Improve README documentation and fix grammar

README.md

@@ -1,35 +1,50 @@
-Partial Least Squares for Arduino/ESP32
-=====================================  
+# Partial Least Squares for Arduino/ESP32
 
+## Introduction
 
-Introduction:  
-------------------------  
-Partial Least Squares (PLS) is a statistical technique that helps to model relationships between groups of variables. It's especially useful when the predictor variables (the ones we use to predict outcomes) are closely related to each other or when there are more predictors than observations. PLS is commonly used in fields like chemistry, social sciences, and bioinformatics.
+Partial Least Squares (PLS) is a statistical technique used to model relationships between groups of variables. It is especially useful when predictor variables are highly correlated or when there are more predictors than observations. PLS is widely used in fields such as chemistry, social sciences, and bioinformatics.
 
+## Usage
 
-Usage:
-==========
-Download all the source files.
-There is one example for the user to use.
->* **examples/basic_usage/basic_usage.ino**,this example shows a simple usage using predefined matrices
-## TODO
->* **examples/read_XY_from_SD_card/read_from_XY_from_SD.ino**, this example shows how to read X (features matrice) and Y (response matrice) from a file saved in an SD card, for example.
+Download all source files and install the library in your Arduino environment.
 
+### Examples
 
-Notice:
-============
->1. This library depends on the Arduino Eigen/Dense library.
->2. Arduino/ESP32 are quite limited in computational capabilities. You can also load a pre-trained matrix B and use it to predict 
-Y (as long as you keep the dimensionality consistent).
+examples/basic_usage/basic_usage.ino
+  Demonstrates basic usage of the library with predefined matrices.
 
+examples/read_XY_from_SD_card/read_from_XY_from_SD.ino
+  Demonstrates how to read the feature matrix (X) and response matrix (Y) from files stored on an SD card.
 
-Reference:
-===============
-Refer to the **/doc** for more details (tbd).
+## Installation
+
+1. Install the Arduino Eigen/Dense library.
+2. Download or clone this repository.
+3. Copy the library into your Arduino libraries folder.
+4. Restart the Arduino IDE.
+
+## Notice
+
+1. This library depends on the Arduino Eigen/Dense library.
+2. Arduino and ESP32 devices have limited computational resources. You can load a pre-trained matrix **B** and use it to predict **Y**, provided that the dimensionality remains consistent.
+
+## Reference
+
+Refer to the /doc directory for additional details (to be completed).
+
+---
+
+## Contributing
+
+Contributions are welcome. To contribute:
+
+1. Fork the repository.
+2. Make your changes.
+3. Commit your modifications.
+4. Submit a pull request.
+
+Adding a changelog and your contact information in the file header is encouraged.
+
+Thank you for your contribution!
 
-***
 
-Contributing to this software is very welcome. You can do this basically by<br>
-[forking](https://help.github.com/articles/fork-a-repo), committing modifications and then [pulling requests](https://help.github.com/articles/using-pull-requests) (follow the links above<br>
-for operating guide). Adding a change log and your contact into the file header is encouraged.<br>
-Thanks for your contribution.