Course Content

Explore the Linear Regression Using Python

1. What is the Linear Regression?

Basic Understanding of the Linear Regression How Mathematically Does It Work?Build the Linear Regression Working with Dataset Useful Functions for Researching and Visualizing Dataset

2. Correlation

What Is Correlation? How To Find Pearson Coefficient Correlation Matrix Calculating the Pearson Coefficient Using NumPy and Pandas Challenge

3. Building and Training Model

Train-split evaluation Fitting Prediction Challenge

4. Metrics to Evaluate the Model

Residuals Mean Absolute Error (MAE)MSE and RMSE R-squared Not Always the Linear Regression?

5. Multivariate Linear Regression

Building the Regression Model Based on Several Variables Try to Evaluate Challenge

Calculating the Pearson Coefficient Using NumPy and Pandas

Let's look at how we can calculate the correlation coefficient if our data's type is np.array. The library has many statistics routines which simplify the calculations. We will use the method np.corrcoef(). It works with 2 arrays of the same length of our data:


              123456789
            
# Import the libraries
import numpy as np

# Define np.arrays
x = np.array([1, 2, 3, 5, 7, 8, 10, 11, 13, 15])
y = np.array([2, 4, 7, 8, 10, 15, 20, 21, 23, 30])

# Find correlation
r = np.corrcoef(x, y)

This function returns the correlation matrix (2-dimensional array) of correlation coefficients. Here is a more convenient version of the array:

The upper right value corresponds to the correlation coefficient for y and x, while the lower-left value is the correlation coefficient for x and y. These values we will always need. The other ones are the correlation coefficients between x and x, y and y. They are always equal to one.

If you want just the Pearson coefficient between x and y use this:


              1
            
print(np.corrcoef(x, y)[0,1])

Pandas correlation calculations also has a function to calculate the correlation coefficient for two of the same length Series objects. You can use .corr() method:


              12345678910
            
# Import the libraries
import pandas as pd

# Define series
x = pd.Series([1, 2, 3, 5, 7, 8, 10, 11, 13, 15])
y = pd.Series([2, 4, 7, 8, 10, 15, 20, 21, 23, 30])

# Print correlation coeffitients
print(x.corr(y))
print(y.corr(x))

Task

You have the initial dataset of Abyssinian cats' weight and height (x and y arrays, respectively). Find the correlation coefficient between x and y using all functions we discussed in this chapter.

[Lines #2-3] Import the pandas, numpy libraries.
[Lines #10-11] Change the type of arrays to np.arrays, find the correlation coefficient between x and y.
[Line #12] Print the correlation coefficient you have found in a such way.
[Lines #15-16] Change the type of arrays to Pandas Series , find the correlation coefficient between x and y.
[Line #17] Print the correlation coefficient you have found in a such way.

Task

[Lines #2-3] Import the pandas, numpy libraries.
[Lines #10-11] Change the type of arrays to np.arrays, find the correlation coefficient between x and y.
[Line #12] Print the correlation coefficient you have found in a such way.
[Lines #15-16] Change the type of arrays to Pandas Series , find the correlation coefficient between x and y.
[Line #17] Print the correlation coefficient you have found in a such way.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Section 2. Chapter 3

Calculating the Pearson Coefficient Using NumPy and Pandas


              123456789
            
# Import the libraries
import numpy as np

# Define np.arrays
x = np.array([1, 2, 3, 5, 7, 8, 10, 11, 13, 15])
y = np.array([2, 4, 7, 8, 10, 15, 20, 21, 23, 30])

# Find correlation
r = np.corrcoef(x, y)

This function returns the correlation matrix (2-dimensional array) of correlation coefficients. Here is a more convenient version of the array:

If you want just the Pearson coefficient between x and y use this:


              1
            
print(np.corrcoef(x, y)[0,1])

Pandas correlation calculations also has a function to calculate the correlation coefficient for two of the same length Series objects. You can use .corr() method:


              12345678910
            
# Import the libraries
import pandas as pd

# Define series
x = pd.Series([1, 2, 3, 5, 7, 8, 10, 11, 13, 15])
y = pd.Series([2, 4, 7, 8, 10, 15, 20, 21, 23, 30])

# Print correlation coeffitients
print(x.corr(y))
print(y.corr(x))

Task

[Lines #2-3] Import the pandas, numpy libraries.
[Lines #10-11] Change the type of arrays to np.arrays, find the correlation coefficient between x and y.
[Line #12] Print the correlation coefficient you have found in a such way.
[Lines #15-16] Change the type of arrays to Pandas Series , find the correlation coefficient between x and y.
[Line #17] Print the correlation coefficient you have found in a such way.

