# Problem 1
data <- read.table("NCBirths2004.csv",header=TRUE,sep=",")

# names(data)
# [1] "ID" "MothersAge" "Tobacco" "Alcohol" "Gender" "Weight" "Gestation" "Smoker"
# (1)
plot(x=data$Weight,y=data$Gestation,xlab="Weight",ylab="Gestation")
cor(data[c("Weight","Gestation")])
# Weight Gestation
# Weight 1.0000000 0.3486057
# Gestation 0.3486057 1.0000000

# (2)
fit <- lm(Weight~Gestation,data=data)
summary(fit)
paste("Weight=",coeffs[1],"+",coeffs[2],"x Gestation")
# Weight= -2379.68957808293 + 148.995383086772 x Gestation

# (3)
# One additional Gestation increases a weight by about 148.
summary(fit)$r.squared
# [1] 0.1215259
# About 12.2% of total variation of Weight is explained by Gestation.

# (4)
plot(data$Gestation,resid(fit),ylab="Residuals",xlab="Gestation")
abline(h=0)
lines(smooth.spline(data$Gestation,resid(fit),df=3),col="blue")
# It shows a slight curvature but it may be a purely random artifact because
# it is really subtle. The small number of observations at the largest Gestation may be
# causing it. But residuals seem scattered equally randomly over all levels o Gestation.

# (5)
# First of all, because there are only 6 levels of Gestation, it may be better to
# treat it as a catergorical variable. The number of observations are large and
# you can afford to have 5 dummy variables, and have each level of Gestation with its
# own effect instead of trying to find a single linear relationship between
# Gestation and Weight.

# (6)
summary(fit)$sigma

The project will involve the analysis of real world data (Boston da...