Dear Students of Prof. Vinod in Econometrics I
Cheers, Let us have fun with econometrics.
The assignments are not so much to judge you as to nudge you to do the work.
My Office Hours are Thursdays 2:45 to 3:45 on Mondays in Dealy E526 ext 4065
MASTER LIST OF possible surprise quiz and Final Exam:
What is sampling distribution? p-value?
Analysis of variance plot in a regression.
What is unbiasedness, mean squared error?
Describe
the computation of expected value.
Multiply
transpose of a vector with another vector.
What
are linear and nonlinear regressions?
What is
the difference between probability distribution function (pdf)
and cumulative distribution function (cdf) (Hint: Wiki has answers)
What is
multiplication of a matrix by a vector?
What is
the variance of fixed scalar k?
If X is
a random variable, what is the variance of kX? (k+X)?
Give an
example of a double summation where the order of summation (i
first or j first) does not matter
Give an
example where it does matter.
Cov(a,b)=Cov(b,a) where a and b are random variables true or false?
Define
correlation in terms of variances and covariances.
Expectation
of sum is sum of expectations. True or False?
Show
that in matrix multiplications AB and BA are diffrernt.
Show
that a matrix times its inverse equals the identity matrix. What about the product of an inverse times
the matrix?
What are five assumptions of the simple linear regression model?
Write the variance covariance matrix if errors are a 3 by 1 vector
Discuss the law of iterated expectations and intuition behind it.
(Hint http://www.columbia.edu/~gjw10/lie.pdf)
Consider the regression model y=xb +u, E(ut|xt)=0. Use the law of iterated expectations to derive the result that E(utxt)=0.
What is the interpretation of slope coefficient in a multiple regression?
How do you define adjusted R2? If R=0.5, n=20,k=2 what is adjusted R2?
What is variance inflation factor? Compute VIF for a regression problem. (ch1 HO)
Discuss nonlinear regression where interactions are involved.(ch1 HO)
Give examples of regression which is (i) nonlinear but linear in parameters and (ii) nonlinear in parameters.
Discuss the issue of collinearity in the context of dummy variables.
Explain how cross product term can be used to assess parameters determined by other variables in a regression (Hint: Kennedy p. 113)
What are influential
observations?
What is a high
leverage point?
When do we have
unbalance design?
What is the hat
matrix? State some properties of diagonals
of the hat matrix.
State some
applications of the FWL theorem.
When is the OLS
estimator biased?
What is condition
number and what are the two ways of obtaining it?
If the condition
number is suspected of being sensitive to units what do you do?
Define MSE in terms
of variance and bias and discuss the tradeoff between the two.
What is MSE in terms
of Euclidian distance in parameter space and how is it related to collinearity?
Why is shrinkage
estimator sensible for collinearity problems?
In what sense is the
shrinking by ridge estimator sensible?
What is ridge trace
and how is it used?
Derive the variance
covariance matrix V of the least squares estimator. How are its diagonals reported in usual
regression computer output? Illustrate
the use of V in testing significance of a linear combination of two or more
coefficients. How is V related to the
precision matrix?
What three things
affecting the precision of a vector of regression coefficients? Show the derivation of the precision
matrix.
If
y~x1+x2 is the model. How
is its V different from the matrix you get from the cov(cbind(x1,x2))?
If a biased
estimator is written as b*=Ab, where A is a matrix
and b is OLS estimator. If the covariance matrix of b is V what is the
covariance matrix of b*?
Give an example of a
quadratic form of dimension 2.
Write the log
quadratic production function as a quadratic form.
If x ~ N(0, W ) is m-variate
normal, what is the distribution of quadratic form x¢W-1x
If P is projection
matrix of rank r and if z~N(0,I), what is the distribution of z¢Pz.
What is the relation
between normal, t and F distributions?
Write the F test
statistic in terms of restricted and unrestricted residual sum of squares.
What is the law of
large numbers and central limit theorem?
What is the
fundamental theorem of statistics?
What are non-nested
models?
Discuss the Cox test
for choosing between models with regressor matrix X versus Z.
Assignment hw091108: (Note the obvious naming convention mmddyy format)
The powerpoint of part of class discussion is downloadable at
http://www.fordham.edu/economics/Vinod/correl-regr.ppt
It has the house price example.
