linear regression equation example equation

Given this approximate target function, we can use our model to make predictions.

Thus, a more concise way to represent this is to use its vectorized form: Where θ represents the parameters and n is the number of features.Įssentially, all that occurs in the above equation is the dot product of θ, and x is being summed. Mathematically it can be represented as follows: Linear regression makes a prediction, y_hat, by computing the weighted sum of input features plus a bias term. Both descriptions work, but what exactly do they mean? We will start with linear regression. Another way to describe the normal equation is as a one-step algorithm used to analytically find the coefficients that minimize the loss function. The normal equation is a closed-form solution used to find the value of θ that minimizes the cost function. Let’s dive deeper… What is the Normal Equation? For now, all you need to know is that it's an effective approach that can help you save lots of time when implementing linear regression under certain conditions. What problem did you ask? We’ll cover that in the remainder of this article. It’s just another way to solve a problem. The normal equation is just an emphasis of this concept. For example, if we wanted to get from one side of a room to another, we may decide to walk around the room until we arrive at the opposing side, or we could just cut across. Most problems we encounter have several ways they can be solved.

Linear regression equation example equation