{"id":4845,"date":"2020-02-20T14:32:53","date_gmt":"2020-02-20T14:32:53","guid":{"rendered":"https:\/\/data36.com\/?p=4845"},"modified":"2022-09-13T11:38:02","modified_gmt":"2022-09-13T11:38:02","slug":"linear-regression-in-python-numpy-polyfit","status":"publish","type":"post","link":"https:\/\/data36.com\/linear-regression-in-python-numpy-polyfit\/","title":{"rendered":"Linear Regression in Python using numpy + polyfit (with code base)"},"content":{"rendered":"\n

I always say that learning linear regression in Python is the best first step towards machine learning.<\/strong> Linear regression is simple and easy to understand even if you are relatively new to data science. So spend time on 100% understanding it! If you get a grasp on its logic, it will serve you as a great foundation for more complex machine learning concepts in the future.<\/p>\n\n\n\n

In this tutorial, I’ll show you everything you’ll need to know about it: the mathematical background, different use-cases and most importantly the implementation. We will do that in Python — by using numpy<\/code> (polyfit<\/code>).<\/p>\n\n\n\n

Note: This is a hands-on tutorial. I highly recommend doing the coding part with me! If you haven\u2019t done so yet, you might want to go through these articles first:<\/em><\/p>\n\n\n\n

  1. How to install Python, R, SQL and bash to practice data science!<\/a><\/li>
  2. Python libraries and packages for Data Scientists<\/a><\/li>
  3. Learn Python from Scratch<\/a><\/li><\/ol>\n\n\n\n

    Download the code base!<\/strong><\/h2>\n\n\n\n

    Find the whole code base for this article (in Jupyter Notebook format) here:<\/p>\n\n\n\n

    Linear Regression in Python (using Numpy polyfit)<\/a><\/p>\n\n\n\n

    Download it from: here<\/a>.<\/p>\n\n\n\n

    The mathematical background<\/strong><\/h2>\n\n\n\n

    Remember when you learned about linear functions<\/em> in math classes?
    I have good news: that knowledge will become useful after all!<\/p>\n\n\n\n

    Here’s a quick recap<\/strong>!<\/p>\n\n\n\n

    For linear functions, we have this formula:<\/p>\n\n\n\n

    y = a*x + b<\/pre>\n\n\n\n
    In this equation, usually, a<\/code> and b<\/code> are given. E.g:<\/p>\n\n\n\n
    a = 2
    b = 5<\/pre>\n\n\n\n
    So:<\/p>\n\n\n\n
    y = 2*x + 5<\/pre>\n\n\n\n
    Knowing this, you can easily calculate all y<\/code> values for given x<\/code> values.<\/p>\n\n\n\n
    E.g.<\/p>\n\n\n\n
    when x<\/code> is…<\/td>y<\/code> is…<\/td><\/tr>
    0<\/td>2*0 + 5 = 5<\/td><\/tr>
    1<\/td>2*1 + 5 = 7<\/td><\/tr>
    2<\/td>2*2 + 5 = 9<\/td><\/tr>
    3<\/td>2*3 + 5 = 11<\/td><\/tr>
    4<\/td>2*4 + 5 = 13<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
    …<\/p>\n\n\n\n
    If you put all the x<\/code>–y<\/code> value pairs on a graph, you’ll get a straight line:<\/p>\n\n\n\n
    \"linear<\/figure>\n\n\n\n
    The relationship between x<\/code> and y<\/code> is linear<\/em>.<\/p>\n\n\n\n
    Using the equation of this specific line (y = 2 * x + 5<\/code>), if you change x<\/code> by 1<\/code>, y<\/code> will always change by 2<\/code>.<\/p>\n\n\n\n
    And it doesn’t matter what a<\/code> and b<\/code> values you use, your graph will always show the same characteristics: it will always be a straight line, only its position and slope change. It also means that x<\/code> and y<\/code> will always be in linear relationship.<\/p>\n\n\n\n
    In the linear function formula:<\/p>\n\n\n\n
    y = a*x + b<\/pre>\n\n\n\n