Question regarding example in 10.2 Regression with ARIMA errors using fable

[MMJansen]

As read at 10.2 Regression with ARIMA errors using fable, in the example there is not much difference in the innovation residuals and the response residuals. Indeed the innovation residuals are not unlike white noise, but neither are the response residuals:
augment(fit) |> features(.resid, ljung_box, dof = 3, lag = 8) has a similar p-value as the .innov has.
I think maybe the dof is not applicable here, but
augment(fit) |> features(.resid, ljung_box, lag = 8) has an even larger p-value.
The ACF plot of the .innov and the .resid is very comparable.
I was wondering, does that mean that in this case, we could have used just the simple regression, without the ARIMA errors? What does the ARIMA error contribute in this case? Thanks!

[robjhyndman]

The .resid column is the same as the .innov column in this example, because no transformation has been used.

To see the effect of the ARIMA errors, you need to compare against the regression residuals.

library(fpp3)
fit <- us_change |>
    model(ARIMA(Consumption ~ Income))
residuals(fit, type = "regression") |>
    ACF(.resid, lag_max = 36) |>
    autoplot()

^{Created on 2025-01-05 with reprex v2.1.1}

These have clear autocorrelation, which is what is being handled by the ARIMA part of the model.

[MMJansen]

Thanks, I confused the .resid with the .regression_resid