What is Multicollinearity in Regression Analysis? Causes, Impacts, and Solutions

What if the data you use to make predictions hides a hidden connection? Multicollinearity is an essential issue in regression analysis. It happens when two or more predictors in a model are closely related. This connection can make it hard to see how each variable affects the outcome, leading to unreliable estimates and incorrect conclusions. 

Understanding multicollinearity is essential not just for statisticians but for anyone creating predictive models. This article will explain multicollinearity, why it matters, and how to find it. This knowledge will help ensure your regression models produce accurate and meaningful insights. 

Let’s get started.

What Is Multicollinearity In Regression Analysis?

Multicollinearity occurs in regression when independent variables are highly correlated, distorting coefficients and reducing model reliability. It is typically identified using the Variance Inflation Factor (VIF), with values above 5 or 10 signaling significant multicollinearity, or through correlation coefficients near ±1. 

For instance, in a house price model, "square footage" and "number of rooms" often correlate strongly; dropping one might simplify interpretation while combining them into an index retains predictive power. 

Identifying multicollinearity early is crucial in machine learning to prevent overfitting and ensure models generalize effectively across unseen data.

Let’s now look at some examples to get a better understanding of multicollinearity.

Examples Of Multicollinearity In Regression Analysis

Multicollinearity in regression analysis can manifest in various ways. Before diving into these examples, it's important to note that these scenarios can distort the results of your regression analysis and lead to misinterpretation of data.

Here are some common examples of where multicollinearity might occur.

1. Predictor Variables with Similar Information

Scenario: You're building a model to predict house prices and include both "Square Footage" and "Number of Rooms" as predictors. These variables are highly correlated because larger houses typically have more rooms.

Hypothetical Data:

• House 1: Square Footage = 2000, Rooms = 4
• House 2: Square Footage = 3000, Rooms = 6
• House 3: Square Footage = 1500, Rooms = 3

Impact: The model might struggle to determine the independent effect of "Square Footage" versus "Number of Rooms" on house prices. This redundancy can inflate standard errors and reduce the reliability of coefficient estimates.

2. Economic Indicators

Scenario: When modeling stock market returns, including predictors like "Inflation Rate" and "Interest Rates" can introduce challenges, as these variables are often correlated due to the interconnectedness of economic policies.

Hypothetical Data:

• Month 1: Inflation = 2%, Interest Rate = 3%
• Month 2: Inflation = 3%, Interest Rate = 4%
• Month 3: Inflation = 1.5%, Interest Rate = 2%

Impact: Multicollinearity can complicate feature selection in predictive models for financial datasets. 

For example, in a machine learning context, training a neural network with collinear inputs might lead to overfitting, as the model struggles to assign appropriate weights to these correlated features. 

This can result in the model incorrectly emphasizing one variable over another, obscuring the true drivers of stock market returns and reducing the model's generalizability.

3. Geographic Data

Scenario: You're building a model to predict crop yields and include both "Average Temperature" and "Rainfall" as predictors. In certain regions, these variables are closely linked—higher temperatures often result in increased evaporation and reduced rainfall.

Hypothetical Data:

• Region 1: Temperature = 25°C, Rainfall = 100mm
• Region 2: Temperature = 30°C, Rainfall = 80mm
• Region 3: Temperature = 20°C, Rainfall = 120mm

Impact: The model may mistakenly attribute the effect of "Temperature" to "Rainfall" (or vice versa), leading to misleading predictions about crop yields.

Multicollinearity can create significant challenges in regression analysis by distorting coefficient estimates and reducing the interpretability of models. 

Identifying and addressing multicollinearity—via techniques such as Variance Inflation Factor (VIF), Principal Component Analysis (PCA), or removing redundant variables—can improve model reliability and predictive power.

Also Read: Linear Regression in Machine Learning: Everything You Need to Know

Next, it is crucial to understand the underlying causes of multicollinearity in machine learning, as this knowledge will help you address it effectively in your models. So, let’s dive in.

What Causes Multicollinearity In Machine Learning?

Multicollinearity in machine learning models hinders model accuracy by distorting variable relationships, especially in regression. It often arises from redundant features (e.g., total sales vs. regional sales) or poorly engineered inputs like overlapping dummy variables. 

High-dimensional datasets can amplify challenges for algorithms sensitive to linear dependence, such as linear regression. These challenges are crucial in machine learning, where algorithms like linear models or even random forests may struggle with feature redundancies, reducing interpretability and performance.

To better understand the impacts, consider the following table that highlights the key challenges brought about by multicollinearity.

