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

Building the Regression Model Based on Several Variables

Often we will need to make predictions based not on one but on several characteristics at once. For example, predict the length of a cat's tail knowing its weight and height. In such a case our equation looks like this:

tail_length = a + b * cat_weight + c * cat_height

Here we need to find we have to find already three unknown variables (the intercept a, coefficients b and c). The more features we have from which we make our forecast, the more unknown variables. In this case, we will fit a plane instead of a line.

So multivariant regression is the way to predict a value based on two or more variables. Let’s indicate the number of flavanoids based on the number of total phenols and nonflavanoid phenols. Dealing with these two characteristics we will use methods from the previous section to find the best model and get missing parameters:


              12345678910
            
# Preparing data
X2 = data[['total_phenols','nonflavanoid_phenols']]
Y = data['flavanoids']

# Train and test model
X2_train, X2_test, Y_train, Y_test = train_test_split(X2, Y, test_size = 0.3, random_state = 1)
model2 = LinearRegression()
model2.fit(X2_train, Y_train)
print(model2.intercept_)
print(model2.coef_)

We use in code the sane random_state parameter to get the same split.

The method of obtaining forecasts is identical to what we considered in the previous chapter for one characteristic:


              1
            
y_test_predicted2 = model2.predict(X2_test)

This code will return predicted values using the trained model:

flavanoids = 2.1 - 0.74 * total_phenols + 1.46 * nonflavanoid_phenols

Task

Let’s indicate the number of total phenols based on the number of flavanoids and nonflavanoid phenols.

[Line #17] Set total_phenols as our target.
[Line #24] Split the data 70-30 (70% of the data is for training and 30% is for testing) and insert 1 as a random parameter.
[Line #25] Initialize linear regression model.
[Line #26] Fit the model using your tain data.
[Lines #29-30] Print model’s parameters (model2.intercept_ and model2.coef_) using the function print() twice.

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

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Section 5. Chapter 1

Building the Regression Model Based on Several Variables

tail_length = a + b * cat_weight + c * cat_height


              12345678910
            
# Preparing data
X2 = data[['total_phenols','nonflavanoid_phenols']]
Y = data['flavanoids']

# Train and test model
X2_train, X2_test, Y_train, Y_test = train_test_split(X2, Y, test_size = 0.3, random_state = 1)
model2 = LinearRegression()
model2.fit(X2_train, Y_train)
print(model2.intercept_)
print(model2.coef_)

We use in code the sane random_state parameter to get the same split.

The method of obtaining forecasts is identical to what we considered in the previous chapter for one characteristic:


              1
            
y_test_predicted2 = model2.predict(X2_test)

This code will return predicted values using the trained model:

Task

Let’s indicate the number of total phenols based on the number of flavanoids and nonflavanoid phenols.

[Line #17] Set total_phenols as our target.
[Line #24] Split the data 70-30 (70% of the data is for training and 30% is for testing) and insert 1 as a random parameter.
[Line #25] Initialize linear regression model.
[Line #26] Fit the model using your tain data.
[Lines #29-30] Print model’s parameters (model2.intercept_ and model2.coef_) using the function print() twice.

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

Everything was clear?

Thanks for your feedback!

Section 5. Chapter 1

Building the Regression Model Based on Several Variables

tail_length = a + b * cat_weight + c * cat_height


              12345678910
            
# Preparing data
X2 = data[['total_phenols','nonflavanoid_phenols']]
Y = data['flavanoids']

# Train and test model
X2_train, X2_test, Y_train, Y_test = train_test_split(X2, Y, test_size = 0.3, random_state = 1)
model2 = LinearRegression()
model2.fit(X2_train, Y_train)
print(model2.intercept_)
print(model2.coef_)

We use in code the sane random_state parameter to get the same split.

The method of obtaining forecasts is identical to what we considered in the previous chapter for one characteristic:


              1
            
y_test_predicted2 = model2.predict(X2_test)

This code will return predicted values using the trained model:

Task

Let’s indicate the number of total phenols based on the number of flavanoids and nonflavanoid phenols.

[Line #17] Set total_phenols as our target.
[Line #24] Split the data 70-30 (70% of the data is for training and 30% is for testing) and insert 1 as a random parameter.
[Line #25] Initialize linear regression model.
[Line #26] Fit the model using your tain data.
[Lines #29-30] Print model’s parameters (model2.intercept_ and model2.coef_) using the function print() twice.

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

Everything was clear?

Thanks for your feedback!

tail_length = a + b * cat_weight + c * cat_height


              12345678910
            
# Preparing data
X2 = data[['total_phenols','nonflavanoid_phenols']]
Y = data['flavanoids']

# Train and test model
X2_train, X2_test, Y_train, Y_test = train_test_split(X2, Y, test_size = 0.3, random_state = 1)
model2 = LinearRegression()
model2.fit(X2_train, Y_train)
print(model2.intercept_)
print(model2.coef_)

We use in code the sane random_state parameter to get the same split.

The method of obtaining forecasts is identical to what we considered in the previous chapter for one characteristic:


              1
            
y_test_predicted2 = model2.predict(X2_test)

This code will return predicted values using the trained model:

Task

Let’s indicate the number of total phenols based on the number of flavanoids and nonflavanoid phenols.

[Line #17] Set total_phenols as our target.
[Line #24] Split the data 70-30 (70% of the data is for training and 30% is for testing) and insert 1 as a random parameter.
[Line #25] Initialize linear regression model.
[Line #26] Fit the model using your tain data.
[Lines #29-30] Print model’s parameters (model2.intercept_ and model2.coef_) using the function print() twice.

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

Section 5. Chapter 1

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