Education <- read.table('http://math.uttyler.edu/nathan/classes/grad-statistics/data/eduspend.data',header=TRUE)
plot(Education)
attach(Education)

income.model <- lm(education ~ income)
summary(income.model)

#            Estimate Std. Error t value Pr(>|t|)    
#(Intercept) 17.710031  28.873840   0.613    0.542    
#income       0.055376   0.008823   6.276 8.76e-08 ***
#---
#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
#
#Residual standard error: 34.94 on 49 degrees of freedom
#Multiple R-Squared: 0.4457,     Adjusted R-squared: 0.4343 
#F-statistic: 39.39 on 1 and 49 DF,  p-value: 8.762e-08 

# equation of the regression line:
#   education = 17.710031 + .055376*income
#
#  rse = 34.94      model: education_i = b0 + b1*income_i + e_i
#                          we assumed Var(e_i) = sigma_e^2
#                          rse is point estimate for sigma_e
#
#  r^2 = .4457  our model explains 44.57% of the variability in ed. spending
#               44.57% of the variability in ed. spending is due to the
#               linear relationship between income and ed. spending
#

# what is the effect of a $100 increase in state per capita income on the 
# state's education spending?  100*.055376 or about $5.54

plot(income,education)
abline(income.model)
identify(income,education)

big.model <- lm(education ~ income + young + urban)
summary(big.model)

#              Estimate Std. Error t value Pr(>|t|)    
#(Intercept) -2.868e+02  6.492e+01  -4.418 5.82e-05 ***
#income       8.065e-02  9.299e-03   8.674 2.56e-11 ***
#young        8.173e-01  1.598e-01   5.115 5.69e-06 ***
#urban       -1.058e-01  3.428e-02  -3.086  0.00339 ** 
#---
#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
#
#Residual standard error: 26.69 on 47 degrees of freedom
#Multiple R-Squared: 0.6896,     Adjusted R-squared: 0.6698 
#F-statistic: 34.81 on 3 and 47 DF,  p-value: 5.337e-12 

# now my model looks like:
#
#    education_i = b_0 + b_1 income_i + b_2 young_i + b3 urban_i + e_i
#                = -286.8 + .08065 income_i + .8173 young_i + -.1058 urban_i 
#                             /\                /\               /\
#                              |                 |                |
#                              |                 |                |
#                             these are now partial derivatives!!!!!!
#                             standard partial derivative interpretation
#                             keep everything else the same, change only
#                             that variable

summary(lm(education ~ urban))                                    
# Coefficients:
#              Estimate Std. Error t value Pr(>|t|)    
# (Intercept) 142.60415   28.81579   4.949 9.22e-06 ***
# urban         0.08083    0.04230   1.911   0.0619 .  

detach(Education)

Prostate <- read.table('http://math.uttyler.edu/nathan/classes/grad-statistics/data/prostate.data',header=TRUE)
attach(Prostate)
Prostate[1:10,]


mod.1 <- lm(lpsa ~ lcavol)
summary(mod.1)

mod.2 <- lm(lpsa ~ lcavol + lweight)
summary(mod.2)

mod.3 <- lm(lpsa ~ lcavol + lweight + svi)
summary(mod.3)

# at the end of problem number 4 you've got 2 lists:
my.rsqs <- c(1,2,8,4,5,3,9)  # the r^2 numbers
my.rses <- c(6,5,4,3,7,5,2)  # the residual std errors

# don't do this:
plot(my.rsqs,my.rses)
# this looks at rse as a function of r^2, it's not, and that's not
# what the problem is about!

# we're looking to combine the following two plots:
plot(my.rsqs)
plot(my.rses)
summary(my.rsqs)
summary(my.rses)
# look at the biggest numbers, here the max is 9, min is 1
# so the range over which I want to plot is 1 < x < 7, 1 < y < 9
# let's go a little wider on each: 0 < x < 8, 0 < y < 10
plot(c(0,8),c(0,10),type='n',main='rse and r^2',xlab='# terms in model',ylab='number')
points(my.rsqs,col='blue',pch=19)
points(my.rses,col='red',pch=22)