Multiple linear regression sklearn. We’re dealing with an iterative process instead.

Parameters: X {array-like, sparse matrix} of shape (n_samples, n_features) The training input samples. Apr 30, 2020 · Is dropping a level required at all when using a regularized regression method? General opinion seems to be yes , but reading the sklearn doc for the parameter drop , it seems like only non-regularized methods or neural networks require dropping the first level. tools. predictmethod to do this. The equation we’re solving remains more or less the same: Image 1 — Multiple linear regression Jan 7, 2021 · Multiple linear regression refers to a statistical technique that is used to predict the outcome of a variable based on the value of two or more variables. 13. reshape(1, -1) if it contains a single sample. We will start with the most familiar linear regression, a straight-line fit to data. It's simple: ml_model = GradientBoostingRegressor() ml_params = {} ml_model. Code: In the following code, we will import some libraries from which we can create the scikit learn non-linearity. Steps 1 and 2: Import packages and classes, and provide data Dec 8, 2020 · If you are new to #python and #machinelearning, in this video you will find some of the important concepts/steps that are followed while predicting the resul Linear perceptron classifier. Up! We can predict the CO2 emission of a car based on the size of the engine, but with May 12, 2020 · SciKit Learn: Just import the Linear Regression module from the Sklearn package and fit the model on the data. See code snippet below - full_results is a dataframe in which all variables are numeric. 7176. See statsmodels. metrics. Well I in its turn recommend tree model from sklearn, which could also be used for feature selection. In the previous video I've explained the concept of linear regression where a single independent variable (X) was used to model the dependent variable (Y). y y. You would typically "one-hot encode" categorical variables. import numpy as np rng = np. It has a breakdown point of about 29. Gaussian Processes #. Furthermore, Pandas and PySpark have similar Mar 24, 2022 · X, y = df[["hours", "prep_exams"]], df. Linear regression attempts to model the relationship between two (or more) variables by fitting a straight line to the data. 3% in case of a simple linear regression which means that it can tolerate arbitrary corrupted data (outliers) of up to 29. Nov 16, 2021 · Since we have only one feature, the following polynomial regression formula applies: y = ß 0 + ß 1 x + ß 2 x 2 + … + ß n x n. linear_model import LinearRegression model = LinearRegression() model. R 2 (coefficient of determination) regression score function. 1. score #fit regression model. e. score(X, y) #view R-squared value. Multi-task L1 regularized linear model with built-in cross-validation. The results of this code is a single coefficient of determination which I believe denotes how much change in y is due to the combination of x1 - x4. drop('sales', axis=1), data. Hence, y(xi) = a1*x + a2. By default, the output is a scalar. api to get a detail summary of the learning result. Across the module, we designate the vector w = ( w 1,, w p) as coef_ and w 0 as intercept_. You can use it like this: from sklearn. , the coefficients of a linear model), the goal of recursive feature elimination (RFE) is to select features by recursively considering smaller and smaller sets of features. In this example, we use scikit-learn to perform linear regression. Pipelines require all steps except the last to be a transformer. Dec 17, 2017 · Step 1. Theil-Sen Estimator: robust multivariate regression model. Oct 10, 2020 · Image by Author. model = LinearRegression() X, y = df[['NumberofEmployees','ValueofContract']], df. The bias term in the underlying linear model. 943 (94. Learning rate schedule for weight updates. In the following example, you’ll see how to perform multiple linear regression for a fictitious economy, where the index_price is the dependent variable, and the 2 independent/input variables are: interest_rate Jan 28, 2022 · Scikit learn non-linear. Linear Regression Example. 6. This notebook introduces different strategies to leverage time-related features for a bike sharing demand regression task that is highly dependent on business cycles (days, weeks, months) and yearly season cycles. 