1. Final projects.
2. R Cookbook ch. 11.
3. XCode.
4. Compiling C and calling C from R.
5. Hello world.
6. pi.
7. dnorm.
8. Sum of squared differences between observations.

1. Final projects. 

I made a couple small changes to the schedule. It only affects teams 5 and 8.
Here is the schedule now.

 Tue, Nov 26
[1] DAS GUPTA, APARUPA .      MAO, JUNHUA .      WANG, PENG .      
[2] CAI, YUAN .      SINGH, VIKRAM VIR .      WU, GUANI .      
[3] LIU, YUNLEI .      KARWA, ROHAN SUNIL .      KUHFELD, MEGAN REBECCA .      
[4] MURPHY, JOHN LEE .      HONG, JI YEON .      SHAH, VAIBHAV CHETAN .      

  Tue, Dec 3 
[5] Csapo, Marika .      LEWIS, BRONWYN ASHLEIGH .      ZHANG, QIANG .      
[6] NAN, XIAOMENG .      ARELLANO, RYAN CHRISTOPHER .      SHU, LE .      
[7] WANG, XINYUE .      CHEN, JIAMIN .      HAN, TIAN .      
[8] THAKUR, MANOJ RAMESHCHANDRA .      POWELL, CHRISTOPHER GRANT .      
[9] XIE, MEIHUI .      WONG, ALEX KING LAP .      XIE, DAN .      
[10] TAN, MENGXIN .      ROBERTS, SHANE WILLIAM STROUTH .      HUANG, PENG JUN .      
[11] YU, CHENGCHENG .      WU, JOHN SHING .      MOUSAVI, SEYED ALI .      

  Thu, Dec 5 
[12] FERNANDEZ, KEITH EDWARD .      AHLUWALIA, ANSUYA .      HAROUNIAN, BENJAMIN .      
[13] GU, JIAYING .      RAMIREZ, ARTURO .      DEMIRDJIAN, LEVON .      
[14] HUYNH, HIEN TRINH .      SHEN, LINLING .      CHANDRASEKHARAN, MANJANA .      
[15] WISNER, TRISTAN GARDNER .      MAGYAR, ZSUZSANNA BLANKA .      HE, JIA .      
[16] KRUMHOLZ, SAMUEL DAVID .      KATTE, SAMIR RAJENDRA .      WAINFAN, KATHRYN TANYA .      
[17] WANG, TENG .      SCHWEIG, JONATHAN DAVID .      Gupta, Hitesh .      

2. R Cookbook ch11.

After today we will have covered all of ch. 1-11, and next week
I'll discuss ch. 13.1 and 13.2, but that's probably it for R Cookbook. The 
rest will be C.

lm, p269-285. lm(y ~ x), y = b0 + b1 x + eps
lm(y ~ u + v + w)
fits y = b0 + b1 u + b2 v + b3 w + eps.

lm(y ~ u + v + w + 0) for no intercept, b0.

lm(y ~ u*v*w) for all interactions. See p279.
y = b0 + b1u + b2v + b3w + b4uv + b5uw + b6vw + b7 uvw + e.

To specify a particular interaction, use :.
lm(y ~ u + v + w + u:v:w) for just the uvw term. See p280.
This fits y = b0 + b1 u + b2 v + b3 w + b4 uvw + eps.

p280, lm(y ~ (u+v+w)^i) for all order i interactions. 

  u = rnorm(10000)
  v = rnorm(10000)
  w = rnorm(10000)
  x = rnorm(10000)
  y = 10 + 20*u + 30*u*v + rnorm(10000,sd=.01)
  j = lm(y ~ (u + v + w + x)^3)
  summary(j)

Use - to eliminate a term. 
  j = lm(y ~ (u + v + w + x)^3 - v:w:x - v)
  summary(j)

step, p281, to do stepwise regression, forward or backward.
  k = step(j,direction="backward")

AIC = Akaike's Information Criterion, lowest AIC is best fitting model.
Assuming eps = iid Normal(mean 0, some variance sigma^2), 
can calculate the likelihood associated with a particular model and 
parameters.
AIC = -2 log (likelihood) + 2p. Lower AIC is preferred.
For comparing nested models, the difference in AIC is generally 
approximately chi square distributed.

  summary(k)

  k2 = step(lm(y ~ 1), direction="forward", scope = ( ~ (u+v+w+x)^4), trace=0)
  summary(k2)

p285, I(u+v) for a term that actually just represents u+v. Similarly, 
I(u^2) for a term that is u^2, or I(u*v) for a column that is u*v.
  k = lm(y ~ I(u*v*w))
  k = lm(y ~ I(x^2 + x))

p292, confint for confidence intervals.
  confint(k2)
p293, plot the residuals with plot(k2, which=1), and other plots with 
plot(k2).

3. XCode, for Mac OSX, includes a C and C++ compiler, among other tools.
You can get XCode from 
http://wildfire.stat.ucla.edu/rick/xcode .
Click on the one choice, xcode_3.2.6_and_ios, to get it. I will only leave 
it up there for a week or so. It takes a couple hours to download.
If you have a PC, you will need a compiler. There are many free ones. 
See for instance http://www.compilers.net/dir/free/compilers/ccpp.htm .

4. Compiling C and calling C from R.

The first step to writing C code is opening a text editor.
Write your C code, call it something.c, then compile it, to create an 
object file called something.so. Then you can load that into R.
It seems to primarily work with R from terminal, but you can run C in R in 
terminal, do save.image(), and then start R, use the same working 
directory, and then do load(".RData") .

5. Hello world.

Create a C function to print "Hello world!" and call this function n 
times in R.

4a. In a text editor, create a C file.  Say it's called hello.c  
The file looks like:

	#include <R.h>
	#include <Rmath.h>

	/* Start a comment.
	   Continue your comment.
        */

       void hello (int *n)
          {
	  int i,j;
	  double a2;
	  a2 = 4.5;
	  j = 3;
	  for(i = 0; i < *n; i++)
	     Rprintf("The %d rd integral is %f .\n", j, a2);
	  }


5b. In UNIX, in same directory where hello.c is, type

	R CMD SHLIB hello.c

or, in R, do system("R CMD SHLIB hello.c")

5c. In R, in the same directory, do

	dyn.load("hello.so")
	
	hello2 <- function(n){
		.C("hello",as.integer(n))
	}

	y = hello2(10)