
---
title: "Getting Started with olr: Optimal Linear Regression"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Getting Started with olr: Optimal Linear Regression}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}

---

```{r html-style, results='asis', echo=FALSE}
cat("
<style>
pre code {
  white-space: pre-wrap;
  word-wrap: break-word;
  overflow-x: auto;
  font-size: 90%;
}
</style>
")
```


```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)
library(olr)
library(ggplot2)
```

## 📦 Introduction

The `olr` package provides a systematic way to identify the best linear regression model by testing **all combinations** of predictor variables. You can choose to optimize based on either **R-squared** or **adjusted R-squared**.

---

## 📊 Load Example Dataset

```{r}
# Load data
crudeoildata <- read.csv(system.file("extdata", "crudeoildata.csv", package = "olr"))
dataset <- crudeoildata[, -1]

# Define variables
responseName <- 'CrudeOil'
predictorNames <- c('RigCount', 'API', 'FieldProduction', 'RefinerNetInput',
                    'OperableCapacity', 'Imports', 'StocksExcludingSPR',
                    'NonCommercialLong', 'NonCommercialShort',
                    'CommercialLong', 'CommercialShort', 'OpenInterest')
```

---

## 🔎 Run OLR Models

```{r}
# Full model using R-squared
model_r2 <- olr(dataset, responseName, predictorNames, adjr2 = FALSE)

# Adjusted R-squared model
model_adjr2 <- olr(dataset, responseName, predictorNames, adjr2 = TRUE)
```

---

## 📈 Visual Comparison of Model Fits

```{r plot-r2-line, fig.align="center", fig.width=6.3, fig.height=4.5, out.width='99%'}
# Actual values
actual <- dataset[[responseName]]
fitted_r2 <- model_r2$fitted.values
fitted_adjr2 <- model_adjr2$fitted.values

# Data frames for ggplot
plot_data <- data.frame(
  Index = 1:length(actual),
  Actual = actual,
  R2_Fitted = fitted_r2,
  AdjR2_Fitted = fitted_adjr2
)

# Plot both fits
ggplot(plot_data, aes(x = Index)) +
  geom_line(aes(y = Actual), color = "black", size = 1, linetype = "dashed") +
  geom_line(aes(y = R2_Fitted), color = "steelblue", size = 1) +
  labs(
    title = "Full Model (R-squared): Actual vs Fitted Values",
    subtitle = "Observation Index used in place of dates (parsed from original dataset)",
    x = "Observation Index",
    y = "CrudeOil % Change"
  ) +
  theme_minimal()
```

```{r plot-adjr2-line, fig.align="center", fig.width=6.3, fig.height=4.5, out.width='99%'}
ggplot(plot_data, aes(x = Index)) +
  geom_line(aes(y = Actual), color = "black", size = 1, linetype = "dashed") +
  geom_line(aes(y = AdjR2_Fitted), color = "limegreen", size = 1.1) +
  labs(
    title = "Optimal Model (Adjusted R-squared): Actual vs Fitted Values",
    subtitle = "Observation Index used in place of dates (parsed from original dataset)",
    x = "Observation Index",
    y = "CrudeOil % Change"
  )+
  theme_minimal() +
  theme(plot.background = element_rect(color = "limegreen", size = 2))
```

---

## 📊 Model Comparison Summary Table

| Metric                    | adjr2 = FALSE (All 12 Predictors) | adjr2 = TRUE (Best Subset of 7 Predictors)  |
|---------------------------|-----------------------------------|---------------------------------------------|
| **Adjusted R-squared**    | 0.6145                            | **0.6531** ✅ (higher is better)            |
| **Multiple R-squared**    | 0.7018                            | 0.699                                       |
| **Residual Std. Error**   | 0.02388                           | **0.02265** ✅ (lower is better)            |
| **F-statistic (p-value)** | 8.042 (1.88e-07)                  | **15.26 (3.99e-10)** ✅ (stronger model)     |
| **Model Complexity**      | 12 predictors                     | **7 predictors** ✅ (simpler, more robust)   |
| **Significant Coeffs**    | 4                                 | **6** ✅ (more signal, less noise)           |
| **R² Difference**         | —                                 | ~0.003 ❗ (negligible)                       |

---

## ✅ Best Practice Tips

- The `olr()` function **automates model selection** by testing every valid predictor combination.
- Use `adjr2 = TRUE` to prioritize models that **balance accuracy and parsimony**.
- A small drop in raw R² is acceptable if the adjusted R² is higher — it means **fewer variables**, better generalization.

---

## 📌 Summary

The adjusted R² model outperformed the full model on:
- Adjusted R²
- F-statistic
- Residual error
- Model simplicity
- # of significant coefficients

👉 Use adjusted R² (`adjr2 = TRUE`) in practice to **avoid overfitting** and ensure interpretability.

<div style="height:50px;"></div>

---

<p style="text-align:center; font-size:90%;">
  Created by <strong>Mathew Fok</strong> • Author of the <code>olr</code> package  
  <br>
  Contact: <a href="mailto:quiksilver67213@yahoo.com">quiksilver67213@yahoo.com</a>
</p>