5. Extracting regression coefficients from a scikit-learn model is a fairly straightforward process. In the general case when the true y is non-constant, a The multi-task lasso allows to fit multiple regression problems jointly enforcing the selected features to be the same across tasks. Read more in the User Guide. This model solves a regression model where the loss function is the linear least squares function and regularization is given by the l2-norm. Diabetes dataset#. print(r_squared) 0. Fit an OLS. l1_ratiofloat, default=0. Training data. x1, x2 and x3 are the feature variables. I don't want to have terms with second degree like x1^2. I 6. fit(X, y) 3. fit(X, y) #calculate R-squared of regression model. Ten baseline variables, age, sex, body mass index, average blood pressure, and six blood serum measurements were obtained for each of n = 442 diabetes patients, as well as the response of interest, a quantitative measure of disease progression one year after baseline. In this section, we will learn how Scikit learn non-linear works in python. Multi-layer Perceptron (MLP) is a supervised learning algorithm that learns a function f: R m → R o by training on a dataset, where m is the number of dimensions for input and o is the number of dimensions for output. learning_rate{‘constant’, ‘invscaling’, ‘adaptive’}, default=’constant’. LinearRegression): """ LinearRegression class after sklearn's, but calculate t-statistics and p-values for model coefficients (betas). To test the regressor, we need to use it to predict on our test data. Section 3: Stepwise Regression The stepwise regression technique is used while dealing with Jul 19, 2016 · I was planning to use sklearn linear_model to plot a graph of linear regression result, and statsmodels. This example simulates sequential measurements, each task is a time instant, and the relevant features vary in amplitude over time while being the same. If you want to use one of the others, you can use a new class for parallelization of regressors for multivariate output: MultiOutputRegressor. dataset = datasets. Additionally, the intercept_ property will return the intercept value of the model. Apr 18, 2020 · 12. Notice how linear regression fits a straight line, but kNN can take non-linear shapes. # y is the label array. ‘constant’ is a constant learning rate given by ‘learning_rate_init’. linear_model import LinearRegression. 1 documentation. from sklearn. LinearRegression() model = ols. Code example: # Linear Regression. The Example. This means that 71. f2 They are bad rooms in the house. 3. Let’s read the dataset which contains the Multiple Linear Regression With scikit-learn. Related: What is a Good R-squared Value? Example 1: Calculate Adjusted R-Squared with sklearn. 8e-14, but the constant term from statsmodels is 48. For numerical reasons, using alpha = 0 with the Lasso object is not advised. Parameters: X{array-like, sparse matrix} of shape (n_samples, n_features) The training input samples. Univariate Feature Selection. preprocessing import linear_model #for implementing multiple linear regression. Any value of n_subsamples between the number of features and samples leads to an estimator with a compromise between robustness and efficiency. coef_ and regressor. If you're looking to compute the confidence interval of the regression parameters, one way is to manually compute it using the results of LinearRegression from scikit-learn and numpy methods. Nov 1, 2023 · Table of Contents. preprocessing. AverageNumberofTickets. datasets import load_linnerud. Unlike, simple linear regression multiple linear regression doesn’t have a line of best fit anymore instead we use plane/hyperplane. In the multiclass case, the training algorithm uses the one-vs-rest (OvR) scheme if the ‘multi_class’ option is set to ‘ovr’, and uses the cross-entropy loss if the ‘multi_class’ option is set to ‘multinomial’. 3% in the two-dimensional case. Import the necessary packages: import numpy as np. reshape(-1, 1) if your data has a single feature or array. MultiTaskLassoCV. , the number of features used to build the linear model used to generate the output. #. The math behind multiple linear regression is a bit more complicated than it was for the simple one, as you can’t simply plug the values into a formula. Jan 13, 2015 · scikit-learn's LinearRegression doesn't calculate this information but you can easily extend the class to do it: from sklearn import linear_model from scipy import stats import numpy as np class LinearRegression(linear_model. m: bias or slope of the regression line c: intercept, shows the point where the estimated regression line crosses the 4. 12. It is a model for predicting the value of one dependent variable based on two or more independent variables. “Our goal is to find the best fit hyper 1. Jan 8, 2021 · 嗨嗨大家，不知道大家有閱讀過我的上一篇[Machine Lesrning — 給自己的機器學習筆記 — Linear Regression — 迴歸模型介紹與原理]嗎，上一篇介紹了迴歸模型的原理與公式算法，這一篇主要是要教大家使用強大的Sklearn來實作迴歸模型喔，那我們開始吧！ . preprocessing import Nov 24, 2023 · This chapter demonstrates how to build, train, evaluate, and use a multiple linear regression model in both Scikit-Learn and PySpark. fit(x_train, y_train) print model. Multiple linear regression basically indicates that we will have many characteristics such as f1, f2, f3, f4, and our output function f5. pyplot as plt #for plotting purpose. In this lesson, we study what linear regression is and how it can be implemented for multiple variables using Scikit-Learn, which is one of the most popular machine learning libraries for Python. Comparing the regression coefficients between OLS and NNLS, we can observe they are highly correlated (the dashed line is the identity relation), but the non-negative constraint shrinks some to 0. 