Dear All,
   
  I would be very appreciative of your help with the following
   
  1). I am running multivariate multiple regression through the manova() function (kindly suggested by Professor Venables) and getting two different answers for test=c("Wilks","Roy","Pillai") and tests=c("Wilks","Roy",'"Pillai") as shown below. In the first case (test=c(list)) I got error message which probably means I can only call one test at a time. I thought I could get ride of this by adding "s" to test; in this case (tests=c(list)), I got Pillai test. Does this mean that Pillai would be the default test and summary(manova()) can only post one test at a time?

> summary(manova(cbind(y1, y2) ~ z1, data =
+ ex7.8),test=c("Wilks","Roy","Pillai"))
Error in match.arg(test) : 'arg' must be of length 1
> summary(manova(cbind(y1, y2) ~ z1, data =
+ ex7.8),tests=c("Wilks","Roy","Pillai"))
          Df  Pillai approx F num Df den Df Pr(>F)  
z1         1  0.9375  15.0000      2      2 0.0625 .
Residuals  3                                        
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

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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