Linear relationship, independent errors, constant error variance, normal errors for inference, and no severe multicollinearity. Check with residual plots, a Durbin Watson or autocorrelation plot, a scale location plot, a Q-Q plot, and VIF.
How to answer it
List them, then say how you would look for each. The check is what interviewers are listening for.
Linearity: the expected outcome is a straight-line function of the features. Plot residuals against fitted values, a curve means a missing transform or interaction.
Independence of errors: one row's error tells you nothing about another's. Time series and repeated users break this. Plot residuals in order, or use Durbin Watson.
Homoscedasticity: constant error variance. A funnel in the residual plot means variance grows with the fitted value, common with revenue. Log the outcome or use robust standard errors.
Normal errors: needed for exact p-values and intervals in small samples, not for the coefficient estimates themselves. Q-Q plot of the residuals. With thousands of rows the CLT covers you.
No perfect multicollinearity: correlated predictors make coefficients unstable. Check VIF, above 5 to 10 is a flag.
import statsmodels.api as sm
model = sm.OLS(y, sm.add_constant(X)).fit()
resid, fitted = model.resid, model.fittedvalues # plot these against each other
The distinction to draw: a violated assumption rarely breaks the predictions much, it breaks the standard errors and therefore the p-values. If the question is "does this feature matter", the assumptions matter. If the question is "predict next month", they matter less.
What they are checking: five assumptions, a check for each, and which ones affect inference versus prediction.
Common mistake: saying the features must be normally distributed. It is the errors, and only for inference.