Residual (in linear regression)

The difference between an observed value of the response variable and the value of the response variable predicted from the regression line.

From bivariate data to be used for a linear regression analysis, consider one observation,(xi, yi). For this value of the explanatory variable, xi, the value of the response variable predicted from the regression line is yi, giving a point (xi, yi) that is on the regression line. The residual for the observation (xi, yi) is yi - yi.

Example

The actual weights and veterinarian-prescribed ideal weights of a random sample of 40 female chimpanzees are displayed on the scatter plot below. A regression line has been drawn. The equation of the regression line is

predicted y = 0.6089x + 18.661 or predicted ideal weight = 0.6089 × actual weight + 18.661

Consider the female whose actual weight is 72kg and whose ideal weight is 70kg.

Her predicted ideal weight is 0.6089 × 72 + 18.661 = 62.5kg

The residual for this observation is 70kg – 62.5kg = 7.5kg

This is also displayed on a scatter plot.

Alternative: prediction error.

Curriculum achievement objectives reference

Statistical investigation: Level 8

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