**The Basics of Supervised Learning**

In supervised learning, we're given both the input features and the output targets. The goal is to learn from this data by creating a model that can make predictions on new, unseen data. This process involves feeding the training set into our machine learning algorithm, which produces a function, commonly referred to as a hypothesis or simply a function f. The job of this function is to take a new input X and output an estimate or prediction, denoted as Y hat.

**The Role of the Model**

In machine learning, the convention is that Y hat represents the estimated value of y, which is the actual true value in the training set. In other words, Y hat is an estimate that may or may not be the actual true value. The model's prediction is the estimated value of y when the symbol refers to the target. For example, if you're helping your client sell their house, the true price of the house is unknown until they sell it, so your model f takes the size or pressure price as input and outputs an estimate of what the true price will be.

**The Function F**

For now, let's stick with a simple function that can be represented by f being a straight line. Your function can be written as F subscript W comma B of x equals W Times X plus b. Here, W and B are numbers that determine the prediction Y hat based on the input feature X. This FWB of X means f is a function that takes X's input and outputs some value of a prediction Y hat.

**Plotting the Training Set**

The linear function F subscript W comma B of x equals W Times X plus b, or more simply f of x equals WX plus b, plots the training set on the graph. The input feature X is on the horizontal axis, and the output targets Y is on the vertical axis. This straight line represents a best fit line created by our learning algorithm.

**The Choice of Function**

You may ask why we're choosing a linear function when other non-linear functions like curves or parabolas might be more suitable. Sometimes, you want to fit more complex non-linear functions as well. However, for now, let's use a line as a foundation that can eventually lead to more complex models.

**Linear Regression**

The particular model we've chosen is called linear regression. More specifically, this is linear regression with one variable, meaning there's only one input variable or feature X – the size of the house. Another name for a linear model with one input variable is univariate linear regression. The "uni" prefix comes from the Latin words "unus," meaning one, and "varius," meaning variable.

**Future Developments**

When you're done watching this video, there's another optional lab that you can review or attempt to complete. In the lab, you'll learn how to define in Python a straight line function and try out different values of w and b to fit the training data. This hands-on experience will give you a deeper understanding of linear regression and its applications.

**Constructing a Cost Function**

In order for you to make this work, one of the most important things you need to do is construct a cost function. The idea of a cost function is one of the most universal and essential ideas in machine learning and is used in both linear regression and training many advanced AI models. In the next video, we'll take a closer look at how to construct a cost function.

