modelling.Rmd

---
title: "Modelling"
output:
  html_document:
    df_print: paged
---

## Here, we aim to build and train models on the preprocessed dataset produced from data_merging.ipynb.  

First, we import the required libraries.
```{r}
library(ISLR)
library(glmnet)
```

Now, we import in our dataset.
```{r}
df1 = read.csv("total_data.csv")
df2 = df1[121:250,-1]
head(df2)
```
We produce a pairsplot for all the features to get an initial look at our data.
```{r}
pairs(df2)
```
### For our first group of models, we perform simple linear regression with each predictor individually
```{r}
lm.fit1 = lm(Value~Exchange, data = df2)
summary(lm.fit1)
```
```{r}
lm.fit2 = lm(Value~Ratio_E_I, data = df2)
summary(lm.fit2)
```
```{r}
lm.fit3 = lm(Value~Interest, data = df2)
summary(lm.fit3)
```
```{r}
lm.fit4 = lm(Value~M1_supply, data = df2)
summary(lm.fit4)
```
```{r}
lm.fit5 = lm(Value~GDP, data = df2)
summary(lm.fit5)
```

### For our second model, do Multiple Linear Regression basd on least squares method
```{r}
set.seed(1)
mlm.fit = lm( Value~., data = df2)
summary(mlm.fit)
```
```{r}
mlm.pred = predict( mlm.fit, df2)
mean((mlm.pred - df2$Value)^2)
```

Now, we plot curves for the original values and the predicted values from our MLR model.
```{r}
plot(as.Date(df1$Time[121:250]), df1$Value[121:250], type = "l", col = "blue", xlab = "Date (mm-yyyy)", ylab = "Inflation Rate (%)", lwd=2, main = "Comparison for Multiple Linear Regression Model (without interaction)", cex.main = 0.8, cex.lab=0.9, ylim = c(0,20))
lines(as.Date(df1$Time[121:250]), mlm.pred, type="l", col="red", lwd=2)
legend(x = "topright", col = c("blue", "red"), legend = c("Observed", "Predicted"), lty = 1, lwd=2)
```
For our third and final model, we perform Multiple Linear Regression with interaction terms based on least squares method.
```{r}
set.seed(1)
mlm.fiti = lm( Value~.^2, data = df2)
summary(mlm.fiti)
```
```{r}
mlm.predi = predict( mlm.fiti, df2)
mean((mlm.predi - df2$Value)^2)
```
Lastly, we plot curves for the original values and the predicted values from our MLR model withg interaction terms.
```{r}
plot(as.Date(df1$Time[121:250]), df1$Value[121:250], type = "l", col = "blue", xlab = "Date (mm-yyyy)", ylab = "Inflation Rate (%)", lwd=2, main = "Comparison for Multiple Linear Regression Model (with interaction)", cex.main = 0.8, cex.lab=0.9, ylim = c(0,20))
lines(as.Date(df1$Time[121:250]), mlm.predi, type="l", col="red", lwd=2)
legend(x = "topright", col = c("blue", "red"), legend = c("Observed", "Predicted"), lty = 1, lwd=2)
```