# In linear regression, why do the assumptions such as normality and homoscedasticity only hold for the residuals?

Why does the distribution of the residuals should be normal and variance of the residuals should be same across the values of the independent variable? Why do we assume these for the residuals only? What are the implications of violating those assumptions? Instead of a mere conceptual explanation, could you please give solid examples such as "at this point in linear regression, we assume this assumption and violating this makes these calculations incorrect" etc?

• You seem to be using the word "residuals" to mean the errors in the model. (Residuals depend on a particular fit whereas the errors are hypothetical random variables.) Is this right? And where you write "for the residuals only," what other aspect of the model are you implicitly suggesting might be subject to comparable assumptions? Please clarify. – whuber Dec 4 '16 at 19:28
• Yes, by residuals I meant errors and variables entered to the regression themselves could have been subject to those assumptions. – behrengi Dec 30 '16 at 16:32