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Explore the Linear Regression Using Python
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Explore the Linear Regression Using Python

Explore the Linear Regression Using Python

1. What is the Linear Regression?
Basic Understanding of the Linear RegressionHow Mathematically Does It Work?Build the Linear RegressionWorking with DatasetUseful Functions for Researching and Visualizing Dataset
2. Correlation
What Is Correlation? How To Find Pearson CoefficientCorrelation MatrixCalculating the Pearson Coefficient Using NumPy and PandasChallenge
3. Building and Training Model
Train-split evaluationFittingPredictionChallenge
4. Metrics to Evaluate the Model
ResidualsMean Absolute Error (MAE)MSE and RMSER-squaredNot Always the Linear Regression?
5. Multivariate Linear Regression
Building the Regression Model Based on Several VariablesTry to EvaluateChallenge

Build the Linear Regression

Here we will learn how to find the intercept and slope for our dataset. For this example, we will use a scientific computation library SciPy, to import stats. Using the method stats.lingress() we can get the most important linear regression parameters for the given dataset (x and y arrays). Pay attention to the first two values (slope and intercept), and other parameters will be analyzed in the following chapters. These two numbers define a straight line. The squares of the residuals of the dataset to points are minimal.


              
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# Import the libraries
import matplotlib.pyplot as plt
from scipy import stats 

# Initialize the data
x = [8, 10, 9.2, 8.4, 9.1, 9.6, 8, 10.2, 9.3, 9.4, 9.9, 8.7] 
y = [3.6, 5.4, 4.8, 3.9, 4.2, 5.2, 3.5, 5.5, 4.4, 4.7, 5.1, 3.7] 

# Get the linear regression parameters 
slope, intercept, r, p, std_err = stats.linregress(x, y) 

# The line shows the dependence of the height of cats on their weight 
def on_weight(x): 
   return slope * x + intercept 

# Define the line 
height_on_weight = list(map(on_weight, x)) 

# Add titles to axes 
ax = plt.gca()
ax.set_xlabel('Cat height (inches)')
ax.set_ylabel('Cat weight (kg)') 

# Visualize our data 
plt.scatter(x, y) 
plt.plot(x, height_on_weight) 
plt.show()
copy

The output of the code execution is identical to your first task. However, now we don't work with predefined values but with a method that returns them to us knowing the dataset.

Tarea

Getting bigger, cats start to eat more. Let's see how these values are dependent. We have a dataset in which the number of calories the cat eats every day at a certain weight is indicated (array x - weight, y - number of calories).

  1. [Lines #2-3] Import the matplotlib.pyplotand also the library SciPy.
  2. [Lines #10-17] Find the slope and the intercept using the method stats.lingress(). Add the missing parameter to the function on_weight and assign the variable feed_on_weight.
  3. [Lines #26-27] Build line on your plot.

Tarea

Getting bigger, cats start to eat more. Let's see how these values are dependent. We have a dataset in which the number of calories the cat eats every day at a certain weight is indicated (array x - weight, y - number of calories).

  1. [Lines #2-3] Import the matplotlib.pyplotand also the library SciPy.
  2. [Lines #10-17] Find the slope and the intercept using the method stats.lingress(). Add the missing parameter to the function on_weight and assign the variable feed_on_weight.
  3. [Lines #26-27] Build line on your plot.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

Sección 1. Capítulo 3
toggle bottom row

Build the Linear Regression

Here we will learn how to find the intercept and slope for our dataset. For this example, we will use a scientific computation library SciPy, to import stats. Using the method stats.lingress() we can get the most important linear regression parameters for the given dataset (x and y arrays). Pay attention to the first two values (slope and intercept), and other parameters will be analyzed in the following chapters. These two numbers define a straight line. The squares of the residuals of the dataset to points are minimal.


              
123456789101112131415161718192021222324252627

            
# Import the libraries
import matplotlib.pyplot as plt
from scipy import stats 

# Initialize the data
x = [8, 10, 9.2, 8.4, 9.1, 9.6, 8, 10.2, 9.3, 9.4, 9.9, 8.7] 
y = [3.6, 5.4, 4.8, 3.9, 4.2, 5.2, 3.5, 5.5, 4.4, 4.7, 5.1, 3.7] 

# Get the linear regression parameters 
slope, intercept, r, p, std_err = stats.linregress(x, y) 

# The line shows the dependence of the height of cats on their weight 
def on_weight(x): 
   return slope * x + intercept 

# Define the line 
height_on_weight = list(map(on_weight, x)) 

# Add titles to axes 
ax = plt.gca()
ax.set_xlabel('Cat height (inches)')
ax.set_ylabel('Cat weight (kg)') 

# Visualize our data 
plt.scatter(x, y) 
plt.plot(x, height_on_weight) 
plt.show()
copy

The output of the code execution is identical to your first task. However, now we don't work with predefined values but with a method that returns them to us knowing the dataset.

Tarea

Getting bigger, cats start to eat more. Let's see how these values are dependent. We have a dataset in which the number of calories the cat eats every day at a certain weight is indicated (array x - weight, y - number of calories).

  1. [Lines #2-3] Import the matplotlib.pyplotand also the library SciPy.
  2. [Lines #10-17] Find the slope and the intercept using the method stats.lingress(). Add the missing parameter to the function on_weight and assign the variable feed_on_weight.
  3. [Lines #26-27] Build line on your plot.

