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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2$\begingroup$ This is because the assumptions you've mentioned all refer to the error term in the regression model and not the original variables. The residuals represent the unexplained variability in Y (that is not explained by X), this is the error term (e) in Y = b1 + b0*X + e. When you look at a QQ-plot of residuals (for example), you are comparing this error term against standard normal counterparts. $\endgroup$– PatrickCommented Jun 21, 2013 at 21:38
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1$\begingroup$ oops: Y = b0 + b1*X + e; In addition, the homogeneity of variance (homoscedasticity) assumption is in regards to the errors at each value of X. Independence also refers to these errors. Hopefully this makes the assumption diagnostic tools more relevant to you. $\endgroup$– PatrickCommented Jun 21, 2013 at 22:57
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1 Answer
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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).
answered Jun 4, 2014 at 12:41