Question

# Download the dataset Nile

rm(list=ls())

library(help = "datasets")

data("Nile")

View(Nile)

# Find the mean and sd of the data. It has only one variable.

# Find out the 90% confidence interval for the population mean mu for the dataset Nile, assuming that the

# population sd is known and is same as the sample sd. (50 points)

# Repeat the same exercise assuming that the population sd is not known. (50 points).

# Show all the necessary steps in each of the questions.

please submit solution in R format

Answer 1

//import dataset Nile
  
#give details of Nile dataset
library (datasets)
data("Nile")
View(Nile)
#display attributes of Nile dataset
names(Nile)
#display dimensions of dataset
dim(Nile)
#view the contents of dataset
View(Nile)
#internal strucutre of dataset
str(Nile)
#minimum value
# symbol "$" is used to choose attribute of dataset
min(Nile$x)
min(Nile$time)
#max value
max(Nile$time)
max(Nile$Nile)
#mean value
mean(Nile$time)
# range of attribute value
range(Nile$Nile)
#standard deviation
sd(Nile$time)
#variance

# with 50\% interval
ts.plot(Nile, pred$pred,
pred$pred + 0.67*pred$se, pred$pred -0.67*pred$se)

var(Nile$x)require(stats); require(graphics)
par(mfrow = c(2,2))
plot(Nile)
acf(Nile)
pacf(Nile)
ar(Nile)
cpgram(ar(Nile)$resid)
par(mfrow = c(1,1))
arima(Nile, c(2, 0, 0))
  
  
NileN <- Nile
NileN[c(20:40, 51:80)] <- NA
arima(NileN, c(2, 0, 0))
plot(NileN)
pred <-
predict(arima(window(NileN, 1861, 1889), c(2,0,0)), n.ahead = 20)
lines(pred$pred, lty = 3, col = "red")
lines(pred$pred + 2*pred$se, lty=2, col="blue")
lines(pred$pred - 2*pred$se, lty=2, col="red")
pred <-
predict(arima(window(NileN, 1861, 1935), c(2,0,0)), n.ahead = 20)
lines(pred$pred, lty = 3, col = "red")
lines(pred$pred + 2*pred$se, lty=2, col="green")
lines(pred$pred - 2*pred$se, lty=2, col="red")
  
## time series models
par(mfrow = c(3, 1))
plot(Nile)
#l model
(fit <- StructTS(Nile, type = "level"))
lines(fitted(fit), lty = 2)
lines(tsSmooth(fit), lty = 2, col = 3)   
plot(residuals(fit)); abline(h = 0, lty = 4)
# local model
(fit2 <- StructTS(Nile, type = "trend"))
pred <- predict(fit, n.ahead = 30)
# 50% interval
ts.plot(Nile, pred$pred,
pred$pred + 0.68*pred$se, pred$pred -0.68*pred$se)
  
  
plot(NileN)
(fit3 <- StructTS(NileN, type = "level"))
lines(fitted(fit3), lty = 2)
lines(tsSmooth(fit3), lty = 3)
plot(residuals(fit3)); abline(h = 0, lty = 3)