MyProject.Rmd

---
title: "Analyzing the Influence of Vehicle Attributes on Fuel Consumption and A Linear Regression Approach"
output: html_notebook
---

```{r}
library(ggplot2)
library(dplyr)
library(car)
```

```{r}
# Read the CSV file
data <- read.csv("/Users/vinay/Desktop/LinearRegression/project/CO2_Emissions.csv")

str(data)
```

```{r}
summary(data)      # Summary statistics
```

```{r}
head(data)
```

```{r}
sum(is.na(data))
```

```{r}
data$Make <- as.factor(data$Make)
data$Model <- as.factor(data$Model)
data$Vehicle_Class <- as.factor(data$Vehicle_Class)
data$Transmission <- as.factor(data$Transmission)
data$Fuel_Type <- as.factor(data$Fuel_Type)
```

```{r}
data <- data %>% 
  mutate(across(c(Make, Model, Vehicle_Class, Transmission, Fuel_Type), as.integer))
```

```{r}
str(data)
```

```{r}
model <- lm(Fuel_Consumption_Comb_L_100km ~ EngineSize_L, data = data)

summary(model)

```

```{r}
# Plot the data and the regression line
ggplot(data, aes(x = EngineSize_L, y = Fuel_Consumption_Comb_L_100km)) +
  geom_point() +
  geom_smooth(method = "lm", col = "blue") +
  labs(x = "Engine Size (L)", y = "Fuel Consumption (L/100 km)", 
       title = "Relationship between Engine Size and Fuel Consumption")
```

```{r}
par(mfrow=c(2,2))
plot(model)
```

```{r}
plot(data$EngineSize_L, data$Fuel_Consumption_Comb_L_100km, 
     xlab = "Engine Size (L)", ylab = "Fuel Consumption (L/100 km)",
     main = "Relationship between Engine Size and Fuel Consumption")

```

```{r}
cylinders_model <- lm(CO2_Emissions_g_per_km ~ Cylinders, data = data)

summary(cylinders_model)

```

```{r}
ggplot(data, aes(x = Cylinders, y = CO2_Emissions_g_per_km)) +
  geom_point() +
  geom_smooth(method = "lm", col = "blue") +
  labs(x = "Number of Cylinders", y = "CO2 Emissions (g/km)", 
       title = "Relationship between Number of Cylinders and CO2 Emissions")
```

```{r}
# Create dummy variables for 'Vehicle_Class' using model.matrix
# This creates a full set of dummy variables (one for each class)



vehicle_class_dummies <- model.matrix(~ Vehicle_Class - 1, data = data)

model_data <- data.frame(Fuel_Consumption_Comb_L_100km = data$Fuel_Consumption_Comb_L_100km, vehicle_class_dummies)

# Fit the linear model
model_vehicle_class <- lm(Fuel_Consumption_Comb_L_100km ~ ., data = model_data)

summary(model_vehicle_class)

```

```{r}
plot(model_vehicle_class)
```

```{r}

vehicle_class_dummies <- model.matrix(~ Vehicle_Class, data = data)[, -1]
fuel_type_dummies <- model.matrix(~ Fuel_Type, data = data)[, -1]
transmission_dummies <- model.matrix(~ Transmission, data = data)[, -1]

data <- cbind(data, vehicle_class_dummies, fuel_type_dummies, transmission_dummies)

```

```{r}
# Fit the multiple linear regression model
model <- lm(CO2_Emissions_g_per_km ~ EngineSize_L + Cylinders + ., data = data)

# View the summary of the model
summary(model)
```

```{r}
model <- lm(CO2_Emissions_g_per_km ~ EngineSize_L + Cylinders + Fuel_Consumption_City_L_100km + Fuel_Consumption_Hwy_L_100km + Fuel_Consumption_Comb_L_100km, data = data)
summary(model)
```

```{r}
vif_model <- vif(model)
vif_model

```

```{r}

data_subset <- data[, c("EngineSize_L", "Cylinders", "Fuel_Consumption_City_L_100km", 
                        "Fuel_Consumption_Hwy_L_100km", "Fuel_Consumption_Comb_L_100km")]

cor.mat <- round(cor(data_subset), 2)

cor.mat

```

```{r}
plot(model)
```

```{r}
revised_model <- lm(CO2_Emissions_g_per_km ~ EngineSize_L + Cylinders + Fuel_Consumption_Comb_L_100km, data = data)

summary(revised_model)
```

```{r}
# Check VIF for the revised model
vif_revised_model <- vif(revised_model)
vif_revised_model
```

```{r}
# Plot diagnostics
plot(revised_model)
```

```{r}
data$log_CO2_Emissions_g_per_km <- log(data$CO2_Emissions_g_per_km)

log_model <- lm(log_CO2_Emissions_g_per_km ~ EngineSize_L + Cylinders + Fuel_Consumption_Comb_L_100km, data = data)

summary(log_model)
```

```{r}
plot(log_model)
```

```{r}
poly_model <- lm(CO2_Emissions_g_per_km ~ poly(EngineSize_L, 2) + Cylinders + Fuel_Consumption_Comb_L_100km, data = data)

interact_model <- lm(CO2_Emissions_g_per_km ~ EngineSize_L * Cylinders + Fuel_Consumption_Comb_L_100km, data = data)

summary(poly_model)

summary(interact_model)
```

```{r}
plot(poly_model)
```

```{r}
plot(interact_model)
```

```{r}
library(MASS)

# Find the optimal Box-Cox transformation for the response variable
bc <- boxcox(CO2_Emissions_g_per_km ~ EngineSize_L + Cylinders + Fuel_Consumption_Comb_L_100km, data = data)

# Identify the lambda that maximizes the log-likelihood
lambda <- bc$x[which.max(bc$y)]

# Apply the Box-Cox transformation with the identified lambda
data$BC_CO2_Emissions <- (data$CO2_Emissions_g_per_km^lambda - 1) / lambda

# Fit the model with the Box-Cox transformed response variable
bc_model <- lm(BC_CO2_Emissions ~ EngineSize_L + Cylinders + Fuel_Consumption_Comb_L_100km, data = data)

# View the summary of the model
summary(bc_model)
```

```{r}
plot(bc_model)
```

```{r}
full_model <- lm(CO2_Emissions_g_per_km ~ EngineSize_L + Cylinders + Fuel_Consumption_Comb_L_100km, data = data)

stepwise_model <- step(full_model, direction="both")

summary(stepwise_model)
```

```{r}

data <- read.csv("/Users/vinay/Desktop/LinearRegression/project/CO2_Emissions.csv")

data$Vehicle_Class <- as.factor(data$Vehicle_Class)
data$Transmission <- as.factor(data$Transmission)
data$Fuel_Type <- as.factor(data$Fuel_Type)

full_model_cat <- lm(CO2_Emissions_g_per_km ~ EngineSize_L + Cylinders + 
                     Fuel_Consumption_Comb_L_100km + Vehicle_Class + 
                     Transmission + Fuel_Type, data = data)

stepwise_model_cat <- step(full_model_cat, direction="both")

summary(stepwise_model_cat)
```

```{r}
data <- read.csv("/Users/vinay/Desktop/LinearRegression/project/CO2_Emissions.csv")

data$Transmission <- as.factor(data$Transmission)
data$Fuel_Type <- as.factor(data$Fuel_Type)

model_fuel_efficiency <- lm(Fuel_Consumption_Comb_L_100km ~ Transmission * Fuel_Type, data = data)

summary(model_fuel_efficiency)
```

```{r}
par(mfrow=c(2,2))
plot(model_fuel_efficiency)
```