From: Michael Friendly <friendly_at_yorku.ca>

Date: Sun, 06 Apr 2008 18:48:31 -0400

*> + z1 = c(123.5, 146.1, 133.9, 128.5, 151.5, 136.2, 92),
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*> + z2 = c(2.108, 9.213, 1.905, .815, 1.061, 8.603, 1.125))
*

> + solve(t(cbind(1,z1,z2)) %*% cbind(1,z1,z2)) %*%

*> + c(1, 130, 7.5)
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*> [1,] 0.36995
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*> y2 5.22 12.57
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> [1] 9.55

*>
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*>
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*>
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> 3). Lastly but not the least, would be too ambitious to draw the axes (i.e, the eigenvalues) to the ellipse?

*>
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*> Thanks and very kind regards,
*

*> Ray
*

*>
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>

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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. Received on Sun 06 Apr 2008 - 22:55:23 GMT

Date: Sun, 06 Apr 2008 18:48:31 -0400

You may be interested in the heplots package for multivariate linear models. For a multivariate regression, it plots a data ellipse of the predicted values (H matrix) together with a data ellipse of the residuals (E ellipse). H is scaled so that it protrudes outside the E ellipse iff the hypothesis is significant by Roy's test.

-Michael

>> ex7.10 <-

> + data.frame(y1 = c(141.5, 168.9, 154.8, 146.5, 172.8, 160.1, 108.5),

> + y2 = c(301.8, 396.1, 328.2, 307.4, 362.4, 369.5, 229.1),

>> attach(ex7.10) >> f.mlm <- lm(cbind(y1,y2)~z1+z2) >> y.hat <- c(1, 130, 7.5) %*% coef(f.mlm) >> round(y.hat, 2)> [1,] 151.84 349.63

> y1 y2

>> qf.z <- t(c(1, 130, 7.5)) %*%

> + solve(t(cbind(1,z1,z2)) %*% cbind(1,z1,z2)) %*%

>> round(qf.z, 5)

> [,1]

>> n.sigma.hat <- SSD(f.mlm)$SSD # same as t(resid(f.mlm)) %*%resid(f.mlm) >> round(n.sigma.hat, 2)> y1 5.80 5.22

> y1 y2

>> F.quant <- qf(.95,2,3) >> round(F.quant, 2)

> [1] 9.55

>>From here how could I calculate a 95% prediction ellipse for y=(y1,y2) at (z1,z2)=(130,7.5) using either ellipse or ellipse.lm? y1 would be the x-axis and y2, the y-axis. The center is different from (0,0) and I don't know what would be the appropriate x (the lm object). Should I used predicted values or residuals? In both cases I have vectors which is different from the example given with ellipse.lm

> 3). Lastly but not the least, would be too ambitious to draw the axes (i.e, the eigenvalues) to the ellipse?

>

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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. Received on Sun 06 Apr 2008 - 22:55:23 GMT

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