1.  If we use all k categories, the A matrix would be of less than full
rank, and A'A would be singular.

2.

# 7 dummies; 2 squared terms; 7x2 interaction terms
2 + 7*2

3.  The glm() function will be run 3 times in either case, but AvA
will work on smaller datasets.

4.  

getTrainAcc <- function(qeObj,xdata,ydata)
{
   xdata <- xdata[-(qeObj$holdIdxs),]
   ydata <- ydata[-(qeObj$holdIdxs)]
   preds <- predict(qeObj,xdata)
   if (!qeObj$classif) {
      return(mean(abs(ydata - preds)))
   } 
   return(mean(preds$predClasses != ydata))
}

set.seed(9999)
data(mlb)
data <- mlb[,c(3:6)]
z <- qePolyLog(data,'Position',deg=4) 
print(z$testAcc)  # 0.68
print(getTrainAcc(z, data[,-1], data[,1]))   # 0.61

5. 

lass <- function(xdata,ydata,b,lam)
{
   xdata <- as.matrix(xdata)
   b <- matrix(b,ncol=1)
   A <- cbind(1,xdata)
   D <- ydata
   tmp <- D - A %*% b
   t(tmp) %*% tmp + lam * sum(abs(b))
}

data(mlb) 
mlb <- mlb[,4:6]   # Height, Weight and Age only, e.g. no Position
lass(mlb[,-2],mlb[,2],c(-100,5.0,1.1),1.5)  # 10184259