On Dec 5, 2006, at 3:42 PM, Leeds, Mark ((IED)) wrote: > If do a scattrplot of data ( x and y ) and there are two clouds of > points. One cloud is in the left > bottom corner of the plot and the other cloud is in the upper right. > > If I fit a regression line to this data ( or equivalently , > calculate a > correlation ), then obviously, it is going to seem like > x and y are related because a line has to be connected between the 2 > clouds. But, there must be a regression assumption that > is violated here because if the regressions are done separately on > each > cloud, then there really isn't > a relationship between x and y. I was just wondering 1) what > assumption > in regression is being violated in > the first case or 2) possibly if the regression is valid and the > results > just have some different interpreation ?
One needs only to look at diagnostic plots: Suppose set.seed(2) xy <- data.frame(y = c(rnorm(300), rnorm(300, 5)), x = c(rnorm(300), rnorm(300, 5))) op <- par(mfrow = c(2,2)) plot(lm(y ~ x, xy)) par(op) The model does not fit well because the residuals aren't flat as a function of fit and because homoscedasticity is violated. When this happens we might try a different approach: require(sm) xy.sm <- sm.regression(xy$x, xy$y) Whenever there's a big discrepancy between an OLS fit and a robust one, we should not pursue the OLS one w/o reinterpretation, which others have discussed in their replies. _____________________________ Professor Michael Kubovy University of Virginia Department of Psychology USPS: P.O.Box 400400 Charlottesville, VA 22904-4400 Parcels: Room 102 Gilmer Hall McCormick Road Charlottesville, VA 22903 Office: B011 +1-434-982-4729 Lab: B019 +1-434-982-4751 Fax: +1-434-982-4766 WWW: http://www.people.virginia.edu/~mk9y/ ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.