#################
##### Problem 1
#################
Davis <-
  read.table('http://math.uttyler.edu/nathan/classes/statistics/data/davis.data',header=TRUE)

attach(Davis)

m1.1 <- lm(weight ~ repwt)
summary(m1.1)
#
#Coefficients:
#            Estimate Std. Error t value Pr(>|t|)    
#(Intercept)  5.46083    3.05765   1.786   0.0758 .  
#repwt        0.92636    0.04556  20.333   <2e-16 ***
#
#Residual standard error: 8.456 on 179 degrees of freedom
#Multiple R-squared: 0.6979,	Adjusted R-squared: 0.6962 
#F-statistic: 413.4 on 1 and 179 DF,  p-value: < 2.2e-16 

confint(m1.1)
#
#                 2.5 %    97.5 %
#(Intercept) -0.5728405 11.494497
#repwt        0.8364585  1.016265

plot(repwt,weight)
abline(m1.1)
identify(repwt,weight)
dev.copy2eps(file='weight.eps')

m1.2 <- lm(weight ~ repwt,subset=-12)
summary(m1.2)
#
#Coefficients:
#            Estimate Std. Error t value Pr(>|t|)    
#(Intercept)  2.83349    0.81208   3.489 0.000611 ***
#repwt        0.95715    0.01209  79.168  < 2e-16 ***
#
#Residual standard error: 2.241 on 178 degrees of freedom
#Multiple R-squared: 0.9724,	Adjusted R-squared: 0.9722 
#F-statistic:  6268 on 1 and 178 DF,  p-value: < 2.2e-16 

confint(m1.2)
#
#                2.5 %   97.5 %
#(Intercept) 1.2309416 4.436043
#repwt       0.9332893 0.981006
detach()


#################
##### Problem 2
#################
Prostate <- read.table('http://math.uttyler.edu/nathan/classes/statistics/data/prostate.data',header=TRUE)

attach(Prostate)
right.order <- data.frame(lpsa,lcavol,lweight,svi,lbph,age,lcp,pgg45,gleason)
detach(Prostate)

r.sqs <- sapply(2:9,
                function(i){summary(lm(lpsa~.,data=data.frame(right.order[1:i])))$r.squared})

rses <- sapply(2:9,
                function(i){summary(lm(lpsa~.,data=data.frame(right.order[1:i])))$sigma})


r.sqs
rses

plot(c(1,8),c(.50,.80),type='n',main='r^2=blue, rse=red',xlab='# x terms in model',ylab='')
points(1:8,r.sqs,col='blue')
points(1:8,rses,col='red')
lines(1:8,r.sqs,col='blue',lty=3)
lines(1:8,rses,col='red',lty=3)

dev.copy2eps(file='prob2.eps')


#################
##### Problem 3
#################


m3 <- lm(lpsa ~ .,data=Prostate)
confint(m3)
confint(m3,level=.9)