Standard error of linear regression fit

Asked Oct 30 '15 at 21:26

Active Oct 30 '15 at 22:02

Viewed 59 times

I have a naive question about regression. How does R function predict.lm compute the 95% confidence interval of the fitted line? In particular why is this not a straight line?

 x <- rnorm(10,0,10)
 y <- 20*x + rnorm(10,0,2)
 fit <- lm(y ~ x)
 newx <- sort(x)
 prd <- predict(fit,newdata=data.frame(x=newx),interval = c("confidence"),level = 0.95,type="response")

 # plot
 plot(x,y)
 abline(fit)
 lines(newx,prd[,2],col="red",lty=2)
 lines(newx,prd[,3],col="red",lty=2)

Can somebody help me understand how the upper and lower bounds of 95% CI of the fitted line are computed by predict?

edited Oct 30 '15 at 22:02

asked Oct 30 '15 at 21:26

user19758

Could you maybe post the picture of the plot? – metjush Oct 30 '15 at 21:31
Added the plot. – user19758 Oct 30 '15 at 22:06
I looked through the previous questions - this thread is most relevant and the questions not answered there: http://stats.stackexchange.com/questions/158306/how-to-generate-confidence-bands-for-haty?rq=1 – user19758 Oct 30 '15 at 22:55
Since you used type = "response", you are not calculating the confidence interval for the line, you are getting the prediction interval. At any rate, if you want the formula, you may want to read my answer here: Linear regression prediction interval. – gung - Reinstate Monica Oct 30 '15 at 23:06

Standard error of linear regression fit

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