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L.I.N.E. assumptions for regressions

We use various charts to interrogate our assumptions about linearity, independence, normality, and equal variance in a regression model. These assumptions are abbreviated as LINE.

Assumption

Supported

Violated

Linearity (or zero mean) of the residuals

In a scatterplot of residuals vs fitted values, the residuals bounce randomly around the zero line

In a scatterplot of residuals vs fitted values, the residuals are mostly below zero for some fitted values, and mostly above zero for other fitted values. Oftentimes, we see residuals above zero for low and high fitted values, and below zero for medium fitted values.

Independence

In a scatterplot of residuals vs order, the residuals bounce randomly around the zero line

In a scatterplot of residuals vs order, the residuals tend to follow one another closely over time.

Normality

In a normal probability plot (QQ plot) of the residuals, the points lie close to the diagonal line. Oftentimes, a Ryan-Joiner test statistic and a corresponding P-value are provided with the QQ plot when using statistical software, for the null hypothesis of normal error terms, and the alternate hypothesis that errors terms are not normal. The P-value will exceed the alpha-value (for example, for a 95% significance level).

In a normal probability plot (QQ plot) of the residuals, the points do not lie close to the diagonal line. The P-value will be less than the alpha-value (for example, for a 95% significance level).

Equal variance

In a scatterplot of residuals vs fitted values, the residuals roughly form a horizontal band around the zero line.

In a scatterplot of residuals vs fitted values, the residuals roughly form a widening megaphone shape around the zero line