"WEBVTTKind: captionsLanguage: enlet's look in this video at the process of how supervised Learning Works supervised learning algorithm will input the data set and then what exactly does it do and what does it output let's find out in this video recall that a training set in supervised learning includes both the input features such as the size of the house and also the output targets such as the price of the house the output targets are the right answers to the model we'll learn from to train the model you feed the trading set both the input features and the output targets to your learning algorithm then your supervised learning algorithm will produce some function we'll write this function as lowercase f where F stands for function historically this function used to be called a hypothesis but I'm just going to call it a function f in this clause and the job of f is to take a new input X and upwards an estimate or prediction which I'm going to call Y hat and it's written like the variable y with this little hat symbol on top in machine learning the convention is that y hat is the estimate or the prediction for y the function f is called the model X is called the input or the input feature and the output of the model is the prediction y hat the model's prediction is the estimated value of y when the symbol is just a letter Y then that refers to the Target which is the actual True Value in the training set in contrast y hat is an estimate it may or may not be the actual True Value well if you're helping your client to sell the house well the true price of the house is unknown until they sell it so your model f given the size or pressure price which is the estimated that is the prediction of what the true price will be now when we design a learning algorithm a key question is how are we going to represent the function f or in other words what is the math formula we're going to use to compute f for now let's stick with f being a straight line so your function can be written as F subscript W comma B of x equals I'm going to use W Times X plus b I'll Define w and B soon but for now just know that W and B are numbers and the values chosen for w and B will determine the prediction y hat based on the input feature X so this FWB of X means f is a function that takes X's input and depending on the values of w and b f will output some value of a prediction y hat as an alternative to writing this FW comma B of X I'll sometimes just write f of x without explicitly including W and B in the subscript it's just a simple notation but means exactly the same thing as FWB of x let's plot the trading set on the graph where the input feature X is on the horizontal axis and the output targets Y is on the vertical axis remember the album learns from this data and generates a best fit line like maybe this one here this straight line is the linear function f w b of x equals W Times X plus b or more simply we can drop W and B and just write f of x equals WX plus b here's what this function is doing is making predictions for the value of y using a straight line function of x so you may ask why are we choosing a linear function where linear function is just a fancy term for a straight line instead of some nonlinear function like a curve or a parabola well sometimes you want to fit more complex non-linear functions as well like a curve like this but since this linear function is relatively simple and easy to work with let's use a line as a foundation that will eventually help you to get to more complex models that are non-linear this particular model as a name is called linear regression more specifically this is linear regression with one variable with a phrase one variable means that there's a single input variable or feature X namely the size of the host another name for a linear model with one input variable is univariate linear regression where uni means one in Latin and where variate means variable so univ variance is just a fancy way of saying one variable in a later video you also see a variation of regression where you want to make a prediction based not just on the size of a hose but on a bunch of other things that you may know about the whole such as number of bedrooms and other features and by the way when you're done with this video there is another optional lab you don't need to write any code just review it run the code and see what it does that will show you how to define in Python a straight line function and the lab will let you choose the values of wmb to try to fit the training data you don't have to do the lab if you don't want to but I hope you play of it when you're done watching this video so that's linear regression in order for you to make this work one of the most important things you have to do is construct a cost function the idea of a cost function is one of the most universal and important ideas in machine learning and is used in both linear regression and in training many of the most advanced AI models in the world so let's go on to the next video and take a look at how you can construct a cost functionlet's look in this video at the process of how supervised Learning Works supervised learning algorithm will input the data set and then what exactly does it do and what does it output let's find out in this video recall that a training set in supervised learning includes both the input features such as the size of the house and also the output targets such as the price of the house the output targets are the right answers to the model we'll learn from to train the model you feed the trading set both the input features and the output targets to your learning algorithm then your supervised learning algorithm will produce some function we'll write this function as lowercase f where F stands for function historically this function used to be called a hypothesis but I'm just going to call it a function f in this clause and the job of f is to take a new input X and upwards an estimate or prediction which I'm going to call Y hat and it's written like the variable y with this little hat symbol on top in machine learning the convention is that y hat is the estimate or the prediction for y the function f is called the model X is called the input or the input feature and the output of the model is the prediction y hat the model's prediction is the estimated value of y when the symbol is just a letter Y then that refers to the Target which is the actual True Value in the training set in contrast y hat is an estimate it may or may not be the actual True Value well if you're helping your client to sell the house well the true price of the house is unknown until they sell it so your model f given the size or pressure price which is the estimated that is the prediction of what the true price will be now when we design a learning algorithm a key question is how are we going to represent the function f or in other words what is the math formula we're going to use to compute f for now let's stick with f being a straight line so your function can be written as F subscript W comma B of x equals I'm going to use W Times X plus b I'll Define w and B soon but for now just know that W and B are numbers and the values chosen for w and B will determine the prediction y hat based on the input feature X so this FWB of X means f is a function that takes X's input and depending on the values of w and b f will output some value of a prediction y hat as an alternative to writing this FW comma B of X I'll sometimes just write f of x without explicitly including W and B in the subscript it's just a simple notation but means exactly the same thing as FWB of x let's plot the trading set on the graph where the input feature X is on the horizontal axis and the output targets Y is on the vertical axis remember the album learns from this data and generates a best fit line like maybe this one here this straight line is the linear function f w b of x equals W Times X plus b or more simply we can drop W and B and just write f of x equals WX plus b here's what this function is doing is making predictions for the value of y using a straight line function of x so you may ask why are we choosing a linear function where linear function is just a fancy term for a straight line instead of some nonlinear function like a curve or a parabola well sometimes you want to fit more complex non-linear functions as well like a curve like this but since this linear function is relatively simple and easy to work with let's use a line as a foundation that will eventually help you to get to more complex models that are non-linear this particular model as a name is called linear regression more specifically this is linear regression with one variable with a phrase one variable means that there's a single input variable or feature X namely the size of the host another name for a linear model with one input variable is univariate linear regression where uni means one in Latin and where variate means variable so univ variance is just a fancy way of saying one variable in a later video you also see a variation of regression where you want to make a prediction based not just on the size of a hose but on a bunch of other things that you may know about the whole such as number of bedrooms and other features and by the way when you're done with this video there is another optional lab you don't need to write any code just review it run the code and see what it does that will show you how to define in Python a straight line function and the lab will let you choose the values of wmb to try to fit the training data you don't have to do the lab if you don't want to but I hope you play of it when you're done watching this video so that's linear regression in order for you to make this work one of the most important things you have to do is construct a cost function the idea of a cost function is one of the most universal and important ideas in machine learning and is used in both linear regression and in training many of the most advanced AI models in the world so let's go on to the next video and take a look at how you can construct a cost function\n"