Read Ch 1 first 30 pages of HO (hands-on text)
Your first assignment is 1) download R into your home computer [2points]
2) create a directory called data in your C drive [2points]
3) Place the data from the Appendix of the following file from my website at:
www.fordham.edu/economics/vinod/R-piesales.txt
into the data directory. [2points]
The data is short
x y z
1 2 3
4 5 7
8 9 10
7 11 11
6 5 10
4) use the R command to read and analyze the data as indicated in the appendix. [6points]
You
will be asked to create and attach "ExecSumNNNNN.xls",
(where NNNNN represents up
to the first five characters of your last name),
file at the end of the semester. An old example for a fictitious the name John Doe is
www.fordham.edu/economics/vinod/ExecSumDoe.xls
Start creating this file as you create the diary.
Assignment hw091808:
Your second assignment is to read
www.fordham.edu/economics/vinod/Matrix_1.pdf
Do all exercises from there that you can do.
Search the word "exercise". Each is worth 2 points.
Assignment hw092508:
[4 points for items below]
Read Gauss-Markov Theorem from the Internet or any other
text.
Download Ecdat package of R
[4 points for items below. Place both the input and the output in the diary]
#cut
and paste following in R
#Main
program in R for regression of house prices on sq feet space
#first
we read the data in
yx=c(245,1400,312,1600,279,1700,308,1875,199,1100,219,1550,405,2350,324,2450,319,1425,255,1700)
#now we
make a matrix out of the data
mx=matrix(yx,10,2, byrow=T)
hprice=mx[,1] #first column has house prices
sqft=mx[,2] #second column has square feet
in space in the house
reg1=lm(hprice~sqft)
#this
creates an object reg1 containing regression output
summary(reg1)
#this prints the output
anova(reg1)
confint(reg1)
#[2 points for items below]
plot(reg1)
#you have to click to get pictures
# you install the package (using the command library as
follows)
#called
car then type
library(car)
durbin.watson(reg1, max.lag=4)
Always be prepared to answer questions from the master list of possible surprise quiz questions near the top of this file. Look for new material as we cover it. Unfortunately, it cannot be in neat sequence. You may have to read ahead. Whatever happens to be mentioned in class is fair game. Start writing answers to the questions somewhere in your notes so that you can use the answers in the Open-book/Notes part of the test. Not everything can be open book, of course!
Assignment hw100208:
No formal diary assignment for Oct. 2 since you will need time to
prepare for the test. You have to read the first 30 pages from the hands-on
textbook, especially the R snippets.
There are 10 questions. One
involves writing a function in R.
Example of writing a function is in the textbook. Also be sure to read
the textbook material on maximum likelihood estimation and normal equations of
a regression (even though it is not in the textbook). Finally you also need to read the first set
of Matrix algebra notes and do all exercises, mostly using R.
How to prepare for the R portion of the test? I will restrict the test to the following.
The test will cover all commands used in the file R-piesales.txt (except
'get.outliers,' copy and paste them to know what they do) plus
snippets from the first 30 pages of the text and the following R functions: abs,
cbind, rbind, sqrt, exp, log, log10, sum, prod, cumsum,
cumprod, min, max, pmin, pmax, cummin, cummax,
range, pi, round, signif,
trunc, ceiling, floor, rep, length, qqp, set.seed, runif, lm, cor, cor.test, basicStats(package fBasics) and sample.
The test will involve use of these R functions. I expect to give
numerical problems involving their use and you will be asked to write the
answer in a bluebook. For example:
1] Set the seed at 34 and create a random sample from the set of
integers from 2 to 46 and place it in a 15 by 3 matrix called yxz. Make y, x and z as names of first three
columns. (hint yxz=matrix(sample(2:46), 15,3) will create the data matrix).
What is the p-value for the coefficient of z in a regression of y on x and z?
What does it suggest? What is the p value of a fourth order Durbin Watson
serial correlation test statistic? What
does it suggest? Use `qq.plot' command to decide whether the regression errors
are close to Student's t.
2] Construct a singular 3 by 3 matrix (by making one row proportional to another)
and find its
determinant. What is the relation
between the determinant and eigenvalues?
Class meets in the Library Ground floor Computer Lab 044. I will test
your knowledge of Regression analysis, R and matrix algebra at that
time. This test will be graded.
3] Write an R function to print a designated element from a vector x.
Assignment hw100908:
In general, when the null hypothesis is false, it should be rejected. The power of a test is the probability of such rejection, given the alpha level of the test.
