{"id":20944,"date":"2024-04-18T16:05:00","date_gmt":"2024-04-18T10:35:00","guid":{"rendered":"https:\/\/www.mygreatlearning.com\/blog\/what-is-ridge-regression\/"},"modified":"2024-09-02T15:21:24","modified_gmt":"2024-09-02T09:51:24","slug":"what-is-ridge-regression","status":"publish","type":"post","link":"https:\/\/www.mygreatlearning.com\/blog\/what-is-ridge-regression\/","title":{"rendered":"What is Ridge Regression?"},"content":{"rendered":"\n<p><em><strong>Contributed by: <a href=\"https:\/\/www.linkedin.com\/in\/prashanth-a-bb122425\/\" target=\"_blank\" rel=\"nofollow noreferrer noopener\">Prashanth Ashok<\/a><\/strong><\/em><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"what-is-ridge-regression\"><strong>What is Ridge regression?<\/strong><\/h2>\n\n\n\n<p>Ridge<a href=\"https:\/\/www.mygreatlearning.com\/blog\/what-is-ridge-regression\/\" target=\"_blank\" rel=\"noreferrer noopener\"> <\/a><a href=\"https:\/\/www.mygreatlearning.com\/blog\/what-is-ridge-regression\/\">regression <\/a>is a model-tuning method that is used to analyze any data that suffers from multicollinearity. This method performs L2 regularization. When the issue of multicollinearity occurs, least-squares are unbiased, and variances are large, this results in predicted values being far away from the actual values.&nbsp;<\/p>\n\n\n\n<p><strong>The cost function for ridge regression:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size\"><strong><em>Min(||Y - X(theta)||^2 + \u03bb||theta||^2)<\/em><\/strong><\/p>\n\n\n\n<p>Lambda is the penalty term. \u03bb given here is denoted by an alpha parameter in the ridge function. So, by changing the values of alpha, we are controlling the penalty term. The higher the values of alpha, the bigger is the penalty and therefore the magnitude of coefficients is reduced.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>It shrinks the parameters. Therefore, it is used to prevent multicollinearity<\/li>\n\n\n\n<li>It reduces the model complexity by coefficient shrinkage<\/li>\n\n\n\n<li>Check out the free course on <a href=\"https:\/\/www.mygreatlearning.com\/academy\/learn-for-free\/courses\/regression-analysis-with-excel-hands-on\" target=\"_blank\" rel=\"noreferrer noopener\">regression analysis<\/a>.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"ridge-regression-models\"><strong>Ridge Regression Models&nbsp;<\/strong><\/h2>\n\n\n\n<p>For any type of regression machine learning model, the usual regression equation forms the base which is written as:<\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size\"><strong><em>Y = XB + e<\/em><\/strong><\/p>\n\n\n\n<p>Where Y is the dependent variable, X represents the independent variables, B is the regression coefficients to be estimated, and e represents the errors are residuals.&nbsp;<\/p>\n\n\n\n<p>Once we add the lambda function to this equation, the variance that is not evaluated by the general model is considered. After the data is ready and identified to be part of L2 regularization, there are steps that one can undertake.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"standardization\"><strong>Standardization&nbsp;<\/strong><\/h2>\n\n\n\n<p>In ridge regression, the first step is to standardize the variables (both dependent and independent) by subtracting their means and dividing by their standard deviations. This causes a challenge in notation since we must somehow indicate whether the variables in a particular formula are standardized or not. As far as standardization is concerned, all ridge regression calculations are based on standardized variables. When the final regression coefficients are displayed, they are adjusted back into their original scale. However, the ridge trace is on a standardized scale.<\/p>\n\n\n\n<p>Also Read: <a href=\"https:\/\/www.mygreatlearning.com\/blog\/support-vector-regression\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"Support Vector Regression in Machine Learning (opens in a new tab)\">Support Vector Regression in Machine Learning<\/a><\/p>\n\n\n\n    <div class=\"courses-cta-container\">\n        <div class=\"courses-cta-card\">\n            <div class=\"courses-cta-header\">\n                <div class=\"courses-learn-icon\"><\/div>\n                <span class=\"courses-learn-text\">Texas McCombs, UT Austin<\/span>\n            <\/div>\n            <p class=\"courses-cta-title\">\n                <a href=\"https:\/\/onlineexeced.mccombs.utexas.edu\/online-ai-machine-learning-course\" class=\"courses-cta-title-link\">Post Graduate Program in AI &amp; Machine Learning: Business Applications<\/a>\n            <\/p>\n            <p class=\"courses-cta-description\">Master in-demand AI and machine learning skills with this executive-level AI course\u2014designed to transform professionals into strategic tech leaders.