Hello and welcome to this video on cost function. In this video you will learn what a cost function is. In the last video we saw that our linear hypothesis y-hat is controlled by two parameters weight and bias. In order to find the best possible model to describe our data, we need to define a way to decide how good a model is. Remember that we are solving a supervised learning task. So, we know the true value of the labels. This is to say we know the actual price of a house for each given house size in the data set. Therefore, we can compare the value predicted by the hypothesis with the actual value of the label, and calculate the error for each data point. These are called residuals and are calculated by subtracting the value of the prediction from the true value of the label. Note that in this definition, a residual carries a sign. It will be positive if our hypothesis underestimates the true price and negative if it overestimates it. 

However, we don't really care about the direction in which our hypothesis is wrong. We only care about the total amount of being wrong. We can therefore define the total error as the sum of the absolute values of the residuals. The total error is one possible example of what is called the cost function. A cost function returns a value once the hypothesis y-hat, the parameters b and w and the training data are set to fix values. For reasons that would be clear later in the course it's often preferable to use another cost function called mean squared error, the mean squared error is calculated by taking the square of each residual, summing all these squares and dividing by the total number of data points . And notice that since the square is a positive function, the mean squared error will be large when the total error is large. And small when the total error is small. In that sense there are some what equivalent. However, the mean squared error will be much larger when the individual differences are large because of the square operation. Also, the mean squared error is preferable because it's smooth and it's guaranteed to have a global minimum. Which is exactly what we are looking for. In conclusion, in this lecture you've learned about cost functions and you've learned two different types of cost functions, the total error and the mean squared error. You've also learned that for given values of training data and hypothesis, the cost only depends on the value of the parameters. Thank you for watching and see you in the next video.