@@ -46,7 +46,7 @@ Let us begin the tutorial with a classical problem called Linear Regression \[[1
...
@@ -46,7 +46,7 @@ Let us begin the tutorial with a classical problem called Linear Regression \[[1
The source code for this tutorial lives on [book/fit_a_line](https://github.com/PaddlePaddle/book/tree/develop/01.fit_a_line). For instructions on getting started with PaddlePaddle, see [PaddlePaddle installation guide](https://github.com/PaddlePaddle/book/blob/develop/README.md#running-the-book).
The source code for this tutorial lives on [book/fit_a_line](https://github.com/PaddlePaddle/book/tree/develop/01.fit_a_line). For instructions on getting started with PaddlePaddle, see [PaddlePaddle installation guide](https://github.com/PaddlePaddle/book/blob/develop/README.md#running-the-book).
## Problem Setup
## Problem Setup
Suppose we have a dataset of $n$ real estate properties. These real estate properties will be referred to as *homes* in this chapter for clarity.
Suppose we have a dataset of $n$ real estate properties. Each real estate property will be referred to as **homes** in this chapter for clarity.
Each home is associated with $d$ attributes. The attributes describe characteristics such the number of rooms in the home, the number of schools or hospitals in the neighborhood, and the traffic condition nearby.
Each home is associated with $d$ attributes. The attributes describe characteristics such the number of rooms in the home, the number of schools or hospitals in the neighborhood, and the traffic condition nearby.
where $\vec{\omega}$ and $b$ are the model parameters we want to estimate. Once they are learned, we will be able to predict the price of a home, given the attributes associated with it. We call this model **Linear Regression**. In other words, we want to regress a value against several values linearly. In practice, a linear model is often too simplistic to capture the real relationships between the variables. Yet, because Linear Regression is easy to train and analyze, it has been applied to a large number of real problems. As a result, it is an important topic in many classic Statistical Learning and Machine Learning textbooks \[[2,3,4](#References)\].
where $\vec{\omega}$ and $b$ are the model parameters we want to estimate. Once they are learned, we will be able to predict the price of a home, given the attributes associated with it. We call this model **Linear Regression**. In other words, we want to regress a value against several values linearly. In practice, a linear model is often too simplistic to capture the real relationships between the variables. Yet, because Linear Regression is easy to train and analyze, it has been applied to a large number of real problems. As a result, it is an important topic in many classic Statistical Learning and Machine Learning textbooks \[[2,3,4](#References)\].
## Results Demonstration
## Results Demonstration
We first show the result of our model. The dataset [UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing) is used to train a linear model to predict the home prices in Boston. The figure below shows the predictions the model makes for some home prices. The $X$-axis represents the median value of the prices of simlilar homes within a bin, while the $Y$-axis represents the home value our linear model predicts. The dotted line represents points where $X=Y$. When reading the diagram, the more precise the model predicts, the closer the point is to the dotted line.
We first show the result of our model. The dataset [UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing) is used to train a linear model to predict the home prices in Boston. The figure below shows the predictions the model makes for some home prices. The $X$-axis represents the median value of the prices of similar homes within a bin, while the $Y$-axis represents the home value our linear model predicts. The dotted line represents points where $X=Y$. When reading the diagram, the more precise the model predicts, the closer the point is to the dotted line.