Tarea

Getting bigger, cats start to eat more. Let's see how these values are dependent. We have a dataset in which the number of calories the cat eats every day at a certain weight is indicated (array x - weight, y - number of calories).

  1. [Lines #2-3] Import the matplotlib.pyplotand also the library SciPy.
  2. [Lines #10-17] Find the slope and the intercept using the method stats.lingress(). Add the missing parameter to the function on_weight and assign the variable feed_on_weight.
  3. [Lines #26-27] Build line on your plot.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

Sección 1. Capítulo 3
toggle bottom row

Build the Linear Regression

Here we will learn how to find the intercept and slope for our dataset. For this example, we will use a scientific computation library SciPy, to import stats. Using the method stats.lingress() we can get the most important linear regression parameters for the given dataset (x and y arrays). Pay attention to the first two values (slope and intercept), and other parameters will be analyzed in the following chapters. These two numbers define a straight line. The squares of the residuals of the dataset to points are minimal.


              
123456789101112131415161718192021222324252627

            
# Import the libraries
import matplotlib.pyplot as plt
from scipy import stats 

# Initialize the data
x = [8, 10, 9.2, 8.4, 9.1, 9.6, 8, 10.2, 9.3, 9.4, 9.9, 8.7] 
y = [3.6, 5.4, 4.8, 3.9, 4.2, 5.2, 3.5, 5.5, 4.4, 4.7, 5.1, 3.7] 

# Get the linear regression parameters 
slope, intercept, r, p, std_err = stats.linregress(x, y) 

# The line shows the dependence of the height of cats on their weight 
def on_weight(x): 
   return slope * x + intercept 

# Define the line 
height_on_weight = list(map(on_weight, x)) 

# Add titles to axes 
ax = plt.gca()
ax.set_xlabel('Cat height (inches)')
ax.set_ylabel('Cat weight (kg)') 

# Visualize our data 
plt.scatter(x, y) 
plt.plot(x, height_on_weight) 
plt.show()
copy

The output of the code execution is identical to your first task. However, now we don't work with predefined values but with a method that returns them to us knowing the dataset.

Tarea

Getting bigger, cats start to eat more. Let's see how these values are dependent. We have a dataset in which the number of calories the cat eats every day at a certain weight is indicated (array x - weight, y - number of calories).

  1. [Lines #2-3] Import the matplotlib.pyplotand also the library SciPy.
  2. [Lines #10-17] Find the slope and the intercept using the method stats.lingress(). Add the missing parameter to the function on_weight and assign the variable feed_on_weight.
  3. [Lines #26-27] Build line on your plot.

Tarea

Getting bigger, cats start to eat more. Let's see how these values are dependent. We have a dataset in which the number of calories the cat eats every day at a certain weight is indicated (array x - weight, y - number of calories).

  1. [Lines #2-3] Import the matplotlib.pyplotand also the library SciPy.
  2. [Lines #10-17] Find the slope and the intercept using the method stats.lingress(). Add the missing parameter to the function on_weight and assign the variable feed_on_weight.
  3. [Lines #26-27] Build line on your plot.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

Here we will learn how to find the intercept and slope for our dataset. For this example, we will use a scientific computation library SciPy, to import stats. Using the method stats.lingress() we can get the most important linear regression parameters for the given dataset (x and y arrays). Pay attention to the first two values (slope and intercept), and other parameters will be analyzed in the following chapters. These two numbers define a straight line. The squares of the residuals of the dataset to points are minimal.


              
123456789101112131415161718192021222324252627

            
# Import the libraries
import matplotlib.pyplot as plt
from scipy import stats 

# Initialize the data
x = [8, 10, 9.2, 8.4, 9.1, 9.6, 8, 10.2, 9.3, 9.4, 9.9, 8.7] 
y = [3.6, 5.4, 4.8, 3.9, 4.2, 5.2, 3.5, 5.5, 4.4, 4.7, 5.1, 3.7] 

# Get the linear regression parameters 
slope, intercept, r, p, std_err = stats.linregress(x, y) 

# The line shows the dependence of the height of cats on their weight 
def on_weight(x): 
   return slope * x + intercept 

# Define the line 
height_on_weight = list(map(on_weight, x)) 

# Add titles to axes 
ax = plt.gca()
ax.set_xlabel('Cat height (inches)')
ax.set_ylabel('Cat weight (kg)') 

# Visualize our data 
plt.scatter(x, y) 
plt.plot(x, height_on_weight) 
plt.show()
copy

The output of the code execution is identical to your first task. However, now we don't work with predefined values but with a method that returns them to us knowing the dataset.

Tarea

Getting bigger, cats start to eat more. Let's see how these values are dependent. We have a dataset in which the number of calories the cat eats every day at a certain weight is indicated (array x - weight, y - number of calories).

  1. [Lines #2-3] Import the matplotlib.pyplotand also the library SciPy.
  2. [Lines #10-17] Find the slope and the intercept using the method stats.lingress(). Add the missing parameter to the function on_weight and assign the variable feed_on_weight.
  3. [Lines #26-27] Build line on your plot.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones
Sección 1. Capítulo 3
Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones
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