76% of the variation in the exam scores can be explained by Oct 30, 2020 · Mathematical Notation: In Multiple linear regression Independent variable (y) is a linear combination of dependent variables (x) theta is the parameter / coefficient. Multi-layer Perceptron #. Thus, given the data X, we wish to find its trend with the result y. coef_[1] corresponds to "feature2". When analyzing our results summary, we can notice that the R-squared of the model is 0. The implementation is a wrapper around SGDClassifier by fixing the loss and learning_rate parameters as: SGDClassifier(loss="perceptron", learning_rate="constant") Other available parameters are described below and are forwarded to SGDClassifier. fit_transform(X) # apply your linear regression as you want. 1 Score. Time-related feature engineering #. head ()` we will get something like the following: size bedroom price. linear_model. i. You can implement multiple linear regression following the same steps as you would for simple regression. The main difference is that your x array will now have two or more columns. If p-value ≤ significant level, we reject the null hypothesis (H 0) If p-value > significant level, we fail to reject the null hypothesis (H 0) We Principal Component Regression vs Partial Least Squares Regression# This example compares Principal Component Regression (PCR) and Partial Least Squares Regression (PLS) on a toy dataset. Examples. Gaussian Processes — scikit-learn 1. predictions = regressor. For prediction purposes, linear models can sometimes outperform fancier nonlinear models, especially in situations with small numbers of training cases, low signal-to-noise ratio, or sparse data (Hastie et al. The implementation is based on Algorithm 2. We’re going to use a couple of libraries in this article: pandas to read the file that contains the dataset, sklearn. . Now I would like to expand the functionality of the task, to get not a single target value, but To illustrate the behaviour of quantile regression, we will generate two synthetic datasets. And the parameters that define the nature of a line are m (slope) and c (intercept). y = a*x1 + b*x2 + c*x3 + d If the solver is ‘lbfgs’, the regressor will not use minibatch. The straight line can be seen in the plot, showing how linear regression attempts to draw a straight line that will best minimize the residual Displaying PolynomialFeatures using $\LaTeX$¶. Nov 16, 2014 · Well using regression. Sparse matrix can be CSC, CSR, COO, DOK, or LIL. In the process, we introduce how to perform periodic feature engineering using the sklearn Jul 11, 2022 · The equation for this problem will be: y = b0+b1x1+b2x2+b3x3. OLS (y,X) Oct 27, 2021 · Summary. In addition to standard scikit-learn estimator API, GaussianProcessRegressor: exposes a method log_marginal_likelihood (theta), which can be used externally for other ways of selecting hyperparameters, e. You can verify that when D = 1, the RSE for multiple linear regression is the same as the RSE for {doc} simple linear regression <simple-linear-regression>. Finding the straight line model that best fits a collection of scattered data points is known as linear regression; we can then extrapolate the curve to foretell new data points. Multiple Regression. Given an external estimator that assigns weights to features (e. For example, the constant term from sklearn is 7. Multivariate linear regression can be thought as multiple regular linear regression models, since you are just comparing the May 18, 2021 · The model gets the best-fit regression line by finding the best m, c values. May 29, 2019 · Let’s directly delve into multiple linear regression using python via Jupyter. the . where. COO, DOK, and LIL are converted May 26, 2015 · I would like to predict multiple dependent variables using multiple predictors. r_squared = model. 05 ). The estimation of the model is done by 1. , when y is a 2d-array of shape (n_samples, n_targets)). 17. linear_model import LinearRegression #initiate linear regression model model = LinearRegression() #define predictor and response variables X, y = df[[' hours ', ' exams Creating a linear regression model (s) is fine, but can't seem to find a reasonable way to get a standard summary of regression output. For l1_ratio = 0 the penalty is an L2 penalty. The cost function is the measure of how accurately the model predicts the target values. This holds true for any given number of variables. Consider the following data, which is scattered about a line with a slope of 2 and an intercept Nov 19, 2021 · I am performing a fairly straight forward multiple linear regression in Python using sklearn. The algorithm calculates least square solutions on subsets with size n_subsamples of the samples in X. predict(x_test)[0:5] However, what I want to do is multivariable regression. n n. This estimator has built-in support for multi-variate regression (i. # X is a numpy array with your features. alpha=0. Feb 26, 2019 · You can transform your features to polynomial using this sklearn module and then use these features in your linear regression model. more_vert. Any explanation behind your choice would also be appreciated. Import the libraries and data: After running the above code let’s take a look at the data by typing `my_data. Metrics and scoring: quantifying the quality of predictions — scikit-learn 1. Put simply, linear regression attempts to predict the value of one variable, based on the value of another (or multiple other variables). fit(X_train, y_train) where y_train is one-dimensional array-like object. 