Three Regression Models for Data Science: Linear Regression, Lasso Regression, and Ridge Regression (2024)

Brandon Wohlwend

21 min read

Jul 14, 2023

Basic Concept of Regression Models in Data Science

Regression models form the bedrock of predictive analytics, and their usage is ubiquitous in data science. They offer a way to understand and predict the relationship between two or more variables. At a high level, regression models can be seen as a function that maps a set of input features (also known as independent variables) to a continuous output (the dependent variable).

In the simplest of terms, regression models aim to construct a best-fit line or curve, known as a regression line, through data points in a manner that minimizes the overall distance between the data points and the line itself. This ‘distance’ is often referred to as an error or residual, and the objective of any regression model is to minimize the sum of these residuals, thereby maximizing the predictive accuracy of the model.

In the context of data science, regression models are used to forecast outcomes, test hypotheses, or determine relationships among variables. They are applicable to a broad range of scenarios, from predicting house prices based on features like size, location, and age, to estimating a person’s risk for a health condition given their age, lifestyle, and genetic makeup.

Although there are various types of regression models, each with unique properties and use cases, the fundamental concept remains the same: utilizing known data to predict unknown outcomes. As we explore Linear, Lasso, and Ridge regression in this article, we will see how they all follow this basic principle while offering unique strategies for handling different data characteristics and tackling common modeling challenges.

Discuss the Differences between Classification and Regression

In the realm of supervised learning, there are two main types of problems we aim to solve: regression and classification. While they share similarities in the sense that they both leverage input data to make predictions, they fundamentally differ in the type of output they produce and the method of evaluating their performance.

Type of Output: The most apparent difference lies in the type of outcome each model produces. Regression models yield continuous or numerical outputs. For example, predicting the price of a house based on various features is a typical regression problem. On the other hand, classification models produce categorical or discrete outputs. An instance of a classification problem is predicting whether an email is spam (yes/no), or determining the type of fruit in an image (apple/banana/orange).
Evaluation Metrics: Another critical difference is how we measure the performance of these models. Regression models use metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R-squared. These metrics essentially measure the difference between the actual and predicted numerical values. In contrast, classification models use metrics like accuracy, precision, recall, F1-score, and Area Under the Receiver Operating Characteristics curve (AUROC). These metrics evaluate how well the model correctly classifies the categorical outcomes. They will be covered in the next article.
Decision Boundary: Regression models predict a numerical value based on input features, and therefore do not require a decision boundary. On the contrary, classification models need to establish a decision boundary to distinguish between the different categories it’s predicting.

Understanding the differences between regression and classification is crucial as it guides data scientists in selecting the appropriate algorithms and evaluation metrics for their specific use case. It’s also important to note that some algorithms can be used for both classification and regression tasks, such as decision trees and neural networks, further highlighting the interconnectedness of these two areas of supervised learning.

The Importance of Choosing the Right Regression Model

Selecting the appropriate regression model is crucial for making accurate and reliable predictions. Each regression model is equipped with its strengths, weaknesses, and assumptions about the data, and choosing the wrong model can lead to misleading results, or at the very least, sub-optimal predictions.

Several factors should be considered when choosing a regression model for your data science project:

Nature of Your Data: The relationship between your independent and dependent variables greatly influences the type of regression model to be used. Linear regression assumes a linear relationship between input and output variables. If the relationship is not linear, another type of regression, like polynomial or logarithmic, might be more suitable.
Presence of Multicollinearity: Multicollinearity occurs when two or more independent variables are highly correlated. It can lead to unstable estimates of the regression coefficients and make the model’s output difficult to interpret. Ridge regression can handle this problem effectively.
Risk of Overfitting: Overfitting occurs when the model is too complex and captures the noise along with the underlying pattern in the data. It leads to great results on the training data but fails to generalize on unseen data. Lasso regression, with its ability to perform feature selection, can help prevent overfitting.
Interpretability: Sometimes, it’s not only the prediction that matters but also the understanding of the relationships between variables. If interpretability is crucial, simpler models like linear regression might be preferable, even at the expense of a slight decrease in prediction accuracy.
Computational Efficiency: For large-scale problems, computational efficiency becomes a significant factor. More complex models will require more computational resources and time to train and make predictions.

