DESCRIPTION

Students:  This is a group quiz.  You are allowed to talk to your
teammates (but no one else), use the Internet and so on.

To get credit, you MUST be logged in under an e-mail address of the form

ajones@ucdavis.edu_jsmith@ucdavis.edu_gyu@ucdavis.edu

where the individual components must EXACTLY MATCH what you have been using
in the quizzes.

QUESTION -ext .R -run 'Rscript omsi_answer1.R'

(50 pts, code) Recall that "ridge regression" fits a linear model but
with an "l2" penalty:  Instead of minimizing (3.6), we minimize
(D - Ab)'(D - Ab) + s b'b.  One can show that this is done by replacing
A'A in (3.11) by A'A + s I.  Write code to implement this.  The call
form will be

ridgelm(xy,s)

and it will return b, the vector of coefficients.  Here xy is a matrix
with the response variable in the last column and the predictors
in the other columns.  Hint:  You may find useful R's solve() and diag()
functions.

ridgelm<- function(xy,s)
{


}

d <- cbind(c(5,1,2,8),c(0,2,2,1),c(8,3,4,2))
print(ridgelm(d,0.2))
#            [,1]
# [1,]  6.5701554
# [2,] -0.1712036
# [3,] -1.5710789



QUESTION -ext .R -run 'Rscript omsi_answer2.R'

This problem concerns Sec. 6.2.2.1 of our book.  You will develop general code 
that adds a new covariate like the "average rating in service courses" example.  
# rsdf: a data frame in the standard (userID, itemID, rating, covs) format
# idCol: column number in rsdf of the grouping ID, either user or item ID
# dummyCol: dummy variable on which average rating is to be found

# returns copy of rsdf, with an exra column: for a given row (u,i,r,covs), 
# the value of the new column will be the mean rating given by user u among 
# all rows for which the given dummy is 1

makeAvgCov <- function(rsdf,idCol,dummyCol) {
   dm <- as.numeric(rsdf[,dummyCol])
   rsdf.sub <- rsdf[dm == 1,]
   id <- as.character(rsdf[,idCol])

   meanNoNA <- function(x) mean(x,na.rm=T)
   tmp <- tapply(         )
   newCol <- 
   cbind(rsdf,newCol)
}

library(rectools)
getInstEval()
ivl15 <- ivl[1:15,]  
makeAvgCov(ivl15,1,6)  
# new col in above return value should be 4 2.5s, then 2 NAs, then 9 3.333s