[R] summary(object, test=c("Roy", "Wilks", "Pillai", ....) AND ellipse(object, center=....)

[Michael Friendly]

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

Ray Haraf wrote:
> 2). My next struggle is to construct prediction ellipse. Both ellipse() and ellipse.lm() are not giving me the solution to "Sampling from multivariate multiple regression prediction regions" posted by Iain Pardoe, Mon May 9 18:43:46 2005. I am working on the same problem and performed all the steps he suggested
> 
>> 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), 
> + z1 = c(123.5, 146.1, 133.9, 128.5, 151.5, 136.2, 92), 
> + z2 = c(2.108, 9.213, 1.905, .815, 1.061, 8.603, 1.125)) 
>> 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) 
>          y1 y2 
> [1,] 151.84 349.63 
>> qf.z <- t(c(1, 130, 7.5)) %*% 
> + solve(t(cbind(1,z1,z2)) %*% cbind(1,z1,z2)) %*% 
> + c(1, 130, 7.5) 
>> round(qf.z, 5) 
>         [,1] 
> [1,] 0.36995 
>> n.sigma.hat <- SSD(f.mlm)$SSD # same as t(resid(f.mlm)) %*%resid(f.mlm) 
>> round(n.sigma.hat, 2) 
>      y1 y2 
> y1 5.80 5.22 
> y2 5.22 12.57 
>> 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?
>  
> Thanks and very kind regards,
> Ray
> 
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