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Prediction Intervals definitions

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  • Prediction Interval
    Range estimating a single y value from regression, reflecting uncertainty and incorporating both model and individual variability.
  • Confidence Interval
    Range estimating a population parameter, expressing certainty about where the true value lies based on sample data.
  • Regression Line
    Equation modeling the relationship between x and y, used to predict y values for given x values.
  • Point Estimate
    Best guess for a predicted y value, calculated by plugging a specific x into the regression equation.
  • Critical Value
    Number from the t-distribution determining the width of the interval, based on confidence level and degrees of freedom.
  • Standard Error
    Measure of variability in predicted y values, calculated from sample data and used in margin of error.
  • Margin of Error
    Amount added and subtracted from the point estimate to form the interval, combining critical value and standard error.
  • Degrees of Freedom
    Value used in t-distribution calculations, typically equal to sample size minus two in regression contexts.
  • Linear Correlation
    Strength and direction of the relationship between x and y, verified before constructing intervals.
  • Sample Size
    Number of x-y pairs in the dataset, affecting calculations for standard error and margin of error.
  • t-Distribution
    Probability distribution used for critical values when sample sizes are small or population variance is unknown.
  • x Bar
    Mean of the x values in the sample, used in margin of error calculations for prediction intervals.
  • Sigma x
    Sum of x values, or sometimes standard deviation of x, used in statistical calculations for regression.
  • Sigma x Squared
    Sum of squared x values, a statistic used in margin of error formulas for prediction intervals.
  • Upper Bound
    Highest value in the prediction interval, found by adding margin of error to the point estimate.