Explain what a multiple linear regression takes for granted and read residual plots for signs that those conditions fail

Least squares inference rests on five assumptions: a linear relationship, errors with constant variance (homoskedasticity), errors independent of one another, errors normally distributed, and independent variables that are not random or at least uncorrelated with the errors. Residual plots are the first check. Plot residuals against each independent variable and against predicted values: a curved pattern suggests non-linearity, and a fan shape that widens suggests heteroskedasticity. Plot residuals in time order: long runs of the same sign suggest serial correlation. A normal Q-Q plot that bends away from the line at the ends signals fat tails. Remember that a clean plot against one variable does not clear the whole model.