<\/p>\n            <div class=\"courses-cta-stats\">\n                <div class=\"courses-stat-item\">\n                    <div class=\"courses-stat-icon courses-user-icon\"><\/div>\n                    <span>Duration: 7 months<\/span>\n                <\/div>\n                <div class=\"courses-stat-item\">\n                    <div class=\"courses-stat-icon courses-star-icon\"><\/div>\n                    <span>4.72\/5 Rating<\/span>\n                <\/div>\n            <\/div>\n            <a href=\"https:\/\/onlineexeced.mccombs.utexas.edu\/online-ai-machine-learning-course\" class=\"courses-cta-button\">\n                Take your First Step\n                <div class=\"courses-arrow-icon\"><\/div>\n            <\/a>\n        <\/div>\n    <\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"bias-and-variance-trade-off\"><strong>Bias and variance trade-off<\/strong><\/h2>\n\n\n\n<p>Bias and variance trade-off is generally complicated when it comes to building ridge regression models on an actual dataset. However, following the general trend which one needs to remember is:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The bias increases as \u03bb increases.<\/li>\n\n\n\n<li>The variance decreases as \u03bb increases.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"assumptions-of-ridge-regressions\"><strong>Assumptions of Ridge Regressions<\/strong><\/h2>\n\n\n\n<p>The assumptions of ridge regression are the same as those of linear regression: linearity, constant variance, and independence. However, as ridge regression does not provide confidence limits, the distribution of errors to be normal need not be assumed.<\/p>\n\n\n\n<p>Now, let\u2019s take an example of a linear regression problem and see how ridge regression if implemented, helps us to reduce the error.<\/p>\n\n\n\n<p>We shall consider a data set on Food restaurants trying to find the best combination of food items to improve their sales in a particular region.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"upload-required-libraries\"><strong>Upload Required Libraries<\/strong><\/h2>\n\n\n\n<pre class=\"wp-block-code has-medium-font-size\"><code>import numpy as np   \nimport pandas as pd\nimport os\n \nimport seaborn as sns\nfrom sklearn.linear_model import LinearRegression\nimport matplotlib.pyplot as plt   \nimport matplotlib.style\nplt.style.use('classic')\n \nimport warnings\nwarnings.filterwarnings(\"ignore\")\n\ndf = pd.read_excel(\"food.xlsx\")\n<\/code><\/pre>\n\n\n\n<p>After conducting all the EDA on the data, and treatment of missing values, we shall now go ahead with creating dummy variables, as we cannot have categorical variables in the dataset.<\/p>\n\n\n\n<pre class=\"wp-block-code has-medium-font-size\"><code>df =pd.get_dummies(df, columns=cat,drop_first=True)\n<\/code><\/pre>\n\n\n\n<p>Where columns=cat is all the categorical variables in the data set.<\/p>\n\n\n\n<p>After this, we need to standardize the data set for the Linear Regression method.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"scaling-the-variables-as-continuous-variables-has-different-weightage\"><strong>Scaling the variables as continuous variables has different weightage<\/strong><\/h2>\n\n\n\n<pre class=\"wp-block-code has-medium-font-size\"><code>#Scales the data. Essentially returns the z-scores of every attribute\n \nfrom sklearn.preprocessing import StandardScaler\nstd_scale = StandardScaler()\nstd_scale\n\ndf&#091;'week'] = std_scale.fit_transform(df&#091;&#091;'week']])\ndf&#091;'final_price'] = std_scale.fit_transform(df&#091;&#091;'final_price']])\ndf&#091;'area_range'] = std_scale.fit_transform(df&#091;&#091;'area_range']])\n<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"train-test-split\"><strong>Train-Test