For example, Chi-sq test statistic becomes noncentral Chi-sq in large samples when the null is false. Hence to compute the power we have to first compute the non-centrality (which depends on unknown parameter) and then compute the power.
Following R function will compute the power of Chi-sq test,
given the alpha level, degrees of freedom (df) and the noncentrality.
chi.power=function(alph,df,noncen){crit=qchisq(1-alph,df)
power=1-pchisq(crit,df,ncp=noncen);return(power)} #For example,
chi.power(0.05,10,noncen=1) #is
0.08198021
chi.power(0.05,10,noncen=10)#is larger
0.5424185 and =1 when noncen=100
x=seq(0,5,by=.5); plot(chi.power(0.05,10,x), typ="l")#plots power curve
6points]
Write a similar power function in R for one-sided t test and two-sided t
test
4points]
Construct artificial data matrix from
set.seed(349);yx=matrix(sample(3:300),30,4)
#ignore warning
define x1 as first column, x2 as second column and so on and compute y as:
y=3+4x1+5x2+6x3 +7x4 + rnorm(30) #insert * before
multiplying numbers by vectors
Now regress y on the 4 regressors with
coefficients beta0 to beta4 and test the hypothesis
beta1+beta3 = 10
4points]
Draw
4 diagnostic plots for the above artificial regression similar to Fig 1.2 in HO
text and discuss each of them with an understanding of what they have.
Assignment
hw101608:
Read pages 30 to 45 of Ch 1 of textbook and Matrix_2.pdf.[0pts]
Do exercises is Section 2 of Matrix_2.pdf.[10pts]
Answer all questions from the quiz and enter them into the diary.[25pts]
1) Using a seed of 45 and a random sample from numbers from 101 to 125 create a square matrix X. What is the fourth diagonal number?
2) Use a seed of 45 and create 60 uniform random numbers between 4 and 100.
Round the numbers to the nearest integer. Make a vector y from the first 20 numbers and a 20 by 2 matrix X having columns of data for regressors x1 and x2 from the remaining.
2a) Write the regression model with intercept and vector of errors in the matrix notation.
2b) Upon regressing y on X what is the coefficient of x2? Its p-value?
2c) Use the F test to decide whether the overall model statistically significant.
3) Summarize the Freedman data from the `car' package of R.
i) Use the fBasics package to find basic stats of all variables and report the kurtosis for each variable. (ii) Which variable has positively skew data? (iii) Are there missing data? If so where? (iv) Find the correlation coefficient between crime and nonwhite. (v) Is it significantly different from zero? (vi) Test the null hypothesis that mean of nonwhite percent is 30. (vii) Regress crime (Crime rate per 100,000, 1969) on nonwhite (Percent nonwhite population, 1960) and density (Population per square mile, 1968). Is this model overall significant? (viii) Which test did you use and which was your null hypothesis?
4) Construct a singular 3 by 3 matrix (by making one row proportional to another) and find its determinant. Write out your R commands.
5) Using a seed of 45 and a random sample from numbers from 101 to 109 create a square matrix X. Replace X[2,1]=0=X[2,3]=x[3,1]. Now use the defining equation for eigenvalues and eigenvectors Ax=lx and write out the characteristic polynomial of this matrix on the bluebook. What is the order of this polynomial? It should be a polynomial in the symbol l.
6) Using a seed of 45 and a random sample from numbers from 11 to 55 create a 15 by 3 matrix X. What command will you use to plot the three curves and label them as y K and L, respectively?
7) Write an R function to compute the rank of a matrix.
8) For the data of problem 7 fit a Cobb-Douglas production function. What is the scale elasticity? What is the elasticity of substitution?
9) What first order conditions you use when implementing maximum likelihood in a standard regression model? Which matrix derivatives are used in writing down the so-called normal equations of the regression model?
Assignment hw102308:
Read pages 45 to 75 of Ch 1 of textbook [0pts]
Redo all the snippets starting with #R1.8.0 after adding an arbitrary number 1 for all data along the second row and adding 7 to all data along fifth row (wherever applicable). Are your results similar to the ones reported in the book?[10pts]
#R1.8.0. WECo
Data from Vinod (J1972a) on production
#of sealed contacts. The variable names are:
L=labor,
#K=capital, G=engineering input, and Y=output. No
data
#on units is available.
