Stat 6601 Project: Bootstrapping Linear Models V

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Stat 6601 Project Bootstrapping Linear Models
(VR 6.6)

• Jaimie Kwon
• Statistics, CSUH

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Goal

• How do we apply bootstrap to linear regression
  models?

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Data

• Phones data the annual numbers of telephone
  calls, in Belgium
• year The last two digits of the year.
• calls The number of telephone calls made (in
  millions of calls).

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Model

• Linear models of the form YX? ??in which
  only ? is considered random.

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Method

• Most obvious form of bootstrapping randomly
  sample pairs (xi, yi) with replacement. (called
  case-based resampling in Davison and Hinkley
  (1997))
• Might not be appropriate
• Alternative Model-based resampling resample
  the residulas.

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Method (Continued)

• Procedure
• After fitting the linear model to getyixib
  ei
• Create a new dataset by yixib ei where ei are
  resample with replacement from the residuals
  (ei).
• Some issues

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Codes

• library(MASS)
• library(boot)
• plot(phonesyear, phonescalls)
• fit lt- lm(calls year, dataphones)
• ph lt- data.frame(phones, resresid(fit),
  fittedfitted(fit))
• ph.fun lt- function(data, i)
• d lt- data
• dcalls lt- dfitted dresi
• coef(update(fit, datad))
• (ph.lm.boot lt- boot(ph, ph.fun, R999))
• plot(ph.lm.boot)

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Results

• Bootstrap Statistics
• original bias std. error
• t1 -260.059246 -3.5164095 96.730498
• t2 5.041478 0.0690514 1.567871

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Summary

• Phones data
• Bootstrap linear models

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Some Tips

• Dont try to cover too much.
• Keep it structured.
• Dont put too much in the slides.
• Let them listen to you.
• Plan to use blackboards as well.
• Dont agonize over equations (or equation
  editor).
• Make slides look neat pleasant.
• Practice and time your presentation.