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影片连结

This episode expands on Implementing Simple Linear Regression In Python. We extend our simple linear regression model to include more variables.

本集扩展了在Python中实现简单线性回归的方法 。 我们扩展了简单的线性回归模型以包含更多变量。

You can view the code used in this Episode here: SampleCode

您可以在此处查看 此剧 集中使用的代码： SampleCode

Setting up your programming environment can be found in the first section of Ep 4.3.

可以在Ep 4.3的第一部分中找到设置您的编程环境的步骤 。

导入我们的数据 (Importing our Data)

The first step is to import our data into python.

第一步是将我们的数据导入python。

We can do that by going on the following link: Data

我们可以通过以下链接进行操作： 数据

Click on “code” and download ZIP.

单击“代码”并下载ZIP。

Locate WeatherDataM.csv and copy it into your local disc under a new file ProjectData

找到WeatherDataM.csv并将其复制到新文件ProjectData下的本地磁盘中

Note: Keep this medium post on a split screen so you can read and implement the code yourself.

注意：请将此帖子张贴在分屏上，以便您自己阅读和实现代码。

Now we are ready to implement our code into our Notebook:

现在我们准备将代码实现到笔记本中：

# Import Pandas Library, used for data manipulation
# Import matplotlib, used to plot our data
# Import nump for mathemtical operationsimport pandas as pd
import matplotlib.pyplot as plt
import numpy as np# Import our WeatherDataM and store it in the variable weather_data_mweather_data_m = pd.read_csv("D:\ProjectData\WeatherDataM.csv") 
# Display the data in the notebookweather_data_m

Here we can see a table with all the variables we will be working with.

在这里，我们可以看到一个包含所有要使用的变量的表。

绘制数据 (Plotting our Data)

Each of our inputs X (Temperature, Wind Speed and Pressure) must form a linear relationship with our output y (Humidity) in order for our multiple linear regression model to be accurate.

我们的每个输入X(温度，风速和压力)必须与我们的输出y(湿度)形成线性关系，以便我们的多元线性回归模型准确。

Let’s plot our variables to confirm this.

让我们绘制变量以确认这一点。

Here we follow common Data Science convention, naming our inputs X and output y.

在这里，我们遵循通用的数据科学约定 ，将输入X和输出y命名为。

# Set the features of our model, these are our potential inputsweather_features = ['Temperature (C)', 'Wind Speed (km/h)', 'Pressure (millibars)']# Set the variable X to be all our input columns: Temperature, Wind Speed and PressureX = weather_data_m[weather_features]# set y to be our output column: Humidityy = weather_data_m.Humidity# plt.subplot enables us to plot mutliple graphs
# we produce scatter plots for Humidity against each of our input variablesplt.subplot(2,2,1)
plt.scatter(X['Temperature (C)'],y)
plt.subplot(2,2,2)
plt.scatter(X['Wind Speed (km/h)'],y)
plt.subplot(2,2,3)
plt.scatter(X['Pressure (millibars)'],y)

• Humidity against Temperature forms a strong linear relationship ✓

  相对于温度的湿度形成很强的线性关系 ✓

• Humidity against Wind Speed forms a linear relationship ✓

  湿度与风速成线性关系 ✓

• Humidity against Pressure forms no linear relationship ✗

  相对于压力的湿度没有线性关系 ✗

Pressure can not be used in our model and is removed with the following code

压力无法在我们的模型中使用，并通过以下代码删除

X = X.drop("Pressure (millibars)", 1)

We specify the the column name went want to drop: Pressure (millibars)

我们指定要删除的列名称： 压力(毫巴)

1 represents our axis number: 1 is used for columns and 0 for rows.

1代表我们的轴号：1代表列，0代表行。

Because we are working with just two input variables we can produce a 3D scatter plot of Humidity against Temperature and Wind speed.

因为我们仅使用两个输入变量，所以可以生成湿度相对于温度和风速的3D散点图 。

With more variables this would not be possible, as this would require a 4D + plot which we as humans can not visualise.

有了更多的变量，这将是不可能的，因为这将需要我们人类无法看到的4D +图。

# Import library to produce a 3D plotfrom mpl_toolkits.mplot3d import Axes3Dfig = plt.figure()
ax = fig.add_subplot(111, projection='3d')x1 = X["Temperature (C)"]
x2 = X["Wind Speed (km/h)"]ax.scatter(x1, x2, y, c='r', marker='o')# Set axis labelsax.set_xlabel('Temperature (C)')
ax.set_ylabel('Wind Speed (km/h)')
ax.set_zlabel('Humidity')

实现多元线性回归 (Implementing Multiple Linear Regression)

In order to calculate our Model we need to import the LinearRegression model from Sci-kit learn library. This function enables us to calculate the parameters for our model (θ₀, θ₁ and θ₂) with one line of code.

为了计算我们的模型，我们需要从Sci-kit学习库中导入LinearRegression模型。 此功能使我们能够使用一行代码来计算模型的参数 ( θ₀，θ₁和θ2) 。

from sklearn.linear_model import LinearRegression# Define the variable mlr_model as our linear regression model
mlr_model = LinearRegression()
mlr_model.fit(X, y)

We can then display the values for θ₀, θ₁ and θ₂:

然后我们可以显示θ₀，θ和θ2的值：

θ₀ is the intercept

θ₀是截距

θ₁ and θ₂ are what we call co-efficients of the model as the come before our X variables.

θ₁和θ²是我们所谓的模型系数 ，即X变量之前的系数。

theta0 = mlr_model.intercept_
theta1, theta2 = mlr_model.coef_theta0, theta1, theta2

Giving our multiple linear regression model as:

给出我们的多元线性回归模型为：

ŷ = 1.14–0.031𝑥¹- 0.004𝑥²

ŷ= 1.14–0.031𝑥¹-0.004𝑥²

使用我们的回归模型进行预测 (Using our Regression Model to make predictions)

Now we have calculated our Model, it’s time to make predictions for Humidity given a Temperature and Wind speed value:

现在我们已经计算了模型，是时候根据温度和风速值对湿度进行预测了：

y_pred = mlr_model.predict([[15, 21]])
y_pred

So a temperature of 15 °C and Wind speed of 21 km/h expects to give us a Humidity of 0.587.

因此，温度为15°C，风速为21 km / h，预计湿度为0.587。

边注 (Side note)

We reshaped all of our inputs into 2D arrays by using double square brackets ( [[]] ) which is a much more efficient method.

我们使用双方括号([[]])将所有输入重塑为2D数组，这是一种更为有效的方法。

如果您有任何疑问，请将其留在下面，希望在下一集见。 (If you have any questions please leave them below and I hope to see you in the next episode.)