# How does one test for no autocorrelation between residuals and linearity in parameters?

I am using Stata and attempting to test for (1) no autocorrelation between residuals and (2) linearity in parameters.

# Attempts I've made for (1)

The only test I've found so far for autocorrelation is something called the Durbin–Watson test, but it seems to be applicable only for time series situations, which is not what I'm doing.

Besides this, I have not found any tests that seem to check for autocorrelation between residuals.

# Attempts I've made for (2)

My professor and TAs said a simple scatter plot like

scatter r variable1

is sufficient to test for linearity and I should just decide based on the graph. However, this seems to be highly subjective and I would prefer a more objective way of determining this.

# My Question

How does one test for no autocorrelation between residuals and linearity in parameters?