Sorry, I misread the question.
The "Response vs fitted" plot also shows the lack of fit,
(though not as well as does the residuals vs fitted plot).
Tim
>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
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