Зміст курсу

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

MSE and RMSE

How else can you get rid of the minus sign? We could square our differences, that is, we take our predictions, subtract the true values from them and square them, thereby obtaining the squared deviation. Now we can sum all the squared deviations and divide by their number of objects. This value shows how much our predictions deviate from the truth squared. It is called the mean square error or MSE. When the MSE goes to zero, in this case, all true values match our predictions perfectly.

We can calculate it:


              1
            
MSE = (residuals**2).mean()

Or just use the similar to the previous chapter method:


              12
            
from sklearn.metrics import mean_squared_error
print(mean_squared_error(Y_test, y_test_predicted))

But there is a small snag here. It is important to note that when calculating the error, the MSE units do not match the original units of the predicted target value. We predict the number of phenols squared, which is sometimes a bit difficult to use for estimation. You can get rid of this square quite simply by taking the square root of MSE. It calls the root mean squared error (RMSE). Thus, it may be common to use the MSE loss to train a regression prediction model and use the RMSE to evaluate and report its performance.


              1
            
RMSE = math.sqrt((residuals**2).mean())

The formula:

Ideally, all the metrics that we considered (MSE, RMSE, MAE) tend to zero when all true values are very close to predictions. But these metrics do not have a right border above which we consider metrics to be useless. Is our prediction good if MSE=13 or not?

Let’s look at an example:

In both cases MSE = 13. For the first table, this is a very large value. We are more than twice wrong in our forecasts. At the same time, for the second sample, this is a fairly good estimate.

Завдання

Let’s continue calculating metrics for our dataset. Find MSE and RMSE:

[Line #32] Import mean_squared_error from the library scikit.metrics for calculating metrics.
[Line #33] Use the method mean_squared_error() to find MSE and assign it to the variable MSE.
[Line #34] Print the variable MSE.
[Line #36] Import the library math.
[Line #37] Find RMSE, assign it to the variable RMSE and print it.
[Line #38] Print the variable MSE.

Завдання

Let’s continue calculating metrics for our dataset. Find MSE and RMSE:

[Line #32] Import mean_squared_error from the library scikit.metrics for calculating metrics.
[Line #33] Use the method mean_squared_error() to find MSE and assign it to the variable MSE.
[Line #34] Print the variable MSE.
[Line #36] Import the library math.
[Line #37] Find RMSE, assign it to the variable RMSE and print it.
[Line #38] Print the variable MSE.

Перейдіть на комп'ютер для реальної практикиПродовжуйте з того місця, де ви зупинились, використовуючи один з наведених нижче варіантів

Все було зрозуміло?

Секція 4. Розділ 3

MSE and RMSE

We can calculate it:


              1
            
MSE = (residuals**2).mean()

Or just use the similar to the previous chapter method:


              12
            
from sklearn.metrics import mean_squared_error
print(mean_squared_error(Y_test, y_test_predicted))


              1
            
RMSE = math.sqrt((residuals**2).mean())

The formula:

Let’s look at an example:

In both cases MSE = 13. For the first table, this is a very large value. We are more than twice wrong in our forecasts. At the same time, for the second sample, this is a fairly good estimate.

Завдання

Let’s continue calculating metrics for our dataset. Find MSE and RMSE:

[Line #32] Import mean_squared_error from the library scikit.metrics for calculating metrics.
[Line #33] Use the method mean_squared_error() to find MSE and assign it to the variable MSE.
[Line #34] Print the variable MSE.
[Line #36] Import the library math.
[Line #37] Find RMSE, assign it to the variable RMSE and print it.
[Line #38] Print the variable MSE.

Завдання

Let’s continue calculating metrics for our dataset. Find MSE and RMSE:

[Line #32] Import mean_squared_error from the library scikit.metrics for calculating metrics.
[Line #33] Use the method mean_squared_error() to find MSE and assign it to the variable MSE.
[Line #34] Print the variable MSE.
[Line #36] Import the library math.
[Line #37] Find RMSE, assign it to the variable RMSE and print it.
[Line #38] Print the variable MSE.

Все було зрозуміло?

Секція 4. Розділ 3

MSE and RMSE

We can calculate it:


              1
            
MSE = (residuals**2).mean()

Or just use the similar to the previous chapter method:


              12
            
from sklearn.metrics import mean_squared_error
print(mean_squared_error(Y_test, y_test_predicted))


              1
            
RMSE = math.sqrt((residuals**2).mean())

The formula:

Let’s look at an example:

In both cases MSE = 13. For the first table, this is a very large value. We are more than twice wrong in our forecasts. At the same time, for the second sample, this is a fairly good estimate.

Завдання

Let’s continue calculating metrics for our dataset. Find MSE and RMSE:

[Line #32] Import mean_squared_error from the library scikit.metrics for calculating metrics.
[Line #33] Use the method mean_squared_error() to find MSE and assign it to the variable MSE.
[Line #34] Print the variable MSE.
[Line #36] Import the library math.
[Line #37] Find RMSE, assign it to the variable RMSE and print it.
[Line #38] Print the variable MSE.

Завдання

Let’s continue calculating metrics for our dataset. Find MSE and RMSE:

[Line #32] Import mean_squared_error from the library scikit.metrics for calculating metrics.
[Line #33] Use the method mean_squared_error() to find MSE and assign it to the variable MSE.
[Line #34] Print the variable MSE.
[Line #36] Import the library math.
[Line #37] Find RMSE, assign it to the variable RMSE and print it.
[Line #38] Print the variable MSE.

Все було зрозуміло?

We can calculate it:


              1
            
MSE = (residuals**2).mean()

Or just use the similar to the previous chapter method:


              12
            
from sklearn.metrics import mean_squared_error
print(mean_squared_error(Y_test, y_test_predicted))


              1
            
RMSE = math.sqrt((residuals**2).mean())

The formula:

Let’s look at an example:

In both cases MSE = 13. For the first table, this is a very large value. We are more than twice wrong in our forecasts. At the same time, for the second sample, this is a fairly good estimate.

Завдання

Let’s continue calculating metrics for our dataset. Find MSE and RMSE:

[Line #32] Import mean_squared_error from the library scikit.metrics for calculating metrics.
[Line #33] Use the method mean_squared_error() to find MSE and assign it to the variable MSE.
[Line #34] Print the variable MSE.
[Line #36] Import the library math.
[Line #37] Find RMSE, assign it to the variable RMSE and print it.
[Line #38] Print the variable MSE.

Секція 4. Розділ 3