Applied Regression Analysis

Draper, N. R., & Smith, H. (1998). Applied Regression Analysis. Wiley.

Type

Book

Intellectual base

Textbook

Year

1998

DOI

10.1002/9781118625590

ISBN

9780471170822

Link

https://doi.org/10.1002/9781118625590

Cited from

mathematics, philosophy, statistics_experimental_design

Cited by

6 citations across 6 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Assumption
  • In statistics and modeling, every model rests on distributional, independence, stationarity, and exchangeability assumptions, and assumption-checking is institutionalized as residual diagnostics and sensitivity analysis.

    This sourceStandard reference institutionalizing residual diagnostics and sensitivity analysis for checking regression assumptions.

• Extrapolation Beyond Sampled Regime
  • Statistical regression: prediction outside the convex hull of the data carries smooth-looking confidence intervals derived from in-sample covariance that do not widen as the input moves into unsampled regions.

    This sourceStandard treatment showing prediction outside the range/convex hull of the data carries intervals derived from in-sample covariance and warns against extrapolation beyond the observed regime.

• Projection
  • The fitted values are \(\hat{y} = X(X^\top X)^{-1}X^\top y = Py\), where \(P\) is the projection (hat) matrix.

    This sourcePresents least-squares regression as orthogonal projection onto the column space via the hat matrix, with the residual sum of squares scoring unexplained variation.

Domain-specific

• Fraction of variance unexplained
  • Fraction of variance unexplained is a regression-fit statistic equal to the proportion of dependent-variable variance left unexplained by the model's predictions.
• Lack-of-Fit Sum of Squares
  • Pure error measures variation among responses at the same setting; lack of fit measures the weighted discrepancy between each setting mean and the fitted model value.
• Partial residual plot
  • … identity and a convenient observable transfers from A canonical example satisfies the full defining rule of Partial residual plot with every parameter and convention explicit. to A careful use of Partial residual plot tests assumptions, boundaries and the nearest confusable rather than relying on the label alone..

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