finalproject1 (1).Rmd

---
title: "R Notebook"
output:
  word_document: default
  html_notebook: default
  pdf_document: default
---
Final Project
```{r}
library(carData)
library(car)
library(ggplot2)
library(hrbrthemes)
library(GGally)
getwd()

day <- read.csv2("Bike-Sharing-Dataset/day.csv",header=TRUE,sep=",")

month <- factor(day$mnth)
day$temp = as.numeric(day$temp)
day$hum = as.numeric(day$hum)
day$registered = as.numeric(day$registered)
day$casual = as.numeric(day$casual)
day$windspeed = as.numeric(day$windspeed)
day$atemp = as.numeric(day$atemp)


training <- day[(day$dteday <= "2011-12-31"),]
validation <- day[(day$dteday > "2011-12-31"),]

```
```{r}
lm(casual~windspeed+hum+atemp+temp+weathersit+workingday+weekday+holiday+mnth+season, training)

step(lm(casual~windspeed+hum+atemp+temp+weathersit+workingday+weekday+holiday+mnth+season, training),direction="both",k=log(365))

# final model: casual ~ windspeed + temp + weathersit + workingday with bic

step(lm(casual~windspeed+hum+atemp+temp+weathersit+workingday+weekday+holiday+mnth+season, training),direction="both",k=2)

# final model:  casual ~ windspeed + temp + weathersit + workingday + mnth + season with aic


step(lm(registered~windspeed+hum+atemp+temp+weathersit+workingday+weekday+holiday+mnth+season, training),direction="both",k=log(365))

# final model: registered ~ windspeed + temp + weathersit + workingday + season with bic

step(lm(registered~windspeed+hum+atemp+temp+weathersit+workingday+weekday+holiday+mnth+season, training),direction="both",k=2)

# registered ~ windspeed + temp + weathersit + workingday + weekday + season with aic

# 
```

```{r}
library(glmnet)
library(ggfortify)
par(mfrow=c(1,1))
x <- model.matrix(casual~windspeed+hum+atemp+temp+weathersit+workingday+weekday+holiday+mnth+season, training)
y <- training$casual
fit1 <- glmnet::glmnet(x, y, alpha = 1)
pallete = c('black', 'red', 'blue', 'green', 'orange','pink','magenta','cyan','yellow','blueviolet','brown','darkolivegreen')
autoplot(fit1) + scale_colour_manual(values=pallete)
```

```{r}
library(glmnet)
library(ggfortify)
par(mfrow=c(1,1))
x <- model.matrix(registered~windspeed+hum+atemp+temp+weathersit+workingday+weekday+holiday+mnth+season, training)
y <- training$registered
fit2 <- glmnet::glmnet(x, y, alpha = 1)
pallete = c('black', 'red', 'blue', 'green', 'orange','pink','magenta','cyan','yellow','blueviolet','brown','darkolivegreen')
autoplot(fit2) + scale_colour_manual(values=pallete)
```

```{r}
lmp.casual <- function(linearmodel){
  plot(linearmodel)
  plot(fitted(linearmodel),rstandard(linearmodel))
  plot(training$casual,rstandard(linearmodel))
  hist(rstandard(linearmodel))
  
}  

lmp.registered <- function(linearmodel){
  plot(linearmodel)
  plot(fitted(linearmodel),rstandard(linearmodel))
  plot(training$registered,rstandard(linearmodel))
  hist(rstandard(linearmodel))
}  
```


```{r}
lm1 <- lm(casual ~ windspeed + temp + weathersit + workingday,training)
lm2 <- lm(casual ~ windspeed + temp + weathersit + workingday + mnth + season,training)
{plot(fitted(lm1),training$casual)
abline(0,1)}
lmp.casual(lm1)
lmp.casual(lm2)

lm3 <- lm(registered ~ windspeed + temp + weathersit + workingday + season,training)
lm4 <- lm(registered ~ windspeed + temp + weathersit + workingday + weekday + season,training)
lmp.registered(lm3)
lmp.registered(lm4)

```

```{r}
lm5 <- lm(casual ~ temp + workingday + atemp + weathersit, training)
lm55 <- lm(casual ~ temp + workingday + atemp, training)
lmp.casual(lm5)
lmp.casual(lm55)

lm6 <- lm(registered ~ season + workingday + atemp + weathersit, training)
lm7 <- lm(registered ~ atemp, training)
lmp.registered(lm6)
lmp.registered(lm7)
```
```{r}
# model 1 summary 
summary(lm1)
```
```{r}
# model 2 summary 
summary(lm2)
```

```{r}
# model 3 summary 
summary(lm3)
```

```{r}
# model 4 summary 
summary(lm4)
```

```{r}
# model 5 summary 
summary(lm5)
```

```{r}
# model 55 summary 
summary(lm55)
```

```{r}
# model 6 summary 
summary(lm6)
```

```{r}
# model 7 summary 
summary(lm7)
```


```{r}
rmse.casual <- function(linearmodel){
  ResValidation <- validation$casual - predict(linearmodel, newdata = validation)
  mean((resid(linearmodel))^2)
  mean((ResValidation)^2)
  rmse <- mean((resid(linearmodel))^2)/mean((ResValidation)^2)
  return(rmse)
}

rmse.reg <- function(linearmodel){
  ResValidation <- validation$registered - predict(linearmodel, newdata = validation)
  mean((resid(linearmodel))^2)
  mean((ResValidation)^2)
  rmse <- mean((resid(linearmodel))^2)/mean((ResValidation)^2)
  return(rmse)
}

rmse.casual(lm1)
rmse.casual(lm2)
rmse.casual(lm5)
rmse.casual(lm55)

rmse.reg(lm3)
rmse.reg(lm4)
rmse.reg(lm6)
rmse.reg(lm7)

```

```{r}
# PI1 <- predict(wlm10, newdata = validation,interval = "predict")

ggplot(data = validation, aes(x = dteday)) +
  geom_line(aes(y = casual, color = "casual"),group = 1) +
  geom_line(aes(y = predict(lm1, newdata = validation), color="predict(lm1)"), linetype="twodash",group = 1) +
  scale_color_manual(name = element_blank(), labels = c("casual","predict(lm1)","conf","conf"),
    values = c("darkred", "steelblue","green","green")) + labs(y = "") +
  ggtitle("Validation")



ggplot(data = validation, aes(x = dteday)) +
  geom_line(aes(y = registered, color = "registered"),group = 1) +
  geom_line(aes(y = predict(lm4, newdata = validation), color="predict(lm4)"), linetype="twodash",group = 1) +
  scale_color_manual(name = element_blank(), labels = c("registered","lm4"),
    values = c("darkred", "steelblue")) + labs(y = "") +
  ggtitle("Validation")


ttlcnt <- predict(lm4, newdata = validation) + predict(lm1, newdata = validation)

ggplot(data = validation, aes(x = dteday)) +
  geom_line(aes(y = cnt, color = "cnt"),group = 1) +
  geom_line(aes(y = ttlcnt, color="ttlcnt"),linetype="twodash",group = 1) +
  scale_color_manual(name = element_blank(), labels = c("cnt","ttlcnt"),
    values = c("darkred", "steelblue")) + labs(y = "") +
  ggtitle("Validation")
```