In this article, we will delve deeper into three popular regression models: Linear, Lasso, and Ridge regression. These models each have their unique ways of dealing with the complexities of data and offer different trade-offs between bias and variance, interpretability and complexity, and accuracy and computational efficiency. Understanding these models and their characteristics will provide you with a robust toolbox for tackling various predictive problems in data science.

Basic Theory and Mathematical Principles Behind Linear Regression

Linear regression, as the name suggests, models the linear relationship between the dependent and independent variables. This is done by fitting a line, or a hyperplane in the case of multiple variables, to the data points that minimizes the sum of the squared residuals.

Mathematically, in simple linear regression, this relationship is often expressed as:

Three Regression Models for Data Science: Linear Regression, Lasso Regression, and Ridge Regression (2)

where:

Y is the dependent variable we want to predict.
X is the independent variable we use to make the prediction.
β0 and β1 are the parameters of the model that we’ll estimate. β0 is the y-intercept and β1 is the slope of the line.
ε is the error term that represents the difference between the actual and predicted values.

The aim is to find the values of β0 and β1 that minimize the sum of the squared differences between the predicted and actual values of the dependent variable. This method of finding the best parameters is known as the least squares method.

Assumptions Made in Linear Regression

Linearity: The relationship between the independent and dependent variables is linear.
Independence: The residuals are independent. In other words, the residuals from one prediction have no effect on the residuals from another.
hom*oscedasticity: The variance of the errors is constant across all levels of the independent variables.
Normality: For any fixed value of the independent variables, the dependent variable is normally distributed.

Violation of these assumptions can lead to issues such as biased parameter estimates, inefficient parameter estimates, and incorrect inference. Therefore, understanding and checking these assumptions is a crucial step in the process of building a linear regression model.

In the next section, we’ll look at how to apply linear regression to a practical problem, interpret the results, and understand its strengths and weaknesses.

Practical Application and Implementation of Linear Regression

Let’s illustrate the application of linear regression through a simple, real-world example: predicting house prices based on their size (in square feet). We’ll use Python and the library scikit-learn, a popular tool for data analysis and modeling.

Step 1 — Import necessary libraries

First, we need to import the libraries necessary for our task:

import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn import metrics

Step 2 — Load and explore the dataset

We will load the house prices dataset and look at the first few rows:

df = pd.read_csv('house_prices.csv')
print(df.head())p

Assume our dataset has two columns: ‘size’ and ‘price’.

Step 3 — Prepare the data

Next, we will split our dataset into features (X) and the target variable (y), and further split it into training and test sets:

Interpretation of Results

Now that we have our predictions, let’s interpret the results.

We’ll start by examining the coefficients of our model. In this case, we have just one coefficient as we have only one feature (size).

print(regressor.coef_)

This coefficient represents the change in house price for each one-unit change in size. For example, if the output is [150], it means that for each additional square foot, the model predicts that the house price will increase by $150.

Next, we can evaluate the performance of our model using metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE):

print('Mean Absolute Error:', metrics.mean_absolute_error(y_test, y_pred)) 
print('Mean Squared Error:', metrics.mean_squared_error(y_test, y_pred)) 
print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(y_test, y_pred)))

These metrics provide different ways of understanding the model’s performance. For instance, RMSE gives an idea of how much error the system typically makes in its predictions, with a higher weight for large errors.

This concludes our quick implementation and interpretation of a simple linear regression model. In the next section, we’ll discuss the strengths and weaknesses of this approach.

Strengths and Limitations of Linear Regression

Linear regression, like any other model, has its strengths and limitations. Understanding these can guide you in choosing the right model for your particular application.

Strengths of Linear Regression:

Simplicity: Linear regression is straightforward to understand and explain, which makes it a great tool not only for prediction but also for interpreting the relationship between variables.
Efficiency: Linear regression is computationally efficient compared to some more complex models. This makes it a practical choice for problems with a large number of features or large datasets.
Predictive Performance: With sufficient, relevant features and proper handling of assumptions, linear regression can provide strong predictive performance.
Flexibility: While named ‘linear’, it can model non-linear relationships when polynomial terms (like x², x³, etc.) or interaction terms are included in the feature set.

