library(readr)
dataMain <- read_delim("C://Users//jborthen//Desktop//DJI19850101To20190305.csv",
           delim = ",")

# plot(dataMain$Date, dataMain$Close, pch=".")
# fit <- lm(Date ~ poly(Close, 2, raw = TRUE), data = dataMain)
# points(dataMain$Date, predict(fit), col="blue", type="l")




# We create 2 vectors x and y
#x <- runif(300, min=-10, max=10)
#y <- 0.1*x^3 - 0.5 * x^2 - x + 10 + rnorm(length(x),0,8)
x <- seq(1, dim(dataMain)[1])
y <- dataMain$Close


# plot of x and y :
plot(x,y,col=rgb(0.4,0.4,0.8,0.6),pch="." , cex=1.3)

# Can we find a polynome that fit this function ?
model=lm(y ~ x + I(x^2))

#I can get the features of this model :
summary(model)
model$coefficients
summary(model)$adj.r.squared

#For each value of x, I can get the value of y estimated by the model, and add it to the current plot !
myPredict <- predict( model )
ix <- sort(x,index.return=T)$ix
lines(x[ix], myPredict[ix], col=2, lwd=2 )
# I add the features of the model to the plot
coeff=round(model$coefficients , 5)
text(5500,1150 , paste("Model : ",coeff[1] , " + " , coeff[2] , "*x" , "+" , coeff[3] , "*x^2" , "+" , coeff[4] , "*x^3" , "\n\n" , "P-value adjusted = ",round(summary(model)$adj.r.squared,2)))