In the method part, it is expected that you explain the functional form you are selecting and the kind of violation you are expected to observe. This discussion should be based on the literature available.
Tests related to the violation of the linear model.
In your paper, it is expected that discuss, test (when appropriate) and correct all the major violations of the linear regression model. It should include:
Inclusion of irrelevant variables
Autocorrelation (spatially or temporally)
Even if your model does not violate one hypothesis, you should explain why it is irrelevant. When you test, you explain the test you are doing, the null hypothesis of the test, the conclusion and the correction.
It is expected that you produce the plot of each independent variable individually with the dependent variable and perform it again with the residual of the regression
Regression results and analysis
This section should explain the nature of the relationship between the dependent variable and the independent variable. For every variable, it is expected that you explain the unit increment. For example: it is a “one-unit increment in the independent variable leads to a 0.4 increase in the dependent variable”, or a percentage change, etc. It is expected that you state if the sign was expected and the implication of the relationship (or no relationship) observed.