6. org Regression# The class SGDRegressor implements a plain stochastic gradient descent learning routine which supports different loss functions and penalties to fit linear regression models. load_diabetes() Sep 26, 2023 · When you call fit on a linear regression model in scikit-learn, it performs this OLS under the hood. The multi-task lasso imposes that features that are selected Linear Regression Example #. Multi-task L1/L2 ElasticNet with built-in cross-validation. g. Nov 13, 2020 · This tutorial shows two examples of how to calculate adjusted R 2 for a regression model in Python. From the documentation for OLS: exog: A nobs x k array where nobs is the number of observations and k is the number of regressors. fit_transform(variables) poly_var_train, poly_var_test, res_train, res_test = train_test_split(poly_variables, results Gallery examples: Early stopping in Gradient Boosting Gradient Boosting regression Prediction Intervals for Gradient Boosting Regression Model Complexity Influence Linear Regression Example Poisson Nov 16, 2023 · For instance, here is the equation for multiple linear regression with two independent variables: Y = a + b1 ∗ X1 + b2 ∗ x2 Y = a + b 1 ∗ X 1 + b 2 ∗ x 2. y = mx + c. Simple Linear Regression. I've created a model using linear regression. Multiple linear regression model has the following structure: y = β1x1 +β2x2 + ⋯ +βnxn + β0 (1) (1) y = β 1 x 1 + β 2 x 2 + ⋯ + β n x n + β 0. the sum of norm of each row. An intercept is not included by default and should be added by the user. Parameters: X {array-like, sparse matrix} of shape (n_samples, n_features). The Non-Negative Least squares inherently yield sparse results. In this guide, you’ll see how to perform multiple linear regression in Python using both sklearn and statsmodels. Feb 23, 2017 · There are many different ways to compute R^2 and the adjusted R^2, the following are few of them (computed with the data you provided): from sklearn. Total running time of the script: (0 minutes 0. where a is commonly known as the slope, and b is commonly known as the intercept. enc = OneHotEncoder(sparse=False) X_transform = enc. from sklearn import datasets. The number of informative features, i. The following code shows how to fit a multiple linear regression model and calculate the adjusted R-squared of the model using sklearn: Examples. There are 3 different APIs for evaluating the quality of a model’s predictions: Estimator score method: Estimators have a score method providing a default evaluation criterion Predict regression value for X. linspace(start=0, stop=10, num=100) X = x Aug 23, 2017 · If I have independent variables [x1, x2, x3] If I fit linear regression in sklearn it will give me something like this: y = a*x1 + b*x2 + c*x3 + intercept Polynomial regression with poly =2 will give me something like. rand (42, 1), axis=0) is used to generate same data. SGDRegressor is well suited for regression problems with a large number of training samples (> 10. 3%) which clearly reveals that our model is doing well and can be used for real Gallery examples: Prediction Latency Comparison of kernel ridge regression and SVR Support Vector Regression (SVR) using linear and non-linear kernels Scikit-learn provides two implementations of gradient-boosted trees: HistGradientBoostingClassifier vs GradientBoostingClassifier for classification, and the corresponding classes for regression. add_constant. fit(data. This section of the user guide covers functionality related to multi-learning problems, including multiclass, multilabel, and multioutput classification and regression. sklearn. 2. This method is pretty straightforward and you can see how to use it below. r2_score(y_true, y_pred, *, sample_weight=None, multioutput='uniform_average', force_finite=True) [source] #. Feb 28, 2020 · I'm starting to learn a bit of sci-kit learn and ML in general and i'm running into a problem. coef_[0] corresponds to "feature1" and regression. f3 is the town of the house. Beside factor, the two main parameters that influence the behaviour of a successive halving search are the min_resources parameter, and the number of candidates (or parameter combinations) that are evaluated. Linear Models #. 1. We can use our model’s . 