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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 self-perceived ideal weights of a random sample of 40 female university students enrolled in an introductory Statistics course at the University of Auckland 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 self-perceived 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 the scatter plot.
Alternative: prediction error
Curriculum achievement objectives reference
Statistical investigation: (Level 8)
