University of Massachusetts Amherst



ILLUSTRATING THE COMPUTATIONS ON PAGES 31-34 IN NOTES USING KISHI DATA IN R. THE CAT COMMAND LIST THINGS WHICH CAN BE

A MIX OF TEXT AND VARIABLES

HERE IS THE SCRIPT

data cat("confidence interval",yhat,seyhat,l95m,u95m,"\n")

confidence interval 13.56695 0.9762317 11.57033 15.56357

> cat("prediction interval",yhat,sepred,l95i,u95i,"\n")

prediction interval 13.56695 3.46849 6.473092 20.66081

>

> cat(" Simultaneous 95% ci's on beta0 and beta 1","\n")

Simultaneous 95% ci's on beta0 and beta 1

> tval2 = qt(1-(alpha/4),dfe)

> lbeta0s=b0-(tval2*seb0)

> ubeta0s=b0+(tval2*seb0)

> lbeta1s=b1-(tval2*seb1)

> ubeta1s=b1+(tval2*seb1)

> cat(lbeta0s,ubeta0s,lbeta1s,ubeta1s,"\n")

-3.873648 4.705977 0.3457223 0.486606

>

> cat("SIMULTANEOUS CONFIDENCE INTERVALS ON THE MEAN/EXPECTED VALUE

+ FOR BALANCE AT intake = 30,60 and 80","\n")

SIMULTANEOUS CONFIDENCE INTERVALS ON THE MEAN/EXPECTED VALUE

FOR BALANCE AT intake = 30,60 and 80

>

> cat("using Bonferroni","\n")

using Bonferroni

>

> tbon = qt(1-(alpha/2*3),dfe)

> yhat30 = b0 + b1*30

> se30 = sqrt(s2b0 + (30**2)*s2b1 + 2*30*sb0b1)

> l30m = yhat30 - tbon*se30

> u30m = yhat30 + tbon*se30

> yhat60 = b0 + b1*60

> se60 = sqrt(s2b0 + (60**2)*s2b1 + 2*60*sb0b1)

> l60m = yhat60 - tbon*se60

> u60m = yhat60 + tbon*se60

> yhat80 = b0 + b1*80

> se80 = sqrt(s2b0 + (80**2)*s2b1 + 2*80*sb0b1)

> l80m = yhat80 - tbon*se80

> u80m = yhat80 + tbon*se80

> cat(l30m, u30m, l60m, u60m, l80m, u80m,"\n")

11.40117 14.40101 24.49524 26.27679 32.38102 35.03758

>

> cat("USING SCHEFFE","\n")

USING SCHEFFE

>

> f= qf(1-alpha,2,dfe)

> mult = sqrt(2*f)

> l30ms = yhat30 - mult*se30

> u30ms = yhat30 + mult*se30

> l60ms = yhat60 - mult*se60

> u60ms = yhat60 + mult*se60

> l80ms = yhat80 - mult*se80

> u80ms = yhat80 + mult*se80

> cat(l30ms, u30ms, l60ms, u60ms, l80ms, u80ms,"\n")

10.28429 15.51789 23.83195 26.94008 31.39194 36.02665

IF THE TEXT FILE WITH THE COMMANDS IS IN f:/s505/r/kishi.R and YOU USE

source("f:/s505/r/kishi.R")

HERE IS WHAT YOU GET IN THE CONSOLE. THERE ARE WAYS TO

LABEL THE OUTPUT WITH THE VARIABLE NAMES THAT I’M NOT SHOWING YOU NOW.

----------------------------------------------------------------------------------

0.4161642 0.4161642 3.293353 0.0008880204 -0.05106117 11.0774

intervals at X = 31.6

confidence interval 13.56695 0.9762317 11.57033 15.56357

prediction interval 13.56695 3.46849 6.473092 20.66081

Simultaneous 95% ci's on beta0 and beta 1

-3.873648 4.705977 0.3457223 0.486606

SIMULTANEOUS CONFIDENCE INTERVALS ON THE MEAN/EXPECTED VALUE

FOR BALANCE AT intake = 30,60 and 80

using Bonferroni

11.40117 14.40101 24.49524 26.27679 32.38102 35.03758

USING SCHEFFE

10.28429 15.51789 23.83195 26.94008 31.39194 36.02665

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