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Prediction Intervals definitions

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  • Prediction Interval
    A range estimating where a single future y value will fall, given a specific x, using a regression line and accounting for uncertainty.
  • Regression Line
    A straight line summarizing the relationship between x and y, used to predict y values for given x values.
  • Point Estimate
    A calculated best guess for y at a specific x, found by plugging x into the regression equation.
  • Margin of Error
    The amount added and subtracted from the point estimate to create the interval, reflecting prediction uncertainty.
  • Critical Value
    A t-distribution value based on confidence level and degrees of freedom, used in margin of error calculations.
  • Standard Error
    A measure of the typical distance between observed y values and the regression line, found as 's' in calculator output.
  • Degrees of Freedom
    A value, usually n minus two for regression, determining which t-distribution to use for interval calculations.
  • Linear Correlation
    A statistical relationship showing how closely x and y values follow a straight-line pattern.
  • X Value Range
    The span of observed x values; prediction is reliable only if the chosen x falls within this interval.
  • Y Hat Equation
    The formula representing the regression line, used to compute predicted y values for given x inputs.
  • X Bar
    The mean of all x values in the dataset, used in margin of error calculations.
  • Sigma X
    The sum of all x values, or sometimes the standard deviation of x, depending on context and calculator output.
  • Sigma X Squared
    The sum of each x value squared, used in the calculation of the margin of error for prediction intervals.
  • Confidence Level
    The probability, often 95%, that the interval contains the true y value for the specified x.