L K G Y
72 0.106
0.338 0.019
112 0.106
0.529 0.049
194 0.11 0.55
0.098
190 0.12
0.573 0.205
114 0.12
0.587 0.142
141 0.121
0.632 0.254
127 0.401
0.907 0.233
135 0.401
0.95 0.358
244 0.772
1.377 0.717
351 0.772
1.436 0.932
438 0.772
1.487 1.222
375 0.778
1.522 1.082
395 0.818
1.553 1.243
472 0.811
1.619 1.756
305 0.812
1.657 1.206
278 0.803
1.856 1.103
237 0.882
1.905 1.079
221 0.889
1.955 1.133
192 0.889
1.992 0.909
176 0.896
2.017 0.854
217 0.896
2.044 1.132
298 0.898
2.087 1.514
175 1.745
2.113 1.223
172 1.745
2.137 1.261
200 1.759
2.166 1.504
183 1.959
2.216 1.357
198 1.977
2.231 1.503
175 1.977
2.257 1.552
105 1.966
2.275 0.846
83 1.972
2.299 0.7
94 1.972
2.317 0.796
56 1.978
2.329 0.478
61 1.99 2.345
0.632
107 2.396
2.364 1.176
98 2.396 2.38
1.268
94 2.413
2.402 1.187
97 2.413
2.426 1.24
98 2.462 2.46
1.468
74 2.474
2.672 1.172
58 2.478
2.485 0.91
52 2.49 2.529
0.952
52 2.49 2.553
0.95
66 2.491
2.562 1.201
90 2.491
2.574 1.706
74 2.491 2.59
1.344
90 2.491
2.612 1.745
240 2.717
2.807 4.695
278 2.771 2.807
5.844
227 2.879
2.81 5.334
200 2.868
2.81 4.467
186 2.944
2.81 4.586
165 2.96
2.826 4.861
238 2.912
2.826 6.978
250 3.176
2.847 8.359
212 3.281
2.891 7.536
218 3.36
2.891 8.424
240 3.438
2.891 8.64
133 3.456
2.902 8.456
157 3.456
2.917 5.767
create a directory called data on
your C drive
SAVE ABOVE DATA AS .. TEXT
FILE NAMED Wecodata.txt
including the header line L K G Y
in the data directory
#R1.8.1 Read data and run multiplicative nonhomogeneous
#production function
rm(list=ls())
#rm means remove, ls()
means every object.
# the above command cleans out memory for a fresh
start
weco =read.table("c:/data/WEcodata.txt",skip=4, header=TRUE)
# there must be 4 distinct extra line feed symbols
in the
#data file. All long lines within a paragraph
(linefeed)
#symbol are treated as a single line by R.
names(weco) #list names as understood
by R
library(fBasics)# call package for
descriptive stats
basicStats(weco)
attach(weco)#Allow access to variables
by header names
length(Y)#should be 59
#Take natural log of each variable and define
#cross products of the
natural logs of 3 inputs.
lY=log(Y);lK=log(K);lG=log(G);lL=log(L)
lKL=lK*lL
lKG=lK*lG
lLG=lL*lG
lK2=lK^2#The next three
regressors are needed for
# the translog production function
regression
lG2=lG^2
lL2=lL^2
reg=lm(lY~lK+lL+lG+lKL+lKG+lLG)#MNH
specification
summary(reg)#prints results
a0=reg$co[1]#Extract The intercept
a1=reg$co[2]#The coefficent for log capital
a2=reg$co[3]#The coefficient for log labor
a3=reg$co[4]#The coefficient for log engineering
a4=reg$co[5]#The coef for interaction term
(log K)(log L)
a5=reg$co[6]#The coef for interaction (log
K)(log G)
a6=reg$co[7]#The coef for interacton (log G)(log L)
# following are vectors not
constants.
MEK=a1+a4*lL+a5*lG
#marginal elasticity of capital
MEL=a2+a4*lK+a6*lG
#ME for labor
MEG=a3+a5*lK+a6*lL #ME for engineering
SCE=(MEK+MEL+MEG) #scale
elasticity
inv.SCE=(MEK+MEL+MEG)^(-1)
#The following commands
generate the charts
plot(MEK, type="l", xlab="month",
main="WECo:
Marginal Elasticity of Capital")
plot(MEL, type="l", xlab="month",
main="WECo:
Marginal Elasticity of Labor")
plot(MEG, type="l", xlab="month",
main="WECo:
Marginal Elasticity of Engineering")
plot(SCE/10, type="l", xlab="month",
main="WECo:
Scale Elasticity =AC/MC")
plot(inv.SCE*10, type="l", xlab="month", main="WECo:
Change
in total cost as output increases by 1%", ylab="MC/AC")
mrtsLK=(MEL/MEK)*(K/L)#marginal
rate of tech substitution
#between L and K
cor(G, mrtsLK)#
if correlation is low then engineering input
#is separable. corr=0.02236146 is indeed low See Sec 1.7.2
#R1.13.1 following data are
from Vinod, H. D. (J1976a)
#"Application of New Ridge Regression Methods
to a Study of
#
#"Journal of the American Statistical
Association
#Vol. 71, December 1976, pp. 835-841.