Split<\/strong><\/h2>\n\n\n\n<pre class=\"wp-block-code has-medium-font-size\"><code># Copy all the predictor variables into X dataframe\nX = df.drop('orders', axis=1)\n \n# Copy target into the y dataframe. Target variable is converted in to Log. \ny = np.log(df&#091;&#091;'orders']])\n\n# Split X and y into training and test set in 75:25 ratio\nfrom sklearn.model_selection import train_test_split\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25 , random_state=1)\n<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"linear-regression-model\"><strong>Linear Regression Model<\/strong><\/h2>\n\n\n\n<p>Also Read: <a href=\"https:\/\/www.mygreatlearning.com\/blog\/linear-regression-in-machine-learning\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"What is Linear Regression?  (opens in a new tab)\">What is Linear Regression? <\/a><\/p>\n\n\n\n<pre class=\"wp-block-code has-medium-font-size\"><code># invoke the LinearRegression function and find the bestfit model on training data\n \nregression_model = LinearRegression()\nregression_model.fit(X_train, y_train)\n\n# Let us explore the coefficients for each of the independent attributes\n \nfor idx, col_name in enumerate(X_train.columns):\n    print(\"The coefficient for {} is {}\".format(col_name, regression_model.coef_&#091;0]&#091;idx]))\n\nThe coefficient for week is -0.0041068045722690814\nThe coefficient for final_price is -0.40354286519747384\nThe coefficient for area_range is 0.16906454326841025\nThe coefficient for website_homepage_mention_1.0 is 0.44689072858872664\nThe coefficient for food_category_Biryani is -0.10369818094671146\nThe coefficient for food_category_Desert is 0.5722054451619581\nThe coefficient for food_category_Extras is -0.22769824296095417\nThe coefficient for food_category_Other Snacks is -0.44682163212660775\nThe coefficient for food_category_Pasta is -0.7352610382529601\nThe coefficient for food_category_Pizza is 0.499963614474803\nThe coefficient for food_category_Rice Bowl is 1.640603292571774\nThe coefficient for food_category_Salad is 0.22723622749570868\nThe coefficient for food_category_Sandwich is 0.3733070983152591\nThe coefficient for food_category_Seafood is -0.07845778484039663\nThe coefficient for food_category_Soup is -1.0586633401722432\nThe coefficient for food_category_Starters is -0.3782239478810047\nThe coefficient for cuisine_Indian is -1.1335822602848094\nThe coefficient for cuisine_Italian is -0.03927567006223066\nThe coefficient for center_type_Gurgaon is -0.16528108967295807\nThe coefficient for center_type_Noida is 0.0501474731039986\nThe coefficient for home_delivery_1.0 is 1.026400462237632\nThe coefficient for night_service_1 is 0.0038398863634691582\n\n\n#checking the magnitude of coefficients\nfrom pandas import Series, DataFrame\npredictors = X_train.columns\n \ncoef = Series(regression_model.coef_.flatten(), predictors).sort_values()\nplt.figure(figsize=(10,8))\n \ncoef.plot(kind='bar', title='Model Coefficients')\nplt.show()\n\n<\/code><\/pre>\n\n\n\n<p>Variables showing Positive effect on regression model are food_category_Rice Bowl, home_delivery_1.0, food_category_Desert,food_category_Pizza ,website_homepage_mention_1.0, food_category_Sandwich, food_category_Salad and area_range - these factors highly influencing our model.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"difference-between-ridge-regression-vs-lasso-regression\"><strong>Difference Between Ridge Regression Vs Lasso Regression<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table class=\"has-ast-global-color-5-background-color has-background\"><tbody><tr><td><strong>Aspect<\/strong><\/td><td><strong>Ridge Regression<\/strong><\/td><td><strong>Lasso Regression<\/strong><\/td><\/tr><tr><td>Regularization Approach<\/td><td>Adds penalty term proportional to square of coefficients<\/td><td>Adds penalty term proportional to absolute value of coefficients<\/td><\/tr><tr><td>Coefficient Shrinkage<\/td><td>Coefficients shrink towards but never exactly to zero<\/td><td>Some coefficients can be reduced exactly to zero<\/td><\/tr><tr><td>Effect on Model Complexity<\/td><td>Reduces model complexity and multicollinearity<\/td><td>Results in simpler, more interpretable models<\/td><\/tr><tr><td>Handling Correlated Inputs<\/td><td>Handles correlated inputs