Also Read: Difference Between Linear and Logistic Regression: A Comprehensive Guide for Beginners in 2025

To dive deeper into the specific causes, it's important to first distinguish between different types of multicollinearity. Let’s have a look at these types.

Structural Multicollinearity

Structural Multicollinearity refers to the correlation between independent variables that arises due to the inherent structure of the data. This issue can distort model predictions and affect the reliability of statistical analyses. 

To better understand the factors contributing to structural multicollinearity, consider the following causes:

• Data Structure: Correlations may naturally arise from the inherent structure of the data, such as time series data or datasets with hierarchical relationships. For example, lagged variables or trends in time series datasets often correlate with each other.
• Model Design Flaws: Poorly designed models or experiments can inadvertently introduce structural multicollinearity. This often happens when predictors are closely related due to how the data is organized or processed.
• Measurement Redundancy: Structural multicollinearity can also result from independent variables capturing similar or overlapping information. For instance, multiple variables representing the same concept can lead to redundancy.

Addressing structural multicollinearity during model design and carefully selecting variables can prevent distorted results and improve the accuracy of the analysis.

Also Read: What is Multinomial Logistic Regression? Definition & Examples

Next, let’s explore data-based causes that arise due to flawed experimental or observational data collection.

Data-Based Multicollinearity

Data-based multicollinearity typically arises in poorly designed experiments or observational data collection, where the independent variables are inherently correlated due to the structure of the data.

Several factors can contribute to this issue, and it is crucial to address them early in the data collection phase. These include:

• Small Sample Size: Limited data points can exacerbate correlations between predictors. For example, analyzing customer purchasing behavior with only 30 observations may yield misleading relationships due to insufficient variability.
• Highly Correlated Variables: Including variables that are inherently related in the dataset can lead to multicollinearity. For instance, when predicting company revenue, metrics like "total sales" and "number of transactions" often overlap conceptually and statistically.
• Improper Sampling Methods: Biased or inconsistent sampling can artificially inflate correlations. For example, gathering data from a single geographic location or demographic group may introduce biases that do not generalize to a broader population.

These data-based causes should be addressed during the initial stages of data collection to prevent multicollinearity from distorting the results.

Also Read: Linear Regression Model: What is & How it Works?

Next, let’s look at how the lack of sufficient data or incorrect handling of dummy variables can also contribute to multicollinearity.

Lack Of Data Or Incorrect Use Of Dummy Variables

Inadequate data or improper handling of dummy variables can create multicollinearity by falsely introducing correlations between variables. Several factors contribute to multicollinearity, and understanding these can help mitigate its impact.

Here are some of the factors.

• Small Data Sets: A lack of sufficient data may lead to artificially strong relationships between variables, causing multicollinearity. For example, if you're analyzing customer satisfaction with only 50 survey responses, the small sample size could result in correlations that don’t exist in a larger, more representative sample.
• Improper Dummy Variable Coding: Incorrectly coding categorical variables can result in redundant variables that overlap. For instance, if you create dummy variables for "Region" with categories like "North", "South", and "East", and mistakenly omit one category, this may cause correlation between the "North" and "South" variables.

These issues can be mitigated by ensuring that the data is comprehensive and correctly formatted, which will reduce the risk of multicollinearity.

Also Read: Linear Regression Explained with Example

As you continue to address multicollinearity, consider other potential sources, such as the inclusion of derived variables.

Inclusion Of Variables Derived From Other Variables

Multicollinearity can arise when variables are derived from other existing variables in the model, leading to high correlations. 

Several sources of this type of multicollinearity include:

• Derived Variables: Including variables like total investment income when individual components (e.g., dividends and interest) are already in the model. For example, using both "total salary" and "salary from overtime" can skew results, as overtime is part of total salary.
• Redundant Metrics: Including multiple forms of the same variable, such as "total sales" and "average sales per customer," which are highly correlated and make it hard to assess their individual impacts.

By eliminating redundant or unnecessary derived variables, multicollinearity can be avoided, ensuring a more accurate and interpretable model.

Also Read: How to Perform Multiple Regression Analysis?

Finally, it is important to recognize how nearly identical variables can cause multicollinearity, even when they seem distinct at first glance.

Use Of Nearly Identical Variables

When nearly identical variables are included in a regression model, they often become highly correlated, resulting in multicollinearity. This can distort the model's ability to estimate relationships between predictors and the outcome variable accurately.

Here are several common scenarios that contribute to this issue, and it’s essential to address them during the data preparation phase.

• Multiple Units of Measurement: Including variables like weight in both pounds and kilograms can lead to multicollinearity due to their strong linear relationship. For example, the correlation between weight in pounds and kilograms is perfect, causing redundancy and multicollinearity.
• Duplicate Variables: Variables that are nearly identical but represented in different forms, such as price in both original and adjusted terms, can also create multicollinearity. For example, including both "initial price" and "inflated price" as separate variables can confuse the model and lead to unreliable results.