#The last column has a
proxy for technological change.
#save the following data in
c:/data/belldata.txt as a text
#file. DO this before the next snippet
!
yr y k
lab poiss6
1947 1866
9473 707.7 19.63616
1948 1995
10996 740.6 18.6777
1949 2041
12140 756.3 18.52005
1950 2243
12945 758.2 19.04078
1951 2516
13348 794.6 19.89037
1952 2694
14690 834.3 20.70211
1953 2839
16132 870.1 21.29981
1954 2940
17269 879.2 21.68806
1955 3237
18715 882.1 22.04506
1956 3538
20271 947.9 22.65129
1957 3816
21798 922 22.79146
1958 3960
23597 923.7 25.60401
1959 4324
25025 886.8 27.97297
1960 4675
26230 886.2 30.62467
1961 4908
28025 880.6 33.26989
1962 5258
29845 885.8 36.1029
1963 5601
31373 886.6 39.57953
1964 6074
33109 914.4 44.0596
1965 6562
35604 945.6 49.55559
1966 7360
37533 985 55.51114
1967 8026
39571 1001.2 61.29436
1968 8875
40856 1019.2 66.49376
1969 9934
43038 1074.2 71.08835
1970 10649
45856 1126.5 75.29503
1971 11188
49449 1141.2 79.39379
1972 12265
52266 1144.4 83.63391
1973 13561
56748 1174 88.23431
1974 14778
59526 1183.8 93.36805
1975 15756
61889 1181 99.03202
1976 17108
63854 1175.7 105.0231
#R1.8.2 New R function to do production function
contours
pfcontour=function(y,K,L,
level=T, z=0, type=c("Cobb-Douglas",
"MNH", "TransLog"),n50=50) {
#fit regression and draw contours using clines
package
Ly=y; LK=K; LL=L
if (level) Ly=log(y)
T=length(y)
if(level) LK=log(K);
LK2=LK^2
if (level) LL=log(L);
LL2=LL^2; LKLL=LK*LL
#print(c(T,length(z)))
if(length(z)==T){
reg1=switch(type,
"Cobb-Douglas" = lm(Ly~LK+LL+z),
"MNH" = lm(Ly~LK+LL+LKLL+z),
"TransLog" = lm(Ly~LK+LL+LKLL+LK2+LL2+z))
print(reg1)
}#end if length(z)
if(length(z)==1){
reg1=switch(type,
"Cobb-Douglas" = lm(Ly~LK+LL),
"MNH" = lm(Ly~LK+LL+LKLL),
"TransLog" = lm(Ly~LK+LL+LKLL+LK2+LL2))
print(reg1)
}#end if length(z)
Lymtx=matrix(NA,n50,n50)
a=as.numeric(reg1$coe)
x=rep(NA,n50)
y=rep(NA,n50)
rangeLK=(max(LK)-min(LK))/n50
rangeLL=(max(LL)-min(LL))/ n50
for (i
in 1:n50){Lk=min(LK)+rangeLK*i;x[i]=Lk
for (j in 1:n50){Ll=min(LL)+rangeLL*j;y[j]=Ll
#
if (length(z)==T){
Lymtx[i,j]= switch(type,
"Cobb-Douglas" =a[1]+a[2]*Lk+a[3]*Ll+a[4]*z,
"MNH"=a[1]+a[2]*Lk+a[3]*Ll+a[4]*Lk*Ll+a[5]*z,
"TransLog" =a[1]+a[2]*Lk+a[3]*Ll+a[4]*Lk*Ll+a[5]*Lk^2+
a[6]*Ll
^2+a[7]*z
) #end switch simple parenthesis
}# end if length z
#
if (length(z)==1){
Lymtx[i,j]= switch(type,
"Cobb-Douglas" =a[1]+a[2]*Lk+a[3]*Ll,
"MNH"=a[1]+a[2]*Lk+a[3]*Ll+a[4]*Lk*Ll,
"TransLog" =a[1]+a[2]*Lk+a[3]*Ll+a[4]*Lk*Ll+a[5]*Lk^2+a[6]*
Ll^2
) #end switch simple parenthesis
}# end if length z
}#end j loop
}#end i
loop
#print(head(Lymtx))
contour(exp(x),exp(y),exp(Lymtx),
main=paste(c("Level Curves
for Production Function",type),
sep=" "), xlab="capital", ylab="labor")
#
list(Lymtx=Lymtx,
reg1=reg1)
#these lists are output of the function.
