chapter1 book check.

01.fit_a_line/README.md

 # Linear Regression
-Let us begin the tutorial with a classical problem called Linear Regression \[[1](#References)\]. In this chapter, we will train a model from a realistic dataset to predict home prices. Some important concepts in Machine Learning will be covered through this example.
+Let us begin the tutorial with a classical problem called Linear Regression \[[1](#references)\]. In this chapter, we will train a model from a realistic dataset to predict home prices. Some important concepts in Machine Learning will be covered through this example.
 
 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).
 
@@ -12,7 +12,7 @@ In our problem setup, the attribute $x_{i,j}$ denotes the $j$th characteristic o
 
 $$y_i = \omega_1x_{i,1} + \omega_2x_{i,2} + \ldots + \omega_dx_{i,d} + b,  i=1,\ldots,n$$
 
-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
 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 closer the point is to the dotted line, better the model's prediction.
@@ -135,10 +135,10 @@ y = paddle.layer.data(name='y', type=paddle.data_type.dense_vector(1))
 cost = paddle.layer.square_error_cost(input=y_predict, label=y)
 ```
 
-### Save Topology
+### Save The Model Topology
 
 ```python
-# Save the inference topology to protobuf.
+# Save the inference topology to protobuf and write to a file.
 inference_topology = paddle.topology.Topology(layers=y_predict)
 with open("inference_topology.pkl", 'wb') as f:
     inference_topology.serialize_for_inference(f)

01.fit_a_line/index.html

@@ -41,7 +41,7 @@
 <!-- This block will be replaced by each markdown file content. Please do not change lines below.-->
 <div id="markdown" style='display:none'>
 # Linear Regression
-Let us begin the tutorial with a classical problem called Linear Regression \[[1](#References)\]. In this chapter, we will train a model from a realistic dataset to predict home prices. Some important concepts in Machine Learning will be covered through this example.
+Let us begin the tutorial with a classical problem called Linear Regression \[[1](#references)\]. In this chapter, we will train a model from a realistic dataset to predict home prices. Some important concepts in Machine Learning will be covered through this example.
 
 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).
 
@@ -54,7 +54,7 @@ In our problem setup, the attribute $x_{i,j}$ denotes the $j$th characteristic o
 
 $$y_i = \omega_1x_{i,1} + \omega_2x_{i,2} + \ldots + \omega_dx_{i,d} + b,  i=1,\ldots,n$$
 
-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
 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 closer the point is to the dotted line, better the model's prediction.
@@ -177,10 +177,10 @@ y = paddle.layer.data(name='y', type=paddle.data_type.dense_vector(1))
 cost = paddle.layer.square_error_cost(input=y_predict, label=y)
 ```
 
-### Save Topology
+### Save The Model Topology
 
 ```python
-# Save the inference topology to protobuf.
+# Save the inference topology to protobuf and write to a file.
 inference_topology = paddle.topology.Topology(layers=y_predict)
 with open("inference_topology.pkl", 'wb') as f:
     inference_topology.serialize_for_inference(f)