Residuals
Definition
Residuals are the differences between observed values and predicted values in a regression analysis. They represent the vertical distances between data points and the least-squares regression line.
Analogy
Imagine you're playing darts, and your goal is to hit the bullseye every time. The residuals would be the distances between where your darts actually land (observed values) and where they were supposed to land (predicted values). Positive residuals mean you overshot, while negative residuals mean you fell short.
Related terms
Standard Deviation of Residuals: The standard deviation of residuals measures the average distance between each residual and the regression line.
Homoscedasticity: Homoscedasticity refers to a situation where the variability of residuals is constant across all levels of an independent variable.
Influential Observations: Influential observations are data points that have a significant impact on the results of a statistical analysis, such as regression coefficients or predictions.
"Residuals" appears in:
Study guides (2)
Additional resources (3)
Practice Questions (10)
What does the standard deviation of the residuals represent?
What are residuals in a linear regression model?
What is the goal of linear regression in terms of residuals?
What do small residuals indicate in a linear regression model?
Which of the following statements about residuals in linear regression is true?
What do negative residuals indicate in the linear regression model?
What formula calculates residuals?
What does it mean if the residuals in a linear regression model are normally distributed?
Why are the residuals squared in the least squares criterion?
What is the standard deviation of the residuals in regression analysis?
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