Blatt_2.Rmd

---
title: "Blatt_2"
author: "Vanessa Kleisch"
date: "2024-04-30"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(here)
library(dplyr)
library(data.table)
library(ggplot2)
library(patchwork)
library(visreg)
```


## 5)
### a)

```{r}
wdi <- get(load(here("C:/Users/famil/Documents/LiMo/data/wdi.Rdata")))
wdi <- wdi %>% filter(year == 2013)
str(wdi)
head(wdi)

a1 <- ggplot(wdi, aes(x = Population)) +
  geom_density()
a2 <- ggplot(wdi, aes(x = CO2emission)) +
  geom_density()
a1 | a2

# Bivariate Analyse
s3 <- ggplot(wdi, aes(x = Population, y = CO2emission)) +
  geom_point() +
  ggtitle("ohne Transformation")
s4 <- ggplot(wdi, aes(x = log10(Population), y = log10(CO2emission))) +
  geom_point() +
  ggtitle("mit Transformation")
s3|s4
```

### b

```{r}
transformed_wdi <- wdi %>% mutate(CO2emission = log10(CO2emission),
                                  Population = log10(Population))
model_1b <- lm(CO2emission ~ Population, wdi)
summary(model_1b)
model_1b2 <- lm(CO2emission ~ Population, transformed_wdi)
summary(model_1b2)

```
Visualisierung

```{r}
s3 + geom_smooth(method = "lm", se =  FALSE) | s4 + geom_smooth(method = "lm", se =  FALSE)
```


### c)
Density functions für alle Variablen machen:

Daten zu long Format machen

```{r}

wdi_long <- reshape2::melt(wdi)
head(wdi_long)
ggplot(wdi_long, aes(x = value)) + 
  geom_density() +
  facet_wrap(facets = ~variable, scales = "free") +
  theme_minimal()
  
```

Verteilungen die sehr linksschief sind transformieren

warum hier bei PopulationRural + 1??

```{r}
wdi_transformed <- wdi %>% mutate(Area = log10(Area), CO2emission = log10(CO2emission),
                            Population = log10(Population), 
                            PopulationRural = log10(PopulationRural),
                            GDP = log10(GDP))
wdi_longer <- reshape2::melt(wdi_transformed)
ggplot(wdi_longer, aes(x = value)) + 
  geom_density() +
  facet_wrap(facets = ~variable, scales = "free") +
  theme_minimal()
```

 wie visulalisiert man diese scatter plots??
 noch aes ändern und facet wrap ausbessern
```{r}
wdi_longer2 <- wdi_longer %>% filter(variable == c("GDP",  "Area",  "Population", "Livestock", "CO2emission") )
ggplot(wdi %>% select("GDP",  "Area",  "Population", "Livestock", "CO2emission") , aes(x = value, )) + 
  geom_point() +
  facet_wrap(facets = scales = "free") +
  theme_minimal()
wdi_longer
```
 
### d)
 
Multiples lineares Regressionsmodell 
```{r}
model_5d <- lm(CO2emission ~ 
                 Area + Population + Livestock + Employees.M.IND, 
               wdi_transformed, 
               na.action = na.exclude)
summary(model_5d)
```
 
### e)

```{r}

```