📂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 $0$.

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

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.

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.

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

• Homoscedasticity
• Independence
• Normality