The model will take the sum of all these squared differences and divide them by m, the number of data points. The regressor will take the difference of y and y-hat for every point in the dataset and square it. To answer this question, we need to talk about what the math behind the formula-but fear not, when broken down, it isn’t all that complex. The purpose of the Mean Squared Error Cost Function is to minimize this error as much as possible for all the points in the dataset. J(b_0, b_1) is the cost, which we will discuss now. M is the number of data points in our dataset. The i subscript below y and y-hat signifies the i’th point in the dataset.

Y is the variable that represents the actual value provided in the training dataset. Y-hat (the y with a little symbol over it) is a variable used in statistics to represent the predicted value of our model when training. This is a scatterplot of the training dataset I showed before, and the blue line represents the regressor’s line of best fit. To do this, we’ll need to take a look at the formula for univariate MSE and break down each of the variables and their purposes. Let’s start by breaking down MSE with one variable. How Does The MSE Cost Function Work? Univariate MSE We’ll first break down the formula for both single and multiple independent variables, and then work through examples so that you can attain a better understanding of the algorithm in practice. In this article, we’ll be talking about the MSE Cost Function by using simple and multiple linear regression algorithms as examples. There are many different cost functions that are used by modern machine learning algorithms, but one of the most popular is known as the Mean Squared Error (MSE) Cost Function. Thus, an optimal machine learning model would have a cost close to 0. A cost function is a mathematical formula that allows a machine learning algorithm to analyze how well its model fits the data given.Ī cost function returns an output value, called the cost, which is a numerical value representing the deviation, or degree of error, between the model representation and the data the greater the cost, the greater the deviation (error).

Mean squared error