Week 8

Author: LProcopi15

Week 7 - Case Study (regression modeling)/Thumbs.db

@@ -5,12 +5,17 @@
 
 ######Step 1: Data exploration############
 #1.1 Load the data
-fb <- read.table("/Users/yuyanzhang/Desktop/RWorkshop/Week 7 - Case Study (regression modeling)/dataset_Facebook.csv", sep = ";", header = TRUE)
+fb <- read.table("C:/Users/Student/Documents/UVA 2016-2017/RWorkshop/Week 7 - Case Study (regression modeling)/dataset_Facebook.csv", sep = ";", header = TRUE)
 #The header = TRUE parameter will tell R to read the first line in the file as the header of the dataset
 View(fb)
 
 #1.2 Check the class of each attribute
+check.class <- function(dataset) {
+  for(i in 1:ncol(dataset))
+    print(paste(colnames(dataset[i]), ": ", class(dataset[,i]), sep = ""))
+}
 
+check.class(fb)
 #Is there any attribute that needs recoding?
 
 

Week 7 - Case Study (regression modeling)/lecture7_case study.R

@@ -0,0 +1,137 @@
+bike <- read.csv("C:/Users/Student/Documents/UVA 2016-2017/RWorkshop/Week 1- Arithmatic and Data Type Intro/bike.csv")
+
+###################
+#
+# Time Series
+#
+###################
+
+bike.ts <- ts(bike$cnt)
+
+# In time series look for 3 things:
+# 1. Trend - overall long acting upward or downward movement
+# 2. Seasonality - repeating patterns within a year
+# 3. Cycles - patterns that repeat in over a year period
+plot(bike.ts)
+
+# 1. Modeling for trend
+
+# Create a new variable time.bike which is a matrix of (length(bike.ts))
+time.bike<-c(1:(length(bike.ts)-7))
+
+# Build a new model, bike.trend which predicts bike.ts based on the time variable, time.bike- use all data except the last week of your bike time series
+bike.trend<-lm(bike.ts[time.bike]~time.bike)
+
+# Use the summary() command on bike.trend
+summary(bike.trend)
+
+# Is time significant in predicting spam frequency? Yes; p-value <= 0.001
+# Add trend line to time series plot
+plot(bike.ts)
+abline(bike.trend,col='red') # Overall upward trend
+
+# 2. Modeling for seasonality
+
+# Get the periodogram from bike.ts
+pg.bike<-spec.pgram(bike.ts,spans=9,demean=T,log='no')
+
+# Find the peak, max.omega.bike
+max.omega.bike<-pg.bike$freq[which(pg.bike$spec==max(pg.bike$spec))]
+
+# What is the period?
+1/max.omega.bike # 23.97; there is a repeating cycle every ~24 days
+
+# Conclusion: there is both seasonality and trend in this data set - need to address both of these in the model
+# Get the residuals for trend
+e.ts.bike <- ts(bike.trend$residuals)
+
+
+# Plot autocorrelation (acf) and partial autocorrelation (pacf)
+par(mfrow=c(1,2))
+acf(e.ts.bike, main="ACF of Residuals from e.ts.bike")
+pacf(e.ts.bike,main="PACF of Residuals from e.ts.bike")
+par(mfrow=c(1,1))
+
+# Use the ACF and PACF to choose a model type
+# See table for details
+# ACF is sidusodial and PACF cannot see any trends
+# Choose AR or ARMA
+
+# Choose r values for AR model
+# ar(3) p=3
+bike.ar3 <- arima(e.ts.bike, order=c(4,0,0))
+summary(bike.ar3)
+AIC(bike.ar3)
+
+# Use the auto.arima from 'forecast' library- Automatically find p, q, & d terms
+library('forecast')
+bike.auto <- auto.arima(e.ts.bike, trace=TRUE)
+# Using autoregressive function the best model is ARIMA(2,1,1)
+AIC(bike.auto)
+
+# Transform weekly info
+Day <- rep(NA, length(bike.ts)-7)
+Day[which((time.bike %% 7)  == 1)] <- "Sat"  
+Day[which((time.bike %% 7)  == 2)] <- "Sun"  
+Day[which((time.bike %% 7)  == 3)] <- "Mon"  
+Day[which((time.bike %% 7)  == 4)] <- "Tue"  
+Day[which((time.bike %% 7)  == 5)] <- "Wed"  
+Day[which((time.bike %% 7)  == 6)] <- "Thr"  
+Day[which((time.bike %% 7)  == 0)] <- "Fri"  
+
+Day <- as.factor(Day)
+
+# View default contrasts
+contrasts(Day)
+
+# Build a model bike.season to model the trend and seasonality of ham.
+bike.season<- lm(bike.ts[time.bike]~Day)
+summary(bike.season)
+
+# Get the residuals from the bike.season model above and store in e.ts.bike2:
+e.ts.bike2 <- ts(bike.season$residuals)
+
+# Plot acf and pacf side by side for easier examination
+par(mfrow=c(1,2))
+acf(e.ts.bike2, main="ACF of Residuals from bike.season")
+pacf(e.ts.bike2,main="PACF of Residuals from bike.season")
+par(mfrow=c(1,1))
+
+# Sinusodial decay on ACF and not on PACF - AR or ARMA
+bike.arma13 <- arima(e.ts.bike2, order=c(1,0,3))
+
+# Use the auto.arima from 'forecast' library- Automatically find p, q, & d terms
+bike2.auto <- auto.arima(e.ts.bike2, trace=TRUE)
+# Best model is ARIMA(2,1,1) 
+
+###################
+#
+# Practice problems
+# 
+###################
+
+# 1. Create a time series dataset base on 'causual'
+
+# 2. Create a model for the trend
+
+# 3. Plot the ts data and the trend line
+
+# 4. Determine if trend is significant
+
+# 5. Obtain the residuals from the trend model
+
+# 6. Plot the ACF and the PACF for this model and determine if AR, ARMA, or ARIMa should be used
+
+# 7. Use auto.arima to determine the optimal model; also create a few other models with varying values for p, q and r
+
+# 8. Compare models using AIC, BIC and adjs-R2
+
+# 9. Create a periodgram for this data
+
+# 10. Determine if seasonality is significant
+
+# 11. Obtain the residuals, plot the ACF and PACF and interpret them
+
+# 12. Create appropriate models for seasonality
+
+# 13. Compare models using AIC, BIC and adjst-R2