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Residuals definitions

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  • Linear Regression
    A statistical method that finds the line minimizing the sum of squared vertical distances from data points.
  • Least Squares Method
    A technique that determines the best-fitting line by minimizing the sum of squared residuals.
  • Line of Best Fit
    A straight line that most closely approximates the data in a scatterplot, based on minimizing residuals.
  • Residual
    The vertical distance between an observed value and its predicted value from the regression line.
  • Residual Plot
    A graph displaying residuals on the y-axis and original x-values on the x-axis to assess model fit.
  • Regression Equation
    A formula used to calculate predicted values for y based on given x values in linear regression.
  • Predicted Value
    The y-value estimated from the regression equation for a specific x-value, often denoted as ŷ.
  • Observed Value
    The actual y-value from the dataset corresponding to a specific x-value.
  • Random Pattern
    A distribution of residuals with no discernible structure, indicating a good model fit.
  • Discernible Pattern
    A recognizable structure in residuals, such as oscillation or divergence, suggesting a poor model fit.
  • Standard Deviation
    A measure of spread in residuals; non-constant values across data suggest model inadequacy.
  • Divergence
    A situation where residuals become increasingly spread out, indicating changing variability in the data.
  • Oscillation
    A pattern in residuals where values alternate above and below the axis, often resembling a wave.
  • Y-Axis
    The vertical axis on a graph, used for plotting residuals in a residual plot.
  • X-Axis
    The horizontal axis on a graph, representing the original data values in a residual plot.