In addition to showing multiple R^2, the plot of residuals vs fitted
can show lack of fit that doesn't show up in plots of y or residuals
against individual x's.
Here's an example:
n = 200
set.seed(0)
x = matrix( runif(n * 20), nrow = n)
temp = rowSums(x)
y = temp + temp^2 + rnorm(n)
fit = lm(y ~ x)
fit
plot(fit)
# Note that the lack of fit shows up clearly in the plot
# of residuals vs fitted
# In constrast, the lack of fit does not show up when
# plotting either y or residuals against individual x's
for(j in 1:4) plot(x[,j], y, ask=T)
for(j in 1:4) plot(x[,j], resid(fit), ask=T)
>---- Original message ----
>>I was trying to explain my use of residual diagnostic plots to a
>>colleague when I realized that I do not have a handle on the use
>>of the 'Response vs Fitted Values' plot.
>
>
>
>In simple linear regression, the plot of y ~ y.hat is essentially the same
>as y ~ x, because y.hat = a + b*x is a rescaling of x.
>
>In multiple regression, the plot of y ~ y.hat is an illustration of multiple
>R^2,
>the proportion of variability explained by the model,
>because the correlation of y and y.hat is exactly R.
>
>My book
>Statistical Analysis and Data Display
>An Intermediate Course
>with examples in S-Plus, R, and SAS
>Series : Springer Texts in Statistics
>Heiberger, Richard M., Holland, Burt
>2004, 754 p., Hardcover
>ISBN: 0-387-40270-5
>with online files at http://springeronline.com/0-387-40270-5
>
>has a very complete discussion of all six of the standard linear model
>diagnostic plots.
>
>Rich
Tim Hesterberg
========================================================
| Tim Hesterberg Research Scientist |
| timh@insightful.com Insightful Corp. |
| (206)802-2319 1700 Westlake Ave. N, Suite 500 |
| (206)283-8691 (fax) Seattle, WA 98109-3012, U.S.A. |
| www.insightful.com/Hesterberg |
========================================================
Download the S+Resample library from www.insightful.com/downloads/libraries
Two Research Scientist positions:
data mining
frailty/mixed effects
http://www.insightful.com/company/jobs.asp
|