What question did this study set out to answer?

This analysis aims to understand the effects of residuals and influential data points in regression models.

September 1, 1983

Residuals and Influence in Regression.

Key Points

This analysis aims to understand the effects of residuals and influential data points in regression models.
Utilizes diagnostic methods including Atkinson's method and Tukey's test.
Incorporates influence curves to assess the impact of data points on model estimates.
Explores various transformations to meet assumptions of normality and variance.
Identified significant outliers affecting model predictions.
Demonstrated the necessity of transformations for maintaining model assumptions.
Found variations in model influence using empirical influence curves.

Abstract

Conlputat ions E.ratnple 2.3.4Jer Jiyhters no.I 2.3.3Partial residual plots Esantple 2.3.5 Jef fiyhrers no. 2 2.3.4Probability plots E.ratrtpIe 2.3.6 Cloud seeditty no. 4 2.4 Transformations 2.4.1 Fanlilies of fratlsjorr~ratiot~s 2.4.2Selectb~g a trat~s/'orrtlatiott Itr~.ariattceNor~rrality Choice c?/'trtodel i ~t t c i scalirlg the predictors It~f'erettce E.uan~ple 2.4.1 Tree data 110.I 2.4.3Diagnostic ntetttods A tkinson 's method Andrew' nterhod Application to the power family Tukey's test E.rample 2.4.2Tree data no. 2 E.~antple 2.4.3Jet fiyhters no. 3 2.4.4Trarrsfor~r~ing the esplana~ory ~lariahles Esatrtple 2.4.4Tree data no. 3 Esatrtple 2.4.5 Cloud see(fittg no. 5 2.5 Residual analysis in two-way tables 2.5.1 Otitliers 2.5.2Nottaciditirity E.\-antple 2.5.1 A y ricultural e-rperintenl 3 Assessment of influence 3.1 Motivation 3.2 The influence curve E.uatrtple 3.2.1The sanlple auerage3.3 The influence curve in the linear model 3.4 Sample versions of the influence curve 3.4.1 E~rtpiricnl ittfl~iet~i-e curves 3.4.2Sotrtple it~fltrettce curres Esntilple 3.4.1 C l o ~i d seeding tlo.6 E.uittr~ple 3.4.2Partial Ffesrs 3.5 Applications of the sample influence curve 3.5.1 Estert~al scalit~g bI = XTX, c = p'62 Euatrtple 3.5.1 C'omhinafion.sqf r f , vii Esanlple 3.5.2Rat data Alrernatice full rank choices for M, c Lower dintensior~al trortrts E.ratiiple 3.5.3Cloud seeding 110.7

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