Splines.R

library(ggplot2)
library(splines)

mydata <- read.csv(file="C:/Users/ellen/Documents/UH/Fall 2020/Data/Ex1LS.csv", header=TRUE, sep=",")

mydata$X1 <- mydata$X

p <- ggplot(data = mydata) + geom_point(aes(x = X1, y = Y), size = 4)
p

model <- lm( formula = Y ~ X, mydata)
modelQ <- lm( formula = Y ~ X + I(X^2), mydata)
modelNS <- lm(data = mydata, Y ~ ns(X, 2)) # you can also specifically set knots, but beware

predData <- data.frame(X = seq(1, 4, .11)) # i'm doing this so we can see how the trained models perform
# on a denser dataset

predData$Y <- predict(model, predData)
predData$Q <- predict(modelQ, predData)
predData$NS <- predict(modelNS, predData)

p <- p + geom_point(data = predData, aes(x=X, y = Y), color = 'black')
p <- p + geom_point(data = predData, aes(x=X, y = Q), color = 'red')
p <- p + geom_point(data = predData, aes(x=X, y = NS), color = 'blue')
p <- p + geom_smooth(data=predData, aes(x=X, y = Y), se=FALSE, color = "black")
p <- p + geom_smooth(data=predData, aes(x=X, y = Q), se=FALSE, color = "red")
p <- p + geom_smooth(data=predData, aes(x=X, y = NS), se=FALSE, color = "blue")
p

summary(model)
summary(modelQ)
summary(modelNS)

# increasing knots

modelNS2 <- lm(data = mydata, Y ~ ns(X, 4)) # you can also specifically set knots, but beware
predData$NS2 <- predict(modelNS2, predData)
p <- p + geom_smooth(data=predData, aes(x=X, y = NS2), se=FALSE, color = "green")
p


# this model is obviously overly complex and it will be high variance




Auto <- read.csv(file="C:/Users/ellen/Documents/UH/Fall 2020/Github Staging/EllenwTerry/Archive/Data_Files/Automobile Price Prediction.csv")

p <- ggplot(Auto, aes(x=horsepower, y=price))+geom_point() 
p

model <- lm(price ~ horsepower + highway.mpg, data = Auto)
modelQ <- lm( formula = price ~ horsepower + I(horsepower^2) + highway.mpg + I(highway.mpg^2), Auto)
modelNS <- lm(data = Auto, price ~  ns(horsepower, 5) + ns(highway.mpg, 5))

predData <- data.frame(horsepower = seq(min(Auto$horsepower), max(Auto$horsepower), length.out = 50), highway.mpg = seq(min(Auto$highway.mpg), max(Auto$highway.mpg), length.out = 50))

predData$Y <- predict(model, predData)
predData$Q <- predict(modelQ, predData)
predData$NS <- predict(modelNS, predData)

p <- ggplot(predData, aes(x=X, y=Y))
p <- p + geom_point(data = predData, aes(x=horsepower, y = Y), color = 'black')
p <- p + geom_point(data = predData, aes(x=horsepower, y = Q), color = 'red')
p <- p + geom_point(data = predData, aes(x=horsepower, y = NS), color = 'blue')
p <- p + geom_smooth(data=predData, aes(x=horsepower, y = Y), se=FALSE, color = "black")
p <- p + geom_smooth(data=predData, aes(x=horsepower, y = Q), se=FALSE, color = "red")
p <- p + geom_smooth(data=predData, aes(x=horsepower, y = NS), se=FALSE, color = "blue")
p

p <- p + geom_point(data = Auto, aes(x=horsepower, y=price))
p

summary(model)
summary(modelQ)
summary(modelNS)