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Demonstrating Least Squares Fitting Properties Using a Plot Equivalent to an F test

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Title: Demonstrating Least Squares Fitting Properties Using a Plot Equivalent to an F test


1
Demonstrating Least Squares Fitting Properties
Using a Plot Equivalent to an F test
  • Frank J. Matejcik Roger W. Johnson
    Industrial Engineering Math Comp SciSouth
    Dakota School of Mines Technology JSM 2003 San
    Francisco

2
Overview
  • Ancient Tools System
  • Notation formulas etc.
  • Examples of Katyas triangle
  • Multiple Regression (comments)
  • Summary

3
Ancient Tools System
  • Plots work like/with Formulas QA task

4
Notation Formulas
5
Anscombe(1973) good case
6
Anscombe(1973) parabola
7
Anscombe(1973) unbalanced
8
Real data example 1
9
Real data example 1 detail
10
1500 meter records
11
1500 meter records residuals
12
Multiple Regression Plots
  • SST, SSR, SSE are analogous
  • Features detected are analogous, too.
  • Katyas Triangle with the observations in any
    order.
  • Orderings of interest include
  • given order, response variables, fit variables
  • predicator variables
  • potential predictor variables
  • transformations of predictor variables

13
Summary
  • Plots for regression ANOVA test calcs
  • Fundamental ANOVA identity for a regression model
  • correct assumptions, other functions, outliers,
    unbalanced, mixed
  • Introduced Ancient Tools
  • Applicable for many statistics
  • Plots supplement (replace) formulas ?
  • Web resourcesLook up Frank Matejcik at
    www.sdsmt.edu
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