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Explore the Linear Regression Using Python
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Course Content

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

Residuals

If we look at the plot that shows the dependence of flavanoids on the number of phenols, it will be obvious that the use of linear regression, in this case, was not entirely correct. Moreover, how do we interpret how good our prediction is?

Some points will lie on our constructed line, and some will lie away from it. We can measure the distance between a point and a line along the y-axis. This distance is called the residual or error. The remainder is the difference between the observed value of the target and the predicted value. The closer the residual is to 0, the better our model performs. Let's calculate the residuals and present them as a chart.


              
12345678

            
residuals = Y_test - y_test_predicted

# Visualize the data 
ax = plt.gca() 
ax.set_xlabel('total_phenols') 
ax.set_ylabel('residuals') 
plt.scatter(X_test, residuals) 
plt.show()
copy

Output:

Our residuals formed three almost straight lines. This distribution is a sign that the model is not working. Ideally, the remains should be arranged symmetrically and randomly around the horizontal axis. Still, if the residual graph shows some pattern (linear or non-linear), it means that our model is not the best.

Task

Try to find residuals to our previous challenge:

  1. [Line #29] Define the variable y_test_predicted as predicted data for X_test.
  2. [Line #30] Assign the difference between variables Y_test and y_test_predicted to the residuals.
  3. [Line #31] Print the variable residuals.

Task

Try to find residuals to our previous challenge:

  1. [Line #29] Define the variable y_test_predicted as predicted data for X_test.
  2. [Line #30] Assign the difference between variables Y_test and y_test_predicted to the residuals.
  3. [Line #31] Print the variable residuals.

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

Everything was clear?

Section 4. Chapter 1
toggle bottom row

Residuals

If we look at the plot that shows the dependence of flavanoids on the number of phenols, it will be obvious that the use of linear regression, in this case, was not entirely correct. Moreover, how do we interpret how good our prediction is?

Some points will lie on our constructed line, and some will lie away from it. We can measure the distance between a point and a line along the y-axis. This distance is called the residual or error. The remainder is the difference between the observed value of the target and the predicted value. The closer the residual is to 0, the better our model performs. Let's calculate the residuals and present them as a chart.


              
12345678

            
residuals = Y_test - y_test_predicted

# Visualize the data 
ax = plt.gca() 
ax.set_xlabel('total_phenols') 
ax.set_ylabel('residuals') 
plt.scatter(X_test, residuals) 
plt.show()
copy

Output:

Our residuals formed three almost straight lines. This distribution is a sign that the model is not working. Ideally, the remains should be arranged symmetrically and randomly around the horizontal axis. Still, if the residual graph shows some pattern (linear or non-linear), it means that our model is not the best.

Task

Try to find residuals to our previous challenge:

  1. [Line #29] Define the variable y_test_predicted as predicted data for X_test.
  2. [Line #30] Assign the difference between variables Y_test and y_test_predicted to the residuals.
  3. [Line #31] Print the variable residuals.

Task

Try to find residuals to our previous challenge:

  1. [Line #29] Define the variable y_test_predicted as predicted data for X_test.
  2. [Line #30] Assign the difference between variables Y_test and y_test_predicted to the residuals.
  3. [Line #31] Print the variable residuals.

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

Everything was clear?

Section 4. Chapter 1
toggle bottom row

Residuals

If we look at the plot that shows the dependence of flavanoids on the number of phenols, it will be obvious that the use of linear regression, in this case, was not entirely correct. Moreover, how do we interpret how good our prediction is?

Some points will lie on our constructed line, and some will lie away from it. We can measure the distance between a point and a line along the y-axis. This distance is called the residual or error. The remainder is the difference between the observed value of the target and the predicted value. The closer the residual is to 0, the better our model performs. Let's calculate the residuals and present them as a chart.


              
12345678

            
residuals = Y_test - y_test_predicted

# Visualize the data 
ax = plt.gca() 
ax.set_xlabel('total_phenols') 
ax.set_ylabel('residuals') 
plt.scatter(X_test, residuals) 
plt.show()
copy

Output:

Our residuals formed three almost straight lines. This distribution is a sign that the model is not working. Ideally, the remains should be arranged symmetrically and randomly around the horizontal axis. Still, if the residual graph shows some pattern (linear or non-linear), it means that our model is not the best.

Task

Try to find residuals to our previous challenge:

  1. [Line #29] Define the variable y_test_predicted as predicted data for X_test.
  2. [Line #30] Assign the difference between variables Y_test and y_test_predicted to the residuals.
  3. [Line #31] Print the variable residuals.

Task

Try to find residuals to our previous challenge:

  1. [Line #29] Define the variable y_test_predicted as predicted data for X_test.
  2. [Line #30] Assign the difference between variables Y_test and y_test_predicted to the residuals.
  3. [Line #31] Print the variable residuals.

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

Everything was clear?

If we look at the plot that shows the dependence of flavanoids on the number of phenols, it will be obvious that the use of linear regression, in this case, was not entirely correct. Moreover, how do we interpret how good our prediction is?

Some points will lie on our constructed line, and some will lie away from it. We can measure the distance between a point and a line along the y-axis. This distance is called the residual or error. The remainder is the difference between the observed value of the target and the predicted value. The closer the residual is to 0, the better our model performs. Let's calculate the residuals and present them as a chart.


              
12345678

            
residuals = Y_test - y_test_predicted

# Visualize the data 
ax = plt.gca() 
ax.set_xlabel('total_phenols') 
ax.set_ylabel('residuals') 
plt.scatter(X_test, residuals) 
plt.show()
copy

Output:

Our residuals formed three almost straight lines. This distribution is a sign that the model is not working. Ideally, the remains should be arranged symmetrically and randomly around the horizontal axis. Still, if the residual graph shows some pattern (linear or non-linear), it means that our model is not the best.

Task

Try to find residuals to our previous challenge:

  1. [Line #29] Define the variable y_test_predicted as predicted data for X_test.
  2. [Line #30] Assign the difference between variables Y_test and y_test_predicted to the residuals.
  3. [Line #31] Print the variable residuals.

Switch to desktop for real-world practiceContinue from where you are using one of the options below
Section 4. Chapter 1
Switch to desktop for real-world practiceContinue from where you are using one of the options below
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