effectively<\/td><td>Can be inconsistent with highly correlated features<\/td><\/tr><tr><td>Feature Selection Capability<\/td><td>Limited<\/td><td>Performs feature selection by reducing some coefficients to zero<\/td><\/tr><tr><td>Preferred Usage Scenarios<\/td><td>All features assumed relevant or dataset has multicollinearity<\/td><td>When parsimony is advantageous, especially in high-dimensional datasets<\/td><\/tr><tr><td>Decision Factors<\/td><td>Nature of data, desired model complexity, multicollinearity<\/td><td>Nature of data, desire for feature selection, potential inconsistency with correlated features<\/td><\/tr><tr><td>Selection Process<\/td><td>Often determined through cross-validation<\/td><td>Often determined through cross-validation and comparative model performance assessment<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n    <div class=\"courses-cta-container\">\n        <div class=\"courses-cta-card\">\n            <div class=\"courses-cta-header\">\n                <div class=\"courses-learn-icon\"><\/div>\n                <span class=\"courses-learn-text\">Advance Your Data Science Career<\/span>\n            <\/div>\n            <p class=\"courses-cta-title\">\n                <a href=\"https:\/\/www.mygreatlearning.com\/pg-program-data-science-and-business-analytics-course\" class=\"courses-cta-title-link\">Post Graduate Program in Data Science<\/a>\n            <\/p>\n            <p class=\"courses-cta-description\">Master data science skills with a focus on in-demand Gen AI through real-world projects and expert-led learning.<\/p>\n            <div class=\"courses-cta-stats\">\n                <div class=\"courses-stat-item\">\n                    <div class=\"courses-stat-icon courses-user-icon\"><\/div>\n                    <span>Duration: 12 months<\/span>\n                <\/div>\n                <div class=\"courses-stat-item\">\n                    <div class=\"courses-stat-icon courses-star-icon\"><\/div>\n                    <span>Ratings: 4.78<\/span>\n                <\/div>\n            <\/div>\n            <a href=\"https:\/\/www.mygreatlearning.com\/pg-program-data-science-and-business-analytics-course\" class=\"courses-cta-button\">\n                Explore the Course\n                <div class=\"courses-arrow-icon\"><\/div>\n            <\/a>\n        <\/div>\n    <\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"ridge-regression-in-machine-learning\">Ridge Regression in Machine Learning<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ridge regression is a key technique in machine learning, indispensable for creating robust models in scenarios prone to overfitting and multicollinearity. This method modifies standard linear regression by introducing a penalty term proportional to the square of the coefficients, which proves particularly useful when dealing with highly correlated independent variables. Among its primary benefits, ridge regression effectively reduces overfitting through added complexity penalties, manages multicollinearity by balancing effects among correlated variables, and enhances model generalization to improve performance on unseen data.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The implementation of ridge regression in practical settings involves the crucial step of selecting the right regularization parameter, commonly known as lambda. This selection, typically done using cross-validation techniques, is vital for balancing the bias-variance tradeoff inherent in model training. Ridge regression enjoys widespread support across various machine learning libraries, with Python's <code>scikit-learn<\/code> being a notable example. Here, implementation entails defining the model, setting the lambda value, and employing built-in functions for fitting and predictions. Its utility is particularly notable in sectors like finance and healthcare analytics, where precise predictions and robust model construction are paramount. Ultimately, ridge regression\u2019s capacity to improve accuracy and handle complex data sets solidifies its ongoing importance in the dynamic field of machine learning.<\/li>\n<\/ul>\n\n\n\n<p>The higher the value of the beta coefficient, the higher is the impact.