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

本集擴展了在Python中實現簡單線性回歸的方法 。 我們擴展了簡單的線性回歸模型以包含更多變量。

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

您可以在此處查看 此劇 集中使用的代碼： SampleCode

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

可以在Ep 4.3的第一部分中找到設置您的編程環境的步驟 。

導入我們的數據 (Importing our Data)

The first step is to import our data into python.

第一步是將我們的數據導入python。

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

我們可以通過以下鏈接進行操作： 數據

Click on “code” and download ZIP.

單擊“代碼”并下載ZIP。

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

找到WeatherDataM.csv并將其復制到新文件ProjectData下的本地磁盤中

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

注意：請將此帖子張貼在分屏上，以便您自己閱讀和實現代碼。

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

現在我們準備將代碼實現到筆記本中：

# 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.

在這里，我們可以看到一個包含所有要使用的變量的表。

繪制數據 (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.

我們的每個輸入X(溫度，風速和壓力)必須與我們的輸出y(濕度)形成線性關系，以便我們的多元線性回歸模型準確。

Let’s plot our variables to confirm this.

讓我們繪制變量以確認這一點。

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

在這里，我們遵循通用的數據科學約定 ，將輸入X和輸出y命名為。

# 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 ?

  相對于溫度的濕度形成很強的線性關系 ?

• Humidity against Wind Speed forms a linear relationship ?

  濕度與風速成線性關系 ?

• Humidity against Pressure forms no linear relationship ?

  相對于壓力的濕度沒有線性關系 ?

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

壓力無法在我們的模型中使用，并通過以下代碼刪除

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

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

我們指定要刪除的列名稱： 壓力(毫巴)

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

1代表我們的軸號：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.

因為我們僅使用兩個輸入變量，所以可以生成濕度相對于溫度和風速的3D散點圖 。

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

有了更多的變量，這將是不可能的，因為這將需要我們人類無法看到的4D +圖。

# 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')

實現多元線性回歸 (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 (θ?, θ? and θ?) with one line of code.

為了計算我們的模型，我們需要從Sci-kit學習庫中導入LinearRegression模型。 此功能使我們能夠使用一行代碼來計算模型的參數 ( θ?，θ?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 θ?, θ? and θ?:

然后我們可以顯示θ?，θ和θ2的值：

θ? is the intercept

θ?是截距

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

θ?和θ2是我們所謂的模型系數 ，即X變量之前的系數。

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

Giving our multiple linear regression model as:

給出我們的多元線性回歸模型為：

? = 1.14–0.031𝑥1- 0.004𝑥2

?= 1.14–0.031𝑥1-0.004𝑥2

使用我們的回歸模型進行預測 (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:

現在我們已經計算了模型，是時候根據溫度和風速值對濕度進行預測了：

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，溫度為15°C，風速為21 km / h，預計濕度為0.587。

邊注 (Side note)

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

我們使用雙方括號([[]])將所有輸入重塑為2D數組，這是一種更為有效的方法。

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