{"id":1394,"date":"2019-02-15T10:32:07","date_gmt":"2019-02-15T10:32:07","guid":{"rendered":"http:\/\/kusuaks7\/?p=999"},"modified":"2023-08-07T12:36:47","modified_gmt":"2023-08-07T12:36:47","slug":"coding-deep-learning-for-beginners-linear-regression-part-2-cost-function","status":"publish","type":"post","link":"https:\/\/www.experfy.com\/blog\/ai-ml\/coding-deep-learning-for-beginners-linear-regression-part-2-cost-function\/","title":{"rendered":"Coding Deep Learning for Beginners\u200a\u2014\u200aLinear Regression (Part 2): Cost Function"},"content":{"rendered":"

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This is the 4th article of series \u201cCoding Deep Learning for Beginners\u201d. Here, you will find\u00a0links to the\u00a01st article<\/a>, the\u00a02nd\u00a0article<\/a>, and the 3rd article<\/a>.<\/p><\/blockquote>\n

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Recap<\/strong><\/h3>\n

The last article has introduced the problem which will be solved after Linear Regression implementation is finished. The goal is to\u00a0predict the prices of Cracow apartments<\/strong>. The dataset consists of samples described by three features:\u00a0distance_to_city_center<\/strong>,\u00a0room<\/strong>, and\u00a0size<\/strong>. To simplify visualizations and make learning more efficient \u2014 only size feature will be used.<\/p>\n

Additionally, the mathematical formula behind Linear Regression model was presented and explained. For the equation to be complete, it\u2019s parameters needs to have assigned values. Then, the formula is ready to return a numerical prediction for any given input sample.<\/p>\n

The two steps described here are called\u00a0Initialization<\/strong>\u00a0and\u00a0Prediction<\/strong>. Both were\u00a0turned into separate Python functions and used to create a Linear Regression model<\/strong>\u00a0with all parameters initialized to zeros and used to predict prices for apartments based on size parameter.<\/p>\n

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Code used to prepare the graph is available under this\u00a0link<\/a>.<\/p>\n

Next problem to\u00a0solve<\/strong><\/h3>\n

Model with current parameters will return a zero for every value of area parameter because of all weights of the model and bias equal to zeros. Now let\u2019s modify the parameters and see how the projection of the model changes.<\/p>\n

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Code used to prepare these graphs is available under this\u00a0link<\/a>.<\/p>\n

There are two sets of parameters that cause a Linear Regression model to return different apartment price for each value of size feature. Because data has the linear pattern, the model could become accurate approximator of the price after proper calibration of the parameters.<\/p>\n

Question to\u00a0answer<\/strong><\/h4>\n

For which set of parameters, the model returns better results?<\/p>\n