Task

[Lines #2-3] Import the pandas, numpy libraries.
[Lines #10-11] Change the type of arrays to np.arrays, find the correlation coefficient between x and y.
[Line #12] Print the correlation coefficient you have found in a such way.
[Lines #15-16] Change the type of arrays to Pandas Series , find the correlation coefficient between x and y.
[Line #17] Print the correlation coefficient you have found in a such way.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Section 2. Chapter 3

Calculating the Pearson Coefficient Using NumPy and Pandas


              123456789
            
# Import the libraries
import numpy as np

# Define np.arrays
x = np.array([1, 2, 3, 5, 7, 8, 10, 11, 13, 15])
y = np.array([2, 4, 7, 8, 10, 15, 20, 21, 23, 30])

# Find correlation
r = np.corrcoef(x, y)

This function returns the correlation matrix (2-dimensional array) of correlation coefficients. Here is a more convenient version of the array:

If you want just the Pearson coefficient between x and y use this:


              1
            
print(np.corrcoef(x, y)[0,1])

Pandas correlation calculations also has a function to calculate the correlation coefficient for two of the same length Series objects. You can use .corr() method:


              12345678910
            
# Import the libraries
import pandas as pd

# Define series
x = pd.Series([1, 2, 3, 5, 7, 8, 10, 11, 13, 15])
y = pd.Series([2, 4, 7, 8, 10, 15, 20, 21, 23, 30])

# Print correlation coeffitients
print(x.corr(y))
print(y.corr(x))

Task

[Lines #2-3] Import the pandas, numpy libraries.
[Lines #10-11] Change the type of arrays to np.arrays, find the correlation coefficient between x and y.
[Line #12] Print the correlation coefficient you have found in a such way.
[Lines #15-16] Change the type of arrays to Pandas Series , find the correlation coefficient between x and y.
[Line #17] Print the correlation coefficient you have found in a such way.

Task

[Lines #2-3] Import the pandas, numpy libraries.
[Lines #10-11] Change the type of arrays to np.arrays, find the correlation coefficient between x and y.
[Line #12] Print the correlation coefficient you have found in a such way.
[Lines #15-16] Change the type of arrays to Pandas Series , find the correlation coefficient between x and y.
[Line #17] Print the correlation coefficient you have found in a such way.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?


              123456789
            
# Import the libraries
import numpy as np

# Define np.arrays
x = np.array([1, 2, 3, 5, 7, 8, 10, 11, 13, 15])
y = np.array([2, 4, 7, 8, 10, 15, 20, 21, 23, 30])

# Find correlation
r = np.corrcoef(x, y)

This function returns the correlation matrix (2-dimensional array) of correlation coefficients. Here is a more convenient version of the array:

If you want just the Pearson coefficient between x and y use this:


              1
            
print(np.corrcoef(x, y)[0,1])

Pandas correlation calculations also has a function to calculate the correlation coefficient for two of the same length Series objects. You can use .corr() method:


              12345678910
            
# Import the libraries
import pandas as pd

# Define series
x = pd.Series([1, 2, 3, 5, 7, 8, 10, 11, 13, 15])
y = pd.Series([2, 4, 7, 8, 10, 15, 20, 21, 23, 30])

# Print correlation coeffitients
print(x.corr(y))
print(y.corr(x))

Task

[Lines #2-3] Import the pandas, numpy libraries.
[Lines #10-11] Change the type of arrays to np.arrays, find the correlation coefficient between x and y.
[Line #12] Print the correlation coefficient you have found in a such way.
[Lines #15-16] Change the type of arrays to Pandas Series , find the correlation coefficient between x and y.
[Line #17] Print the correlation coefficient you have found in a such way.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Section 2. Chapter 3

Switch to desktop for real-world practiceContinue from where you are using one of the options below