# I use a program called R for tasks like this.  You can download it for
# free from http://cran.r-project.org/
# Input to the program is given here; lines beginning with # are comments.
#
# I first exported the data from Excell into a CSV file, and removed the
# quotes.  This split some fields into two, fortunately in a regular manner.
# So my file now contains five fields that I will ignore, followed by months
# and miles.  The function scan will read in the data, with a first argument
# my file name, the second argument a sampling of the data types for the
# fields, and the third the field seperator.  The syntax <- is an assignment
# operator; data sets and the output of model fits are all assigned to
# objects.  The data are put into the data set rr; variables within a 
# data set are accessed by data set name, $, and the variable name; hence
# rr$monthssq is the months squared.
# I then call the regression
# fitter.  R does this in two steps; the first fits the model, and the
# second formats the results for easy viewing.  The fitter is lm; first 
# argument to lm is formula, the second is the data source, and the third
# picks out the first three elements.  The formula has the syntax first  
# response variable, then a tilde, then the explanatory variables.  The  
# -1 removes the intercept.
# Here's code to do the intercept-set-to-zero fit:
rr<-as.data.frame(
  scan("UnionPacificDec3.csv",what=list(a="",b="",c="",d="",e="",
   months=0,miles=0), sep=","))
rr$monthssq<-rr$months^2
cat("Model with 0 intercept, linear in months, for first three ponts\n")
summary(lma<-lm(miles~-1+months, data = rr, subset = 1:3))
cat("Model with 0 intercept, quadratic in months, for next three portions\n")
summary(lmb<-lm(miles~months+monthssq, data = rr, subset = 3:7))
summary(lmc<-lm(miles~months+monthssq, data = rr, subset = 7:12))
summary(lmd<-lm(miles~months+monthssq, data = rr, subset = 12:17))
# Here's my suggestion about seasonality terms using sines and cosines.
# -1 after cosine forces it to be zero at 0 months.
rr$smonths<-sin(rr$months/12)
rr$cmonths<-cos(rr$months/12)-1
lm0<-lm(miles~-1+months+monthssq,data=rr)
lmout<-lm(miles~-1+months+monthssq+smonths+cmonths, data = rr)
cat("Model with 0 intercept, quadratic in months, with seasonal effects\n")
summary(lmout)
pdf("railroad.pdf")
plot(rr$months,rr$miles,main="Data",xlab="Months",ylab="Miles")
lines(rr$months,fitted(lmout))
detrend<-list(months=rr$months,miles=lm0$residuals)
plot(detrend$months,detrend$miles,
   main="Residuals from quadratic fit, to show the potential for a trig. seasonal effect",xlab="Months",ylab="Miles",
   sub="Note poor performance during the final winter")