linear_regression.Rmd

---
title: "Linear Regression"
author: "Ghinwa Moujaes"
date: "22/03/2022"
output: html_document
---

```{r}
rm(list = ls())
library(dplyr)
library(tidyverse)
library(texreg)

df <- read_csv("../data/Titanic_Data/titanic.csv")
```

```{r}
df$male[df$Sex=="male"] <- 1 
df$male[df$Sex=="female"] <- 0 
```

1. Estimate a linear model for Fare using Age as continuous predictor

```{r}
model_1 <- lm(Fare ~ Age, data=df)
summary(model_1)
```

Estimate a linear model only including the Sex as categorical predictor/dummy variable (Model 2)
```{r}
model_v2 <- lm(Fare ~ male, data = df)
summary(model_v2)
```

Estimate a linear model including both predictors simultaneously (Model 3)
```{r}
model_v3 <- lm(Fare ~ male + Age, data = df)
summary(model_v3)
```
What do the slope coefficients mean?

1. On average, male fares were 20 units cheaper then female fares
2. On average, one additional year in a passenger's age is correlated with a higher fare of 0.45 units

Compare slope coefficients across the models: Do they change? How?
- In the full model, both coefficients slightly change in value (age increases, male decreases) but their significance stays the same 

Estimate a linear regression regressing the continuous predictor on the categorical predictor (dummy variable). (Model 4)

```{r}
model_v4 <- lm(Age ~ male, data = df)
summary(model_v4)
```
Calculate and save the residuals. Use these residuals as a predictor of the dependent variable Fare

```{r}
df$residual_age_male <- resid(model_v4)

model_v5 <- lm(Fare ~ residual_age_male, data = df)
summary(model_v5)
```

Estimate a linear regression regressing the dummy predictor on the continuous predictor
```{r}
model_v6 <- lm(male ~ Age, data = df)
summary(model_v6)
```

Calculate and save the residuals. Use these residuals as a predictor of the dependent variable Fare.
```{r}
df$residual_male_age <- resid(model_v6)

model_v7 <- lm(Fare ~ residual_male_age, data = df)
summary(model_v7)
```

```{r}
screenreg(c(model_v3, model_v5, model_v7))
```