Limitations of Linear Regression:

Linearity Assumption: Linear regression assumes a linear relationship between the dependent and independent variables. This may not hold true for many real-world scenarios where relationships can be more complex.
Sensitive to Outliers: Linear regression is sensitive to outliers, which can have a significant impact on the regression line and, consequently, prediction accuracy.
Multicollinearity: Linear regression doesn’t handle multicollinearity well. Multicollinearity, a situation where two or more features are highly correlated, can make the model’s estimates less reliable.
Overfitting and Underfitting: Linear regression can overfit with many input features and underfit if the relationship is complex and non-linear.
Lack of Fit Tests: It’s challenging to define the complexity of the model (like degree in polynomial regression) as there’s no definitive way of determining which degree is best without trying all.

By understanding these strengths and limitations, you can make an informed decision about when to use linear regression and when to consider alternative models. In the following sections, we’ll explore two other types of regression models — Lasso and Ridge Regression, which offer some ways to overcome a few limitations of Linear Regression.

Basic Theory and Mathematical Principles Behind Lasso Regression

Lasso Regression, an acronym for Least Absolute Shrinkage and Selection Operator, is a type of linear regression that uses a technique called regularization to improve the model’s predictability and interpretability.

Like linear regression, Lasso regression starts by calculating the sum of squared residuals. However, Lasso regression adds a penalty term to this calculation to discourage the coefficients of the independent variables from getting too large. This penalty term is the absolute value of the magnitude of the coefficients, hence the ‘Least Absolute Shrinkage’ in Lasso. The magnitude of this penalty term is governed by a parameter, typically denoted as λ (lambda).

The Lasso regression cost function is expressed as:

Minimize

Three Regression Models for Data Science: Linear Regression, Lasso Regression, and Ridge Regression (3)

where:

yi is the ith value of the variable we want to predict.
β0 is the y-intercept.
βj is the coefficient for the jth predictor variable xij.
λ is the regularization parameter.

How Lasso Regression Tackles the Overfitting Problem

Overfitting is a common problem in machine learning where a model performs well on training data but poorly on unseen data. Essentially, the model learns the training data too well, capturing the noise along with the underlying pattern.

Lasso regression addresses overfitting through its regularization term. By adding a penalty for large coefficients, Lasso regression discourages the model from relying too heavily on any one feature, promoting a more generalized model.

Another fascinating aspect of Lasso regression is that it can shrink some coefficients to zero, effectively performing feature selection. This is especially useful when dealing with datasets with a large number of features, as it makes the model easier to interpret and can reveal the most important features.

In the next sections, we’ll take a look at how to implement Lasso regression and interpret its results, as well as its strengths and limitations.

Practical Application and Implementation of Lasso Regression

Assuming that we are using the same dataset as in the Linear Regression example, let’s walk through how to implement Lasso Regression.

Step 1 — Train the Model

To use Lasso Regression, we need to import the appropriate function from scikit-learn. Then we can train our model, similar to how we did with Linear Regression:

from sklearn.linear_model import Lasso

lasso = Lasso(alpha=0.1) # set the regularization parameter; you may need to adjust this based on your data
lasso.fit(X_train, y_train)

Step 2 — Make Predictions

Once the model is trained, we can make predictions on the test data:

y_pred = lasso.predict(X_test)

Interpretation of Results

Now that we have our predictions, let’s interpret the results.

Like with Linear Regression, we can look at the coefficients of our Lasso model:

print(lasso.coef_)

The coefficients represent the change in the house price for each one-unit change in the corresponding feature, taking into account the penalty term that we added. A coefficient of zero means that the corresponding feature was not selected by the model.

Next, we can compute some metrics to evaluate the performance of our model:

print('Mean Absolute Error:', metrics.mean_absolute_error(y_test, y_pred)) 
print('Mean Squared Error:', metrics.mean_squared_error(y_test, y_pred)) 
print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(y_test, y_pred)))

These metrics provide different ways of understanding the model’s performance. You may notice differences in these metrics compared to those from the Linear Regression model. These differences can give you insights into whether Lasso Regression, with its built-in feature selection, provides an advantage for your specific dataset.

In the next section, we’ll discuss the strengths and limitations of Lasso Regression.

Strengths and Limitations of Lasso Regression

Lasso Regression is a powerful tool in the data scientist’s toolkit, but it’s not without its strengths and limitations. Understanding these can help you decide when to use Lasso Regression.