To address these issues, it is advisable to eliminate redundant variables that measure the same underlying concept, ensuring a more stable and accurate regression model.

Join upGrad's Linear Regression - Step by Step Guide course that can help you understand regression techniques and handle challenges effectively!

Effective Methods To Check For Multicollinearity

To assess the presence of multicollinearity in your regression analysis, you need to implement specific methods that can effectively detect its occurrence. Multicollinearity in machine learning can lead to unreliable predictions and misleading statistical inference, so recognizing it early is crucial. 

One of the most effective techniques to identify multicollinearity is by calculating the Variance Inflation Factor (VIF). A high VIF indicates that a predictor variable is highly correlated with others, suggesting multicollinearity. In social sciences, a VIF above 5 is concerning, while in machine learning, a VIF over 10 signals significant issues.

Here are some key steps to help you identify multicollinearity.

1. Calculate Variance Inflation Factor (VIF)

The Variance Inflation Factor quantifies how much the variance of a regression coefficient is inflated due to collinearity with other predictors. A higher VIF indicates stronger multicollinearity:

• Thresholds: In machine learning, a VIF exceeding 10 suggests significant multicollinearity. In social sciences, a VIF over 5 might already be concerning.
• Implementation: During data preprocessing, calculate VIF for each feature after standardization. Remove or combine highly correlated variables with a VIF > 10 to simplify the model.
• Example: In a housing price model, the VIF for "square footage" was 12, indicating it was highly correlated with "house size." Removing one improved model stability.

2. Examine the Correlation Matrix

A correlation matrix reveals pairwise correlations among features. High correlations often indicate multicollinearity:

• Thresholds: Correlation coefficients above 0.8 typically suggest a problem.
• Implementation: Visualize correlations using a heatmap to identify clusters of highly correlated features. Consider dimensionality reduction techniques like PCA to address issues.
• Example: In an economic model, a correlation of 0.88 between "GDP growth rate" and "interest rates" signaled multicollinearity. Combining these into an index variable improved the analysis.

3. Evaluate Tolerance Values

Tolerance measures the extent to which a variable is independent of others. It is the reciprocal of VIF (Tolerance = 1 / VIF):

• Thresholds: Tolerance values below 0.1 indicate significant multicollinearity.
• Implementation: Include tolerance checks as part of the feature selection pipeline to identify problematic predictors early.
• Example: In an advertising budget model, the tolerance for "advertising spend" was 0.05, highlighting a strong correlation with "promotion budgets." Addressing this improved feature interpretability.

4. Perform Eigenvalue Analysis

Eigenvalue analysis examines the linear dependency structure of predictors. Small eigenvalues indicate strong multicollinearity:

• Thresholds: Eigenvalues close to zero suggest potential issues.
• Implementation: Decompose the covariance matrix of predictors and analyze the eigenvalues. Features contributing to small eigenvalues may be removed or transformed.
• Example: In an employee performance dataset, an eigenvalue close to zero indicated a dependency between "experience" and "training hours," necessitating feature engineering.

5. Run a Condition Index Test

The condition index, derived from eigenvalues, measures multicollinearity severity:

• Thresholds: A condition index above 30 signals severe multicollinearity.
• Implementation: Use condition index diagnostics alongside eigenvalue analysis. Address high condition indices by dropping or combining correlated features.
• Example: In a marketing model, a condition index of 35 pointed to high correlation between "TV ads" and "online ads." Merging these into a composite feature enhanced model performance.

Detecting multicollinearity early in your regression analysis is essential for building a reliable and interpretable model. 

Strengthen your analysis skills—enroll in upGrad’s Linear Algebra for Analysis course today and master multicollinearity detection with confidence!

How To Detect Multicollinearity Using A Variance Inflation Factor Machine Learning (VIF)

Detecting multicollinearity in regression analysis using the variance inflation factor machine learning (VIF) is one of the most effective methods for understanding the relationships between predictor variables. 

In machine learning, the VIF can help uncover the severity of multicollinearity, which can distort the interpretation of model coefficients and affect predictive accuracy. By using the VIF, you can pinpoint problematic variables that may need adjustment or removal. 

Here's a step-by-step guide on how to detect multicollinearity in a dataset using VIF.