1 of [RW2006]. import matplotlib. A straight-line fit is a model of the form: y = ax + b. score is good (above 0. In mathematical notation, if y ^ is the predicted value. Take a look at the data set below, it contains some information about cars. xn x n. model_selection to split the training and testing dataset, and Explore and run machine learning code with Kaggle Notebooks | Using data from 50 Startups. See full list on geeksforgeeks. sort (5 * num. Gaussian Processes (GP) are a nonparametric supervised learning method used to solve regression and probabilistic classification problems. Multiclass and multioutput algorithms #. model_selection import train_test_split X_train, Multiple linear regression ¶. 7. Given this, you should use the LinearRegression object. So, the model will be CompressibilityFactor(Z) = intercept + coef*Temperature(K) + coef*Pressure(ATM) Dec 9, 2019 · Step #1. The code below computes the 95%-confidence interval ( alpha=0. , 2009). Aug 29, 2019 · I am solving the classic regression problem using the python language and the scikit-learn library. y = a*x1^2 + b*x1*x2 . The following are a set of methods intended for regression in which the target value is expected to be a linear combination of the features. regression. Sep 30, 2020 · 1. The modules in this section implement meta-estimators, which require a base estimator to be provided in their constructor. We’re dealing with an iterative process instead. StandardScaler before fitting your model then the regression coefficients should be the Beta coefficients you're looking for. From sklearn. Mar 28, 2024 · Any linear regression model comprises of 3 parts:- a cost function, gradient descent and the learning rate. Recursive feature elimination#. Sep 20, 2022 · Multiple linear regression is one of the most fundamental statistical models due to its simplicity and interpretability of results. Also known as Ridge Regression or Tikhonov regularization. Multiple regression is like linear regression, but with more than one independent value, meaning that we try to predict a value based on two or more variables. The ElasticNet mixing parameter, with 0 <= l1_ratio <= 1. 8) but i want to get it better (perhaps to 0. If we take the same example we discussed earlier, suppose: f1 is the size of the house. Best possible score is 1. The most common tool used for composing estimators is a Pipeline. I referred to an example and tried implementing the same way with my dataframe - but ended up getting. Scikit-learn makes this easy: Oct 31, 2022 · We can use the following code to fit a multiple linear regression model using hours and exams as the predictor variables and score as the response variable: from sklearn. This should be what you desire. LogisticRegression. x = num. full code Oct 22, 2020 · Training the Multiple Linear Regression model on the Training set. The true generative random processes for both datasets will be composed by the same expected value with a linear relationship with a single feature x. preprocessing import OneHotEncoder. If you use sklearn. : number of features. When set to “auto”, batch_size=min (200,n_samples). You will also want to "standardize" the numerical variables. y_test = dataTest['CompressibilityFactor(Z)'] ols = linear_model. This Math Behind Multiple Linear Regression. how can I get . Linear Model trained with L1 prior as regularizer (aka the Lasso). However, I'm unsure if I should use scikitlearn or the statsmodels libraries as I found other posts/youtube videos that use both. As we have multiple feature variables and a single outcome variable, it’s a Multiple linear regression. Learning objectives: Oct 24, 2017 · I started working on sklearn and have been trying to implement multilinear regression. Given a set of features X = x 1, x 2,, x m and a target y, it can learn a non-linear Jul 29, 2021 · Sorted by: 3. You can do like: from sklearn. We will use data on house sales in King County (Seattle, WA) to predict prices using multiple regression. preprocessing import PolynomialFeatures from sklearn import linear_model poly = PolynomialFeatures(degree=2) poly_variables = poly. Dataset transformations. 7175541714105901. The example below uses only the first feature of the diabetes dataset, in order to illustrate the data points within the two-dimensional plot. model. b is where the line starts at the Y-axis, also called the Y-axis intercept and a defines if the line is going to be more towards the upper or lower part of the graph (the angle of the line), so it is called the slope of the line. Pipelines and composite estimators #. The R-squared of the model turns out to be 0. Comparison between grid search and successive halving. 