#In Lymtx=Lymtx the Lymtx on left of
equality is
# the output name released
outside the function and the same
# Lymtx on right side of
(=) in the name inside this function
}######END of the function
#Now read data. See data Appendix of this chapter
#use hints from subsection 1.8.1.1
bell=read.table(file="c:/data/belldata.csv", header=T,
sep=",")
#sometimes use file extension to be csv
#csv are comma separated
files created from excel worksheet,
#need sep to be a comma
summary(bell); attach(bell)
pfc= pfcontour(y,k,lab,level=T, type="MNH",n50=50,z=0)
#above line creates an object called pfc holding the output
#from the function pfcontour. This way, R will not print
#the entire Lymtx and reg1
and clutter the screen
#It will create and show
Figure on the screen
#file menu of R allows one to save the figure in
many formats.
Which snippet writes a function in R. [2pts]
Why level=T is set in that function? [2pts]
How does the switch function in R work?[4pts]
Can this be useful elsewhere in economics or finance? Illustrate. [4pts]
Assignment hw103008:
Snippet 1.9.1 use the temperature data in Fh scale x1 as (55, 69, 80,
90, 101)
Convert these to Celsius scale and make it as x2 using the "scale' function in R
[2pts]
Use the same y as in the snippet and explain why this illustrates perfect
collinearity [2pts]
Implement all the ridge regression and related
Assignment hw111308:
library(AER)
data(Equipment)
attach(Equipment)
reg1=lm(log(valueadded/firms) ~ log(capital/firms) + log(labor/firms),
data = Equipment)
Estimate ridge regression for a translog version of this model and data
by various methods discussed in the text, including
finding the condition number, [2pts]
(HINT:
yx=reg1$model; yx;
x=yx[,2:ncol(yx)]; cor(x) )
choosing index m, [2pts]
choices of k from k, [2pts]
ridge trace, [2pts]
standardize and unstandardize [2pts]
Assignment hw112008:
read 30 pages Chapter 2 of Hands on text
redo all the snippets and furthermore apply relevant snippets to "ArgentinaCPI" data from the
"AER" package, wherever it makes sense to do so. Note that for quarterly data seasons will be
different from those for monthly data. [Total 10 points]
Assignment
hw120408
Complete at least 9 exercises out of 18 for Chapter 2 of the Hands on
text numbered 3.1 to 3.18 at the website URL:
http://www.fordham.edu/economics/Vinod/exercises.pdf
Each is worth 3 points.
Computer Lab 044 inside the Library Ground Floor is reserved for Oct. 2,
Nov. 6 . You will be tested about your knowledge of R at those times and
places.
Your Grade Calculation:
We already have had one test involving R. It will be worth 10% of your grade after adjustment for contributed
exercises. The adjustments will be decided along with your final grade.
Diaries will be worth 40 % of your
grade. You have to grade yourself
honestly, calculate how many points you have earned in all diary assignments
including the one due Dec. 4 where each exercise among 3.1
to 3.18 is worth 3 points and you are asked to do nine of them.
FINAL EXAM will be on December 18, 2008
It is cheating if you try to compare
the answers in any way or help each other.
The penalty for cheating is an F grade or worse.
Your final exam will have 3 parts.
Part 1 worth 20% will test your proficiency in R in a take-home test e-mailed to you late night (before midnight) on December 17, the night before the final exam. You will bring the output consisting of printout of your R code and answers to the exam at 7.30 pm in Dealy Hall.
Part 2 (closed book, worth 10%) Mostly true or false and fill in the blanks type questions designed to test your general understanding of the material.
Part 3 (open book, open notes, etc. worth 20% ) theoretical questions about the material covered in the class checking your real understanding.