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Dishes like Rice Bowl, Pizza, Desert with a facility like home delivery and website_homepage_mention plays an important role in demand or number of orders being placed in high frequency.<\/li>\n\n\n\n<li>Variables showing negative effect on regression model for predicting restaurant orders: cuisine_Indian,food_category_Soup , food_category_Pasta , food_category_Other_Snacks.<\/li>\n\n\n\n<li>Final_price has a negative effect on the order - as expected.<\/li>\n\n\n\n<li>Dishes like Soup, Pasta, other_snacks, Indian food categories hurt model prediction on the number of orders being placed at restaurants, keeping all other predictors constant.<\/li>\n\n\n\n<li>Some variables which are hardly affecting model prediction for order frequency are week and night_service.<\/li>\n\n\n\n<li>Through the model, we are able to see object types of variables or categorical variables are more significant than continuous variables.<\/li>\n<\/ul>\n\n\n\n<p>Also Read: <a rel=\"noreferrer noopener\" aria-label=\"Introduction to Regular Expression in Python  (opens in a new tab)\" href=\"https:\/\/www.mygreatlearning.com\/blog\/regular-expression-in-python\/\" target=\"_blank\">Introduction to Regular Expression in Python <\/a><\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"Linear Regression Algorithm |  Linear Regression Machine Learning | Linear Regression Full Course\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/tFi4Y_y-GNM?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"regularization\"><strong>Regularization<\/strong><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Value of alpha, which is a hyperparameter of Ridge, which means that they are not automatically learned by the model instead they have to be set manually. We run a grid search for optimum alpha values<\/li>\n\n\n\n<li>To find optimum alpha for Ridge Regularization we are applying GridSearchCV<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-code has-medium-font-size\"><code>from sklearn.linear_model import Ridge\nfrom sklearn.model_selection import GridSearchCV\n \nridge=Ridge()\nparameters={'alpha':&#091;1e-15,1e-10,1e-8,1e-3,1e-2,1,5,10,20,30,35,40,45,50,55,100]}\nridge_regressor=GridSearchCV(ridge,parameters,scoring='neg_mean_squared_error',cv=5)\nridge_regressor.fit(X,y)\n\nprint(ridge_regressor.best_params_)\nprint(ridge_regressor.best_score_)\n\n{'alpha': 0.01}\n-0.3751867421112124\n<\/code><\/pre>\n\n\n\n<p>The negative sign is because of the known error in the Grid Search Cross Validation library, so ignore the negative sign.<\/p>\n\n\n\n<pre class=\"wp-block-code has-medium-font-size\"><code>predictors = X_train.columns\n \ncoef = Series(ridgeReg.coef_.flatten(),predictors).sort_values()\nplt.figure(figsize=(10,8))\ncoef.plot(kind='bar', title='Model Coefficients')\nplt.show()\n\n<\/code><\/pre>\n\n\n\n<p>From the above analysis we can decide that the final model can be defined as:<\/p>\n\n\n\n<p>Orders = 4.65 + 1.02home_delivery_1.0 + .46 website_homepage_mention_1 0+ (-.40* final_price) +.17area_range + 0.57food_category_Desert + (-0.22food_category_Extras) + (-0.73food_category_Pasta) + 0.49food_category_Pizza + 1.6food_category_Rice_Bowl + 0.22food_category_Salad + 0.37food_category_Sandwich + (-1.05food_category_Soup) + (-0.37food_category_Starters) + (-1.13cuisine_Indian) + (-0.16center_type_Gurgaon)<\/p>\n\n\n\n<p>Top 5 variables influencing regression model are:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>food_category_Rice Bowl<\/li>\n\n\n\n<li>home_delivery_1.0<\/li>\n\n\n\n<li>food_category_Pizza<\/li>\n\n\n\n<li>food_category_Desert<\/li>\n\n\n\n<li>website_homepage_mention_1<\/li>\n<\/ol>\n\n\n\n<p>The higher the beta coefficient, the more significant is the predictor. Hence, with certain level model tuning, we can find out the best variables that influence a business problem.<\/p>\n\n\n\n<p>If you found this blog helpful and want to learn more about such concepts, you can join <a href=\"https:\/\/www.mygreatlearning.com\/academy\" target=\"_blank\" rel=\"noreferrer noopener\">Great Learning Academy's free online courses<\/a> today. <\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"rideg-regression-faqs\"><strong>Rideg Regression FAQs<\/strong><\/h2>\n\n\n\n<div class=\"schema-faq wp-block-yoast-faq-block\"><div class=\"schema-faq-section\" id=\"faq-question-1705833425614\"><strong class=\"schema-faq-question\">What is Ridge Regression?