Linear Regression RStudio

Linear Regression is a fundamental statistical technique used to model the relationship between a dependent variable and one or more independent variables. The goal is to fit a straight line through the data points that best predicts the dependent variable. The simplest form, known as Simple Linear Regression, involves one independent variable and is represented by the familiar equation "y = mx + c", where "y" is the dependent variable, "x" is the independent variable, "m" is the slope, and "c" is the intercept.

Linear Regression is widely used because of its simplicity, interpretability, and efficiency. It provides a clear understanding of the relationships between variables and allows for easy interpretation of coefficients. This method is highly effective for making predictions when the relationship between variables is approximately linear. It's also computationally efficient, making it suitable for large datasets. Additionally, Linear Regression serves as a foundation for more complex regression methods, making it a valuable tool in both academic research and industry applications.

We start by installing and loading the necessary packages. These libraries provide essential tools for building, evaluating, and visualising the Linear Regression model. The datasets library is used for loading the Iris dataset, caTools for splitting the data, and ggplot2 for creating visualisations.

We start by loading the Iris dataset, which is conveniently built into R, so we don't need to download anything. Exploring the dataset helps us understand its structure, the types of variables it contains, and the overall data distribution. This initial step is essential to get familiar with what we're working with.

Splitting the data into training and testing sets is crucial because it allows us to train the model on one part of the data and test its performance on unseen data. This helps ensure that the model generalises well to new data and isn't just memorising the training data.

Building and training the linear regression model helps us understand the relationship between the input variables (e.g., Sepal Width, Petal Length, Petal Width) and the target variable (Sepal Length). This step creates a mathematical model that predicts the target variable based on the input variables.

After training the model, we use it to make predictions on the test set to see how well it performs on new data. Evaluating the model's performance using metrics like RMSE helps us measure the accuracy of the predictions.

RMSE stands for Root Mean Squared Error. It is a commonly used metric to evaluate the accuracy of a regression model. RMSE measures the average magnitude of the errors between the predicted values and the actual values.

- Lower RMSE: Indicates that the model's predictions are closer to the actual values, which means the model is more accurate.

- Higher RMSE: Indicates that the model's predictions are further away from the actual values, which means the model is less accurate.

Visualisation helps us assess the model's performance visually. By creating scatter plots with residual lines, we can see how well the predicted values match the actual values and identify any discrepancies. This step provides a clear and intuitive understanding of the model's accuracy.

In this project, we successfully built a linear regression model to predict Sepal Length using the Iris dataset. By following the steps of loading and exploring the data, splitting it into training and testing sets, training the model, making predictions, and evaluating the results with visualisations and RMSE, we demonstrated the practical application of linear regression. The final visualisations provided insights into the model's accuracy and highlighted areas for potential improvement. This project serves as a valuable exercise in understanding and implementing linear regression in R.