Strengths of Lasso Regression:

Feature Selection: One of the main advantages of Lasso Regression is its ability to perform feature selection. By shrinking some coefficients to zero, it effectively removes the corresponding feature from the model. This can be especially useful in datasets with a large number of features, making the model easier to interpret and more efficient to compute.
Prevention of Overfitting: The regularization term in Lasso Regression discourages the model from fitting the training data too closely, thus helping prevent overfitting. It encourages the model to be simpler and more generalizable.
Handling Multicollinearity: Lasso can handle multicollinearity between features by arbitrarily selecting one and setting the coefficient of the other correlated features to zero.

Limitations of Lasso Regression:

Selection of Regularization Parameter: The performance of Lasso Regression is heavily dependent on the choice of the regularization parameter. If it’s too large, important features may be neglected. If it’s too small, the model may overfit the data. Selecting the appropriate value often requires trial and error or techniques like cross-validation.
Limitations in Feature Selection: While Lasso can perform feature selection, it tends to favor selecting one feature from a group of highly correlated features, which might not always be ideal from an interpretation perspective.
Difficulty Handling Complex Relationships: While Lasso can prevent overfitting, it might not perform well if the true relationship between features and the target variable is highly complex and non-linear.

Understanding the balance of these strengths and limitations is crucial in deciding whether to use Lasso Regression for a particular problem. In the next section, we’ll look at Ridge Regression, another variant of linear regression that uses a different kind of regularization and can sometimes overcome some of the limitations of Lasso Regression.

Basic Theory and Mathematical Principles Behind Ridge Regression

Ridge Regression, like Lasso Regression, is a type of linear regression that uses a technique called regularization to improve the model’s accuracy and interpretability. While Lasso uses the absolute value of the coefficients in its penalty term, Ridge uses the square of the coefficients. This difference has significant implications for how these two models behave.

The Ridge Regression cost function is expressed as:

Minimize

Three Regression Models for Data Science: Linear Regression, Lasso Regression, and Ridge Regression (4)

where:

yi is the ith value of the variable we want to predict.
β0 is the y-intercept.
βj is the coefficient for the jth predictor variable xij.
λ is the regularization parameter.

This penalty term discourages large coefficients, like in Lasso, but because of the squaring, it does not force them to zero. This leads to models that are less likely to completely ignore any given feature, unlike Lasso.

How Ridge Regression Deals with Multicollinearity

Multicollinearity refers to the situation where two or more features are highly correlated with each other. This can make it difficult for a model to determine which feature is contributing to the prediction, leading to instability and strange results.

Ridge Regression handles multicollinearity by introducing bias to the model (the penalty term), which can reduce the variance of the model and improve its generalizability. Essentially, Ridge Regression “shrinks” the coefficients of correlated features, distributing the contribution more evenly and creating a more stable model.

In the next sections, we will discuss how to implement Ridge Regression and interpret its results, as well as its strengths and limitations.

Practical Application and Implementation of Ridge Regression

Using the same dataset as in the Linear and Lasso Regression examples, let’s walk through how to implement Ridge Regression.

Step 1 — Train the Model

We first need to import the appropriate function from scikit-learn. We then train our model similarly to how we did with Linear and Lasso Regression:

from sklearn.linear_model import Ridge

ridge = Ridge(alpha=0.1) # set the regularization parameter; you may need to adjust this based on your data
ridge.fit(X_train, y_train)

Step 2 — Make Predictions

Once the model is trained, we can use it to make predictions on the test data:

y_pred = ridge.predict(X_test)

Interpretation of Results

Like with Linear and Lasso Regression, we can examine the coefficients of our model:

print(ridge.coef_)

These coefficients represent the change in the house price for each one-unit change in the corresponding feature, taking into account the penalty term we added. Unlike Lasso, Ridge is less likely to result in a coefficient of zero, meaning that it tends to use all the available features.

Next, we evaluate the performance of our model using the same metrics as before:

print('Mean Absolute Error:', metrics.mean_absolute_error(y_test, y_pred)) 
print('Mean Squared Error:', metrics.mean_squared_error(y_test, y_pred)) 
print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(y_test, y_pred)))

These metrics can provide insight into the performance of Ridge Regression and how it compares to the other models we’ve discussed.