• Step 1: Prepare Your Dataset
  Ensure your dataset is cleaned and preprocessed. Remove missing values or outliers before proceeding with VIF calculation.
• Step 2: Calculate the Correlation Matrix
  Begin by checking the correlation matrix between all independent variables. This helps identify potential high correlations that might signal multicollinearity.
• Step 3: Compute the VIF for Each Predictor
  Using a statistical software package like Python or R, compute the VIF for each independent variable. A VIF score over 10 is a red flag.
• Step 4: Interpret the VIF Results
  Analyze the VIF values for each variable. If any predictor has a high VIF, it suggests that the variable is highly correlated with one or more other predictors.
• Step 5: Address Multicollinearity
  If high VIF values are found, you can either remove variables causing the multicollinearity or combine them into a single predictor using dimensionality reduction techniques such as Principal Component Analysis (PCA).

Example: In a housing price prediction model, "square footage" and "number of bedrooms" show a high correlation (r = 0.85), indicating potential multicollinearity. The VIF for "square footage" is 15, signaling strong correlation with other predictors. 

After removing "square footage" and retaining "number of bedrooms," VIF values decrease, improving the model's accuracy. This example illustrates how detecting multicollinearity with VIF enhances model reliability.

Also Read: Recursive Feature Elimination: What It Is and Why It Matters?

Factors To Consider While Interpreting Multicollinearity In SPSS

When interpreting multicollinearity in SPSS, several factors come into play that can significantly affect your regression analysis. It's essential to keep these factors in mind, as multicollinearity can skew your results, making it difficult to identify individual variable effects. 

The variance inflation factor machine learning (VIF) is commonly used within SPSS to detect multicollinearity. 

Here are the factors that influence its interpretation, which is crucial for accurately assessing your model's integrity.

• VIF and Tolerance: SPSS provides both VIF and tolerance values. VIF values above 10 and tolerance values below 0.1 indicate high multicollinearity, suggesting that the predictors are linearly dependent.
• Significance of Predictor Variables: Pay attention to the significance of each predictor variable. High multicollinearity leads to inflated standard errors, which could cause significant variables to appear insignificant.
• Eigenvalues: Eigenvalues provide insights into the multicollinearity in the dataset. Small eigenvalues indicate linear dependence among variables, while larger eigenvalues suggest less correlation.
• Correlation Matrix: The correlation matrix is an excellent first step in identifying multicollinearity. Strong correlations (above 0.9) between predictors suggest that multicollinearity might be an issue.
• Variance Inflation Factor (VIF) in SPSS Output: SPSS provides VIF as part of the regression output. A VIF score exceeding 10 typically signals multicollinearity, meaning you should investigate potential corrections for it.

Accurately interpreting multicollinearity in SPSS requires careful consideration of various statistical outputs, including VIF, tolerance, eigenvalues, and the correlation matrix. 

5 Practical Approaches To Fix Multicollinearity

Multicollinearity can complicate regression analysis, making it difficult to isolate the individual effects of predictor variables. Fortunately, several practical approaches can help mitigate or eliminate multicollinearity. 

By applying these techniques, you can not only reduce multicollinearity but also enhance the reliability and accuracy of your results. Below are five practical approaches to fixing multicollinearity.

Selection of Variables

One of the simplest methods to tackle multicollinearity is to remove redundant or highly correlated predictor variables. Often, variables that are highly correlated with one another can introduce noise and lead to inflated coefficients. 

Key Points to Consider:

• Identify Correlated Variables: Start by examining the correlation matrix to identify highly correlated variables. For example, in a sales prediction model, "advertising budget" and "marketing spend" may show a correlation of 0.9, indicating redundancy. Removing one of these predictors can help reduce multicollinearity.
• Use Domain Knowledge: Domain expertise helps to distinguish which variables are truly important. For instance, in a healthcare model, "patient age" and "age group" might be correlated. However, you could remove "age group" based on the understanding that "patient age" captures all necessary information.
• Refine the Model: After removing collinear variables, refit the model and evaluate its performance. For example, removing redundant financial variables in a stock market prediction model can lead to a more stable and efficient model, with improved performance metrics.

Now that you understand how selecting variables can resolve multicollinearity, let’s explore the next technique: transformation of variables.

Also Read: What is Linear Discriminant Analysis for Machine Learning?

Transformation of Variables

Another practical approach involves transforming the variables. Methods such as logarithmic or square root transformations can help reduce the correlation between highly correlated predictors. 

Key Points to Consider:

• Logarithmic Transformation: In a dataset predicting sales, "advertising spend" shows a skewed distribution. By applying a log transformation to "advertising spend," you linearize the relationship between it and other variables, reducing collinearity with "sales growth." 
• Square Root Transformation: In a model predicting property prices, "land area" and "number of rooms" are highly correlated. Applying a square root transformation to "land area" helps reduce the correlation between the two, making the model more stable.
• Effectiveness of Transformation: After transforming variables, revisit the correlation matrix to confirm reduced collinearity. If the adjusted model performs better in terms of accuracy and stability, the transformations were successful.

