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Residual Linearity Verified through Model Diagnostics 📂Statistical Analysis

Residual Linearity Verified through Model Diagnostics

Diagnostic Techniques 1

Standardized residual plots can be used to check if the regression analysis was performed correctly.

To check for linearity, see if the residuals are symmetrically distributed around $0$.

20180831\_124928.png Looking at the figure on the right, it is evident that there is a lack of linearity.

20180831\_134939.png If it were a simple regression analysis, it would result in an inability to explain the trend of the data at all.

Let’s look at some shapes to be wary of.

20180831\_124938.png The left side shows that the green residuals violate various assumptions of regression analysis but satisfy linearity itself.

The right side shows residuals that are distributed around $0$ on average, but there are issues calling it symmetric. If the residual plot turns out like this, it can be almost certainly inferred that some important condition or data is missing.

20180831\_135538.png If it were a simple regression analysis, the trend of the data would roughly be correct, but there would always be large errors on an all-or-nothing level.

See Also


  1. Hadi. (2006). Regression Analysis by Example(4th Edition): p91. ↩︎