In the next section, we’ll discuss the strengths and limitations of Ridge Regression.

Strengths and Limitations of Ridge Regression

Like all models, Ridge Regression has its strengths and limitations. These should be carefully considered when deciding whether it’s the right model for a particular problem.

Strengths of Ridge Regression:

Prevention of Overfitting: Just like Lasso, Ridge uses a penalty term, which discourages complexity in the model and helps to prevent overfitting.
Multicollinearity Handling: Ridge Regression is particularly good at handling multicollinearity, a situation where two or more predictors are highly correlated. It does this by distributing coefficients among correlated predictors, which can lead to a more stable and robust model.
Performance with Many Features: Ridge tends to perform well even when there are many features, or when there are more features than observations.

Limitations of Ridge Regression:

Selection of Regularization Parameter: The performance of Ridge Regression is sensitive to the choice of the regularization parameter, λ. Choosing the best value often requires trial and error or techniques like cross-validation.
Does Not Perform Feature Selection: Unlike Lasso, Ridge does not force any coefficients to be exactly zero. This means it does not perform feature selection and can lead to models that are harder to interpret.
Bias Introducing: The regularization term in Ridge Regression introduces bias into the model, which could lead to underfitting if the λ value is too high.

Understanding these strengths and limitations will allow you to make an informed decision on when to use Ridge Regression and when to consider other models. In the next section, we’ll compare the three regression models we’ve discussed and provide some practical tips on choosing the right one for your data.

Comparison of Linear, Lasso, and Ridge Regression

In the previous sections, we discussed three different types of regression models — Linear, Lasso, and Ridge. Let’s now compare these models to understand their unique strengths and weaknesses.

Model Complexity and Overfitting: All three models aim to minimize the sum of squared residuals, but Lasso and Ridge Regression include a penalty term to limit the model’s complexity. This regularization helps prevent overfitting, especially when dealing with datasets with many features or high multicollinearity. Linear Regression, on the other hand, does not have this penalty term and may therefore be more prone to overfitting.
Feature Selection: Lasso Regression has the unique ability to perform feature selection, shrinking some coefficients to exactly zero and thereby eliminating the corresponding features from the model. This can be particularly beneficial when dealing with datasets with many features, as it can improve computational efficiency and interpretability. In contrast, while Ridge Regression does shrink the coefficients, it does not force them to zero, meaning it does not perform feature selection. Linear Regression does not perform any shrinkage or feature selection.
Multicollinearity: Linear Regression can be significantly affected by multicollinearity, which can lead to unstable coefficient estimates and strange results. Both Lasso and Ridge Regression handle multicollinearity better due to their penalty terms, distributing the influence among the correlated features.
Interpretability: Linear Regression, without any penalty term or feature selection, can often be the most straightforward to interpret, as each coefficient directly corresponds to the change in the output with a one-unit change in the corresponding input. The introduction of the penalty term in Lasso and Ridge Regression can make these models less straightforward to interpret, especially for Ridge Regression, which keeps all features in the model.
Bias-Variance Tradeoff: Linear Regression can have low bias but high variance, particularly in the presence of many features or multicollinearity. Lasso and Ridge Regression introduce bias into the model with their penalty terms, which can lower variance and lead to a better overall model. However, if the penalty term is too large, these models may become overly simplified and exhibit high bias, leading to underfitting.

The choice between Linear, Lasso, and Ridge Regression depends largely on your specific dataset and problem. If interpretability is key, and you have a smaller set of important features, then Linear Regression may be the best choice. If you have many features or expect multicollinearity, then Lasso or Ridge Regression may be more appropriate. Lasso Regression can be particularly useful if you believe some features may not be important and can be removed. Ultimately, understanding the differences and trade-offs between these three models will allow you to select the most appropriate model for your needs.

