Added categorical variables, training/testing sets

Author: AmberYZ

Week 5 - Introduction to Modeling/Lecture5.R

@@ -1,4 +1,4 @@
-fire <- read.csv("C:/Users/Student/Documents/UVA 2016-2017/RWorkshop/Week 5 - Introduction to Modeling/forestfires.csv")
+fire <- read.csv("/Users/yuyanzhang/Desktop/RWorkshop/Week 5 - Introduction to Modeling/forestfires.csv")
 View(fire)
 
 #####################
@@ -11,7 +11,6 @@ View(fire)
 summary(fire)
 # No NA's, all numeric data is normalized
 
-
 # Check class of each attribute
 for (i in 1:ncol(fire)){
   print(paste(colnames(fire[i]), ": ", class(fire[,i]),sep = ""))
@@ -24,12 +23,6 @@ upperwhisk <- areabox$stats[5,]
 
 xtm_fire <- subset(fire, area >= upperwhisk, select = c('FFMC', 'DMC', 'DC', 'ISI', 'temp', 'RH', 'wind', 'rain', 'area'))
 
-# Transforming the data
-hist(fire$area) # highly skewed to the left
-hist(log(fire$area))
-
-fire$area_log <- log(fire$area + 0.1)
-
 ####################
 #
 # Basic modeling - Linear Regression
@@ -45,16 +38,7 @@ abline(lm1, col = "orange")
 # Statistical information about this lm
 summary(lm1)
 
-# Plot two variables
-plot(fire$temp, fire$area_log)
-# Create linear regression model between the two
-lm1_log <- lm(area_log~temp, data = fire)
-# Add regression line to plot
-abline(lm1_log, col = "orange")
-# Statistical information about this lm
-summary(lm1_log)
-
-# Can add many more factors to any lm
+# Can add many more factors to this lm
 lm2 <- lm(area~temp+FFMC+wind, data = xtm_fire)
 summary(lm2)
 
@@ -67,12 +51,12 @@ lm3 <- lm(area~temp+FFMC+wind+(DC+DMC)^2+(ISI+FFMC)^2+(temp+FFMC)^2, data = xtm_
 summary(lm3)
 
 # compare models
-anova(lm1, lm1_log) 
-anova(lm1, lm2)
+anova(lm1, lm2) 
 # Large p-value means that the additional factors do not contribute to predicting the value of the response
 anova(lm1, lm3)
 anova(lm2, lm3)
 
+
 #####################
 #
 # Practice Problems
@@ -94,3 +78,81 @@ anova(lm2, lm3)
 # Call this model lm2_ISI
 
 # 7. Compare these two models and determine which model is better at predicting the size of the area burned
+
+
+#####################
+#
+# Categorical variables
+#
+###################
+
+#Suppose we want to develop a model to predict the area and also using month and day attributes
+class(fire$month)
+contrasts(fire$month)
+class(fire$day)
+contrasts(fire$day)
+
+#Get the right dataset
+xtm_fire_withCategorical <- subset(fire, area >= upperwhisk, select = c('FFMC', 'DMC', 'DC', 'ISI', 'temp', 'RH', 'wind', 'rain', 'area','month','day'))
+lm4 <- lm(area~temp+FFMC+wind+(DC+DMC)^2+(ISI+FFMC)^2+(temp+FFMC)^2+month+day, data = xtm_fire_withCategorical)
+
+#Practice problem: is lm4 better than lm3? How do you know?
+
+
+
+#####################
+#
+# Evaluating the performance of model: training set and testing set
+#
+###################
+
+#Why? Because we want to test the robustness of the model on unseen data
+
+#Suppose we want to develop a model to predict the temp. Let's use the entire dataset (not just extreme cases)
+
+#Set up training set and testing set
+set.seed(123456) #Setting the seed of the random process
+smp_size <- floor(0.75 * nrow(fire)) #We are seperating 75% of the data as the training data, and 25% as the testing data
+train_ind <- sample(seq_len(nrow(fire)), size = smp_size)
+train <- fire[train_ind, ]
+test <- fire[-train_ind, ]
+
+#Train the model on the training set
+lm.train <- lm(temp~area+FFMC+wind+(DC+DMC)^2+(ISI+FFMC)^2+FFMC+month+day, data = train)
+summary(lm.train)
+
+#Use the trained model to generate predictions for the testing sets
+predict(lm.train,test) #The command gives a list of predicted value for each datapoint in the testing set
+pred <- as.vector(predict(lm.train,test)) 
+
+#Evaluate the performance of the model based on the predictions: calculating the MSE (mean squared error) of predictions
+mse <- function(p, r)
+{
+  mean((p-r)^2)
+  
+}
+
+pmse.lm.train<-mse(pred,test$temp)
+pmse.lm.train
+
+#Practice question: how does pmse.lm.train compared to the MSE on the training set? Which value better represents the robustness of the model?
+#Hint: use mean((lm.train$residuals)^2) to compute the MSE on training set
+
+#####################
+#
+# Practice Problems
+#
+###################
+#1. Develop a linear model to predict the rain, using all attributes (hint: you can write the formula this way: lm(rain~., data = fire) to indicate you are using all attributes)
+
+#2. Look at the summary of the model. Which attributes are statistically significant? (with p-value < 0.05)
+
+#3. Develop a linear model only using attributes that are statistically significant
+
+#4. Compare model 1 and model 3. Are they statistically different? Which one would you choose?
+
+#5. Split the dataset into trainning and testing set. Then use the training set to train the model you selected. 
+
+#6. Generate predictions for the testing sets.
+
+#7. Compute the mean squared error of the predictions