Why do we analyze residual plot in regression analysis and NOT between two individual variables?

For example when checking for normality, heteroscedasticity etc. we don't analyze two individual variables but residual plot, why so?

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#### Best Answer

As stated by Patrick, the majority of assumptions in linear regression refers to residuals. The only exception is the condition of linearity between the response variable (dependent variable) and the explanatory variables (independent variables).

The other three assumptions are:

- The distribution of residuals needs to follow a normal distribution.
- Constant variance of error terms (also known as homoscedasticity).
- Independence of residuals (no serial correlation).

Even the linearity assumption can verified with plots using residuals information. Here is a reference which talks about how to detect violation of such presuppositions and possibilities to fix them (people.duke.edu).

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