000), for other problems we recommend Ridge, Lasso, or ElasticNet. Aug 9, 2021 · I have the created a simple multiple linear regression model and would like to print the model summary - ei the OLS/regression summary. The number of regression targets, i. 4. Sparse matrices are accepted only if they are supported by the base estimator. Let’s see how to do this step-wise. 0 and it can be negative (because the model can be arbitrarily worse). [ ] Nov 16, 2023 · The equation that describes any straight line is: $$ y = a*x+b $$ In this equation, y represents the score percentage, x represents the hours studied. Successive Halving Iterations. To build a composite estimator, transformers are usually combined with other transformers or with predictors (such as classifiers or regressors). : response variable. I've searched the documentation of sklearn and googled this question but I cannot seem to find the answer. Logistic Regression (aka logit, MaxEnt) classifier. LinearRegression documentation page you can find the coefficients (slope) and intercept at regressor. To do this, all you need to do is call the model’s coef_ property, which will return the regression coefficients as a numpy array. Jan 17, 2024 · Scikit-learn, a machine learning library in Python, can be used to implement multiple linear regression models and to read, preprocess, and split data. Learning the parameters of a prediction function and testing it on the same data is a methodological mistake: a model that would just repeat the labels of the samples that it has just seen would have a perfect score but would fail to predict anything useful on yet-unseen data. Cross-validation: evaluating estimator performance #. The predicted regression value of an input sample is computed as the weighted median prediction of the regressors in the ensemble. random. f4 is the state of the house and, f5 it is our exit 20. , via Markov chain Monte Carlo. import pandas as pd. 074 seconds) Apr 9, 2024 · As we know, the equation of a straight line is. However, the two packages produce very different results on the same input. # Load the diabetes datasets. In this lesson on how to find p-value (significance) in scikit-learn, we compared the p-value to the pre-defined significant level to see if we can reject the null hypothesis (threshold). If I understood correctly, in principle one could make a bunch of linear regression models that each predict one dependent variable, but if the dependent variables are correlated, it makes more sense to use multivariate regression. 01 would compute 99%-confidence interval etc. intercept_ respectively. X = sm. The advantages of Gaussian processes are: The prediction interpolates the observations (at least for regular kernels). , the dimension of the y output vector associated with a sample. Our goal is to illustrate how PLS can outperform PCR when the target is strongly correlated with some directions in the data that have a low variance. coef_ does get the corresponding coefficients to the features, i. sales) Compared to the OLS (ordinary least squares) estimator, the Theil-Sen estimator is robust against outliers. 3. import numpy as np. Choosing min_resources and the number of candidates#. Reshape your data either using array. 9). This is also called "adding dummy variables". Moreover, it is possible to extend linear regression to polynomial regression by using scikit-learn's PolynomialFeatures, which lets you fit a slope for your features raised to the power of n, where n=1,2,3,4 in our example. Metrics and scoring: quantifying the quality of predictions #. add_constant (x) sm. To be specific, check out Dec 31, 2022 · Multiple linear regression is an extension of simple linear regression. Run the following code to fit and then evaluate a multiple linear regression model using scikit-learn: Firstly, fit a linear regression to sales using TV and radio as predictors. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. The former can be orders of magnitude faster than the latter when the number of samples is larger than tens of thousands of samples. From the predicted regression line, the model will predict a y given an X. It shows that the steps involved in machine learning, including splitting data, model training, model evaluation, and prediction, are the same in both frameworks. For l1_ratio = 1 it is an L1 penalty. In this equation the number of coefficients ( ß s) is determined by the feature’s highest power (aka the degree of our polynomial; not considering ß 0, because it’s the intercept). Sep 2, 2020 · Step 4: Testing the Linear Regressor. RandomState(42) x = np. Jan 5, 2022 · Linear regression is a simple and common type of predictive analysis. predict(x_test) Now the model’s predictions are stored in the variable predictions, which is a Numpy array. Categorical variables can be handled in multiple linear regression using one-hot encoding or label encoding. It is The predicted regression target of an input sample is computed as the mean predicted regression targets of the estimators in the ensemble. Comparison of F-test and mutual information. 7. As already mentioned, only some models support multivariate output. MultiTaskElasticNetCV. A Python package called Scikit-learn simplifies using various Machine Learning (ML) methods for studying predictive data, including linear regression. wt db dy bt ze ve dl cf wu dw