the code has capital_gain as the explanatory variable, but removing it or replacing it with another variable doesn't change anything in the output. The estimate and confusion matrix remain the same. So why is capital_gain there in that place?

library(yardstick)
pred <- train %>%
  select(income, capital_gain) %>% #why 'capital_gain' is here? 
  bind_cols(
    predict(mod_null, new_data = train, type = "class")
  ) %>%
  rename(income_null = .pred_class)
accuracy(pred, income, income_null)


confusion_null <- pred %>%
  conf_mat(truth = income, estimate = income_null)
confusion_null

EDIT: path to the data used -> http://archive.ics.uci.edu/ml/machine-learning-databases/adult/adult.data

EDIT: this post is migrated to CrossValidated

You do not explain what your data is (something form the yardstick package?), but the situation that omitting a predictor varaible does not change the predictions of a linear model typically occurs when you have multi-collinearity in your data. In this case, any of the collinear variables can be omitted without losing predicton accuracy.

You can test for exact mutli-collinearity in your data by checking whether the rank of your predictor matrix is equal to the number of independent variables. If not, you have exact collinearity:

> A <- cbind(iris[,-5], 2*iris[,1]+iris[,2])
> ncol(A)
[1] 5
> qr(A)$rank
[1] 4

If there is only approximate collinearity, you can compute the "variance inflation factor" (VIF) of your variables. High values indicate (say greater than 5) multi-collinearity. VIF implementations do not come with vanilla R, but there are many packages that implement it.