#######################################################################
#
# Dataset: Grade Point Average (GPA)
#
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#
# Summary: Data on 4,137 US college students.
#
#  1. sat                       combined SAT score
#  2. hsize                   total hours through fall semest
#  3. colgpa                 GPA after fall semester
#  4. athlete                 =1 if athlete
#  5. verbmath             verbal/math SAT score
#  6. hsize                    size graduating class, 100s
#  7. hsrank                  rank in graduating class
#  8. hsperc                 100*(hsrank/hssize)
#  9. female                  =1 if female
# 10. white                   =1 if white
# 11. black                   =1 if black
# 12. hsizesq               hsize^2
#
# colgpa is measured on a four-point scale
# hsperc is the percentile in the high school graduating class (defined so that, for
# example, hsperc 5 5 means the top 5% of the class)
# sat is the combined math and verbal scores on the student achievement test.
#
#######################################################################
#
# Source: Wooldridge (2012) 
# Introductory Econometrics: A Modern Approach (5th edition)
# South-Western, Cengage Learning
#
#######################################################################
#
# Copyright of R code by:
#
# Hedibert Freitas Lopes 
# Professor of Statistics and Econometrics
# Insper - Institute for Education and Research
#
#######################################################################

data = read.table("gpa2-wooldridge.txt",header=TRUE)
n    = nrow(data)
k    = ncol(data)
data = data-matrix(apply(data,2,mean),n,k,byrow=TRUE)
for (i in 1:k)
  data[,i] = data[,i]/sqrt(var(data[,i]))

data1 = as.data.frame(data)

ols   = lm(sat ~ hsize*athlete+hsize*female+hsize*white+hsize*black+
colgpa*athlete+colgpa*female+colgpa*white+colgpa*black+
verbmath*athlete+verbmath*female+verbmath*white+verbmath*black+
hsize*athlete+hsize*female+hsize*white+hsize*black+
hsrank*athlete+hsrank*female+hsrank*white+hsrank*black+
hsperc*athlete+hsperc*female+hsperc*white+hsperc*black+
tothrs*athlete+tothrs*female+tothrs*white+tothrs*black-1, data=data1)

summary(ols)

p = length(ols$coef)

bhat = ols$coef
se   = summary(ols)$sigma*sqrt(diag(summary(ols)$cov.unscaled))
L    = bhat-2*se
U    = bhat+2*se

plot(bhat,pch=16,ylim=range(L,U))
for (i in 1:p)
  segments(i,L[i],i,U[i])
abline(h=0,lty=2)