[R] confidence interval in "predict.lm"
Martin Maechler
maechler at stat.math.ethz.ch
Fri Nov 15 18:42:05 CET 2002
You are looking for some (most?) statisticians call
``prediction interval''
==> just give "prediction" instead of "confidence" :
> predict(mod,data.frame(temp = 45),level = .95,
+ interval = "prediction", se.fit = TRUE)
$fit
fit lwr upr
[1,] 32.96429 26.48597 39.4426
$se.fit
[1] 0.9148715
$df
[1] 5
$residual.scale
[1] 2.348252
>>>>> "Fred" == Fred Mellender <fredm at frontiernet.net>
>>>>> on Fri, 15 Nov 2002 11:43:28 -0500 writes:
Fred> I am studying statistics using R and a book
Fred> "Understandable Statistics", by Brase and Brase. The
Fred> book has two worked examples for calculating a
Fred> confidence interval around a predicted value from a
Fred> linear model. The answers to the two examples in the
Fred> book differ from those I get from R. The regression
Fred> line, the standard error, and the predicted value in R
Fred> and the book all agree for the examples. Hence I
Fred> gather that R and the book use different formula to
Fred> calculate the confidence interval. Could someone
Fred> explain why the difference exists, and which
Fred> function(s) in R I might use to get the answers in the
Fred> book, and (perhaps) an explanation as to which method
Fred> to use in various situations).
Fred> The example:
>> x<-c(10,20,30,40,50,60,70) y<-c(17,21,25,28,33,40,49) dat
>> <- data.frame(temp=x,amnt=y)
Fred> temp amnt 1 10 17 2 20 21 3 30 25 4 40 28 5 50 33 6
Fred> 60 40 7 70 49
Fred> being a table of temperatures (temp) and the
Fred> corresponding amounts of copper sulfate that disolve
Fred> in 100g of water at that temperature.
Fred> The regression line:
>> mod <- lm(amnt ~ temp,dat) summary(mod)
Fred> Call: lm(formula = amnt ~ temp, data = dat)
Fred> Residuals: 1 2 3 4 5 6 7 1.7857 0.7143 -0.3571 -2.4286
Fred> -2.5000 -0.5714 3.3571
Fred> Coefficients: Estimate Std. Error t value Pr(>|t|)
Fred> (Intercept) 10.14286 1.98463 5.111 0.00374 ** temp
Fred> 0.50714 0.04438 11.428 8.98e-05 *** --- Signif. codes:
Fred> 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
Fred> Residual standard error: 2.348 on 5 degrees of freedom
Fred> Multiple R-Squared: 0.9631, Adjusted R-squared: 0.9558
Fred> F-statistic: 130.6 on 1 and 5 DF, p-value: 8.985e-05
Fred> The .95 confidence interval for a temperature of 45
Fred> degrees:
>>
Fred> foo<-predict(mod,data.frame(temp=45),level=.95,interval="confidence",se.fit=
Fred> T)
>> foo
Fred> $fit fit lwr upr [1,] 32.96429 30.61253 35.31604
Fred> $se.fit [1] 0.9148715
Fred> $df [1] 5
Fred> $residual.scale [1] 2.348252
Fred> The book gives the confidence interval as 26.5 <= y <=
Fred> 39.5. The book defines the confidence interval
Fred> calculation thus:
Fred> yp - E <= y <= yp + E
Fred> Where E = tc*sC *sqrt(1 + 1/n + (x-xBar)^2/SSx) yp
Fred> is the predicted value from the regression line tc is
Fred> the value from Student's t distribution for a
Fred> confidence level, c, using n-2 degrees of freedom, sC
Fred> is the standard error of estimate SSx is
Fred> Sum(x^2)-[Sum(x)]^2/n n is the number of data pairs.
Fred> So that even though the model, predicted value,
Fred> standard error all agree, R gives a much smaller
Fred> confidence interval than the book does.
Fred> Thanks for any advice/help.
Fred> -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
Fred> r-help mailing list -- Read
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Fred> the subject !) To: r-help-request at stat.math.ethz.ch
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