<\/strong> <p class=\"schema-faq-answer\">Ridge regression is a linear regression method that adds a bias to reduce overfitting and improve prediction accuracy.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1705833440332\"><strong class=\"schema-faq-question\">How Does Ridge Regression Differ from Ordinary Least Squares?<\/strong> <p class=\"schema-faq-answer\">Unlike ordinary least squares, ridge regression includes a penalty on the magnitude of coefficients to reduce model complexity.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1705833455135\"><strong class=\"schema-faq-question\">When Should You Use Ridge Regression?<\/strong> <p class=\"schema-faq-answer\">Use ridge regression when dealing with multicollinearity or when there are more predictors than observations.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1705833466886\"><strong class=\"schema-faq-question\">What is the Role of the Regularization Parameter in Ridge Regression?<\/strong> <p class=\"schema-faq-answer\">The regularization parameter controls the extent of coefficient shrinkage, influencing model simplicity.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1705833480837\"><strong class=\"schema-faq-question\">Can Ridge Regression Handle Non-Linear Relationships?<\/strong> <p class=\"schema-faq-answer\">While primarily for linear relationships, ridge regression can include polynomial terms for non-linearities.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1705833495053\"><strong class=\"schema-faq-question\">How is Ridge Regression Implemented in Software?<\/strong> <p class=\"schema-faq-answer\">Most statistical software offers built-in functions for ridge regression, requiring variable specification and parameter value.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1705833505149\"><strong class=\"schema-faq-question\">How to Choose the Best Regularization Parameter?<\/strong> <p class=\"schema-faq-answer\">The best parameter is often found through cross-validation, using techniques like grid or random search.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1705833517357\"><strong class=\"schema-faq-question\">What are the Limitations of Ridge Regression?<\/strong> <p class=\"schema-faq-answer\">It includes all predictors, which can complicate interpretation, and choosing the optimal parameter can be challenging.<\/p> <\/div> <\/div>\n","protected":false},"excerpt":{"rendered":"<p>Ridge Regression is a technique for analyzing multiple regression data that suffer from multicollinearity. It adds a penalty to the regression coefficients to prevent 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which can complicate interpretation, and choosing the optimal parameter can be challenging.","inLanguage":"en-US"},"inLanguage":"en-US"}]}},"uagb_featured_image_src":{"full":["https:\/\/www.mygreatlearning.com\/blog\/wp-content\/uploads\/2020\/09\/iStock-1137271250.jpg",1365,768,false],"thumbnail":["https:\/\/www.mygreatlearning.com\/blog\/wp-content\/uploads\/2020\/09\/iStock-1137271250-150x150.jpg",150,150,true],"medium":["https:\/\/www.mygreatlearning.com\/blog\/wp-content\/uploads\/2020\/09\/iStock-1137271250-300x169.jpg",300,169,true],"medium_large":["https:\/\/www.mygreatlearning.com\/blog\/wp-content\/uploads\/2020\/09\/iStock-1137271250-768x432.jpg",768,432,true],"large":["https:\/\/www.mygreatlearning.com\/blog\/wp-content\/uploads\/2020\/09\/iStock-1137271250-1024x576.jpg",1024,576,true],"1536x1536":["https:\/\/www.mygreatlearning.com\/blog\/wp-content\/uploads\/2020\/09\/iStock-1137271250.jpg",1365,768,false],"2048x2048":["https:\/\/www.mygreatlearning.com\/blog\/wp-content\/uploads\/2020\/09\/iStock-1137271250.jpg",1365,768,false],"web-stories-poster-portrait":["https:\/\/www.mygreatlearning.com\/blog\/wp-content\/uploads\/2020\/09\/iStock-1137271250.jpg",640,360,false],"web-stories-publisher-logo":["https:\/\/www.mygreatlearning.com\/blog\/wp-content\/uploads\/2020\/09\/iStock-1137271250.jpg",96,54,false],"web-stories-thumbnail":["https:\/\/www.mygreatlearning.com\/blog\/wp-content\/uploads\/2020\/09\/iStock-1137271250.jpg",150,84,false]},"uagb_author_info":{"display_name":"Great 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