A regression will run on almost anything. It will produce coefficients, standard errors and a satisfying p-value whether or not the data has any business being modelled that way. The output looks identical either way, which is the whole problem.
1. Look at the data before you model it
Plot every variable. Histograms for the continuous ones, bar charts for the categorical ones, and a scatterplot matrix for anything you intend to put on the right-hand side. You are looking for impossible values, a variable that is 95% one category, a bimodal distribution hiding two populations, and the reversed-scale item nobody recoded.
Most of the serious errors we find in datasets arriving here would have been visible in the first ten minutes of plotting.
2. Decide about missing data explicitly
Listwise deletion is the default in most software, which means the decision gets made for you and often silently discards a third of the sample. Report how much is missing per variable, form a view on whether it is missing completely at random, and choose accordingly — multiple imputation where the mechanism supports it, complete-case with a stated justification where it does not. Never delete and say nothing.
3. Check linearity, not just correlation
Linear regression assumes a linear relationship. A curved relationship can produce a near-zero correlation and a non-significant coefficient while being one of the strongest effects in your data. Plot each predictor against the outcome. If it bends, model the bend.
4. Examine the residuals
This is the single highest-value check and the one most often skipped. Residuals versus fitted values tells you about homoscedasticity and functional form; a Q-Q plot tells you about normality of the errors — which is the actual assumption, not normality of the raw variables, a confusion that survives in an alarming number of methods sections.
Normality of the residuals. Not normality of your variables. These are different claims and only one of them is an assumption of the model.
5. Test multicollinearity properly
Correlations between predictors are a starting point, not an answer — collinearity can arise from combinations of variables that no pairwise correlation reveals. Use variance inflation factors. VIF above 5 warrants attention, above 10 warrants action, and the action is usually theoretical: decide which construct you actually mean to measure rather than mechanically dropping whichever variable happens to have the larger VIF.
6. Find the influential cases
Cook's distance and leverage values identify observations that are moving your model on their own. Finding one is not permission to delete it. Investigate: a data-entry error gets corrected, a genuine extreme case gets reported, and either way you say what you found. Reporting the model with and without an influential case is more convincing than a clean model with a quietly missing row.
And report the checks
All of this belongs in the write-up, briefly. Two or three sentences stating that assumptions were assessed, how, and what was found. It costs a paragraph and removes the most common line of attack a reviewer has.