Scenarios to Choose One Over the Others

Each of the regression models we’ve discussed has its unique strengths, making it more suitable for certain scenarios than others. Let’s explore some situations where you might choose one type of regression over another:

Linear Regression: If your dataset is small to moderate in size, has few features, and little to no multicollinearity, Linear Regression is often a good starting point. It is simple, fast, and the resulting model is easy to interpret. This model is also preferred when the focus is on interpretability over prediction accuracy.
Lasso Regression: If your dataset is large with many features, and you suspect that some of the features are not important or are redundant, Lasso Regression is a good choice. It can help you simplify your model by performing feature selection, improving computational efficiency, and making the model easier to interpret. It’s also useful when you want to prevent overfitting in a model with many features.
Ridge Regression: If your dataset has high multicollinearity, meaning that some of the features are highly correlated with each other, Ridge Regression can be a better choice. It distributes the coefficients among correlated predictors, which can lead to a more stable and robust model. Also, when there are more predictors than observations, Ridge Regression tends to perform well.
Tuning and Cross-Validation: For both Lasso and Ridge Regression, the value of the penalty term, λ, is crucial for the performance of the model. To find the best value, you typically need to try out several possibilities and see which one gives you the best model. Techniques such as cross-validation can be particularly useful here.

The right choice of regression model will depend on the specifics of your dataset and the problem you’re trying to solve. Practical considerations, such as computational resources and the need for interpretability, can also play a role. It’s also often a good idea to try out several models and compare their performance. This can give you a sense of what works best for your particular problem and help you gain a deeper understanding of the data you’re working with.

Practical Tips on When to Use Which Model

Deciding which regression model to use can be a daunting task, especially with numerous factors to consider, such as dataset size, feature count, multicollinearity, interpretability, and prediction performance. Here are some practical tips to guide you in choosing the appropriate model:

Start Simple: It’s often a good idea to start with the simplest model, which is Linear Regression in this case. This can give you a baseline to compare with more complex models. If Linear Regression provides adequate performance, there may be no need to complicate things with regularization.
Use Lasso for Feature Selection: If you’re dealing with high-dimensional data where you suspect that some features may be irrelevant, Lasso Regression can be a great tool. It performs L1 regularization, which can shrink some of the model coefficients to zero, effectively performing feature selection.
Use Ridge for Multicollinearity: If you suspect multicollinearity, i.e., high correlation among predictor variables, Ridge Regression can be a better option. Ridge Regression performs L2 regularization, which distributes the coefficients among correlated predictors, leading to a more stable and generalized model.
Consider Computation Time: For very large datasets, the computational cost of the model becomes a significant factor. In such cases, simpler models like Linear Regression can be advantageous as they tend to be more computationally efficient.
Cross-Validation is Your Friend: The regularization parameter (λ) in Lasso and Ridge plays a significant role in how these models perform. Using cross-validation to tune this hyperparameter can be extremely helpful in optimizing model performance.
Always Test Multiple Models: Even with these guidelines, it’s usually a good idea to test multiple models. This can give you a sense of what works best for your specific problem and can also offer insights that may not be obvious at the outset.
Interpretability Matters: Always consider the need for interpretability. In some cases, a slightly worse performing model might be preferable if it offers significantly better interpretability. In such scenarios, simpler models like Linear Regression might be more suitable.

Remember, these are guidelines, not hard-and-fast rules. The best approach will often depend on the specifics of your data and the problem you’re trying to solve.

In this article, we have explored three different types of regression models — Linear Regression, Lasso Regression, and Ridge Regression.

We started with Linear Regression, the most straightforward of the three, which models a linear relationship between the dependent and independent variables.
We then moved onto Lasso Regression, a regularized version of Linear Regression that can perform feature selection, simplifying the model and potentially improving interpretability.
Finally, we covered Ridge Regression, another regularized version of Linear Regression that deals particularly well with multicollinearity and performs well when there are more features than observations.

For each model, we delved into the underlying theory and mathematical principles, discussed practical implementation with a real-world example, interpreted the results, and discussed the strengths and limitations.

The world of data science is vast and constantly evolving, with new methodologies and techniques emerging regularly. However, the core models we’ve discussed in this article remain fundamental tools in the data scientist’s arsenal.

As you continue your data science journey, I encourage you to explore these models further. Each has its unique strengths, making it more suitable for certain scenarios than others. Understanding these models and knowing when to use each one is a valuable skill that will serve you well in your data science projects.

Experiment with these models, tweak their parameters, and see how they perform with different datasets. Hands-on experience is the best way to understand these models deeply and intuitively.

Remember, the best data scientists are not those who know the most sophisticated models but those who know how to choose the right model for the task at hand. So, keep exploring, keep learning, and enjoy the journey!