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Allen Akinkunle

As a loss function we will use mean squared error just like we did for simple linear regression. The only difference is that now we are getting our predicted output from a different function. For optimization purposes we will still use Gradient Descent only that now we need to update not only m and b like we needed to do for simple linear regression but now we need to update each weight.

Normaly this is a classification problem but we will treat it as an regression problem by using the pental width as our label. Lastly I will like to a few great resources which you can use to learn more about linear regression.

Business Calculus

In this article, we went over what Linear Regression is, how it works and how we can implement it using Python and Numpy. If you liked this article consider subscribing on my Youtube Channel and following me on social media. Gilbert Tanner. Articles About me Contact me. Gilbert Tanner Articles About me Contact me. Linear Regression Explained In this article we will go over what linear regression is, how it works and how you can implement it using Python.

What is Linear Regression? Since the number of bikes they produce may vary from year to year, a variable would be used in this function to represent the unknown number of bikes produced.

Since the cost of manufacturing bikes depends on the number of bikes produced, cost also needs a variable. Let's use C to represent the cost and b to represent the number of bikes produced. Therefore the cost function would look as follows:.

Linear Regression Explained

With this function they could determine their cost once they know the number of bikes they produce. In business, "breaking even" means that costs equal revenues, that is, the company neither makes a profit, nor takes a loss. The "break-even point" for this bike manufacturer would have to represent the exact number of bikes needed in order for their cost, C, to equal their revenue, R.

It is always a good idea to first isolate the terms including the variable from the constants to begin with as we did above by subtracting or adding before dividing or multiplying away the coefficient in front of the variable. As long as you do the same thing on both sides of the equal sign you can do whatever you want and in which order you want. Above we began by subtracting the constant on both sides.

Key Concepts

We could have begun by dividing by 2 instead. It would have looked like.

If your equation contains like terms it is preferable to begin by combining the like terms before continuing solving the equation. Now it's time to isolate the variable from the constant part.


  • Worked example: matching an input to a function's output (equation).
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This is done by subtracting 16 from both sides. If you have an equation where you have variables on both sides you do basically the same thing as before.

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You collect all like terms. Before you have worked by first collecting all constant terms on one side and keep the variable terms on the other side. The same applies here.