Also Read: How to Compute Square Roots in Python

Having covered variable transformation, let's now look at another powerful tool: Principal Component Analysis (PCA).

Principal Component Analysis (PCA)

Principal Component Analysis (PCA) is a dimensionality reduction technique often used to address multicollinearity. It creates new, uncorrelated variables called principal components, which are linear combinations of the original features.

Key Points to Consider:

• Dimensionality Reduction: PCA combines correlated variables into fewer components. For example, variables like age, income, and education in customer behavior data can be condensed into a single component, such as "socioeconomic status."
• Application in Regression: By transforming correlated features into principal components, PCA simplifies models while retaining key patterns. For instance, in house price prediction, PCA can combine square footage, number of rooms, and lot size into one component to improve model stability.
• Trade-offs: While PCA reduces complexity, principal components lose direct interpretability. For example, understanding how "socioeconomic status" affects predictions may require interpreting multiple original variables.
• Selecting Components: Focus on components that explain most of the variance. If the first two components explain 90% of the variance in customer segmentation, they are sufficient for further analysis.

Also Read: What is Ridge Regression in Machine Learning?

With PCA as an option, let’s now explore regularization methods as a technique to handle multicollinearity.

Use Regularization Methods

Regularization methods such as RIDGE, LASSO, and Bayesian linear regression are effective in addressing multicollinearity. These methods apply penalty terms to the regression model, helping to shrink the coefficients and reduce the impact of collinearity. 

Key Points to Consider:

• Ridge Regression: Penalizes large coefficients, reducing the influence of correlated features. For example, in predicting housing prices, Ridge regression ensures balanced contributions from square footage and number of rooms.
• Lasso Regression: Performs feature selection by shrinking some coefficients to zero. In predictive healthcare models, Lasso can eliminate redundant features like closely related medical tests, focusing only on the most critical predictors.
• Bayesian Regression: Incorporates prior knowledge to refine predictions. For instance, in clinical trials, Bayesian regression uses prior medical insights to account for correlations between treatment variables and patient characteristics.

Also Read: Isotonic Regression in Machine Learning: Understanding Regressions in Machine Learning

Having discussed regularization, let’s turn to the final approach: increasing the sample size.

Increase Sample Size

Increasing the sample size can help alleviate the effects of multicollinearity. With larger datasets, it becomes easier to distinguish the individual effects of predictor variables. A larger sample size reduces the possibility of collinearity distorting the results.

Key Points to Consider:

• Larger Dataset: When you add more observations, the model can better distinguish between correlated predictors, reducing multicollinearity. Example: In a marketing campaign analysis, adding more customer data allows the model to better distinguish between the effects of age and income, reducing multicollinearity.
• Improved Precision: Larger datasets lead to more precise estimates, making it easier to interpret the effects of each variable. Example: In real estate price prediction, a larger dataset helps provide more accurate coefficient estimates for features like location and square footage, improving model stability.
• Practical Limitations: Increasing sample size may not always be feasible, but when possible, it is a highly effective method for reducing multicollinearity. Example: In healthcare studies, while increasing sample size can reduce multicollinearity, limited access to patient data might make it impractical to gather a larger dataset.

Fixing multicollinearity is not always a one-size-fits-all solution. Each of these methods can help mitigate its effects, but the right approach depends on the nature of your data and the context of your analysis.

Also Read: What is Bayesian Statistics: Beginner’s Guide

Now, let’s have a look at some of the real life scenarios of multicollinearity in data analysis.

Real-Life Scenarios Of Multicollinearity In Data Analysis

Multicollinearity in regression analysis can distort the interpretation of coefficients, leading to unreliable results. One type of multicollinearity is structural multicollinearity, where the predictors are inherently related through the underlying structure of the model. 

The relationship between these two variables can cause multicollinearity, making it difficult to discern the individual effect of each on house price. 

Here's a step-by-step approach to resolving structural multicollinearity.

• Step 1: Examine the Correlation Matrix
  Begin by checking the correlation matrix of your independent variables. A high correlation (typically above 0.8) between square footage and the number of rooms suggests potential multicollinearity.
• Step 2: Calculate the Variance Inflation Factor (VIF)
  Use the variance inflation factor machine learning (VIF) to quantify the severity of multicollinearity. VIF values greater than 5 or 10 indicate high multicollinearity. In our case, if both square footage and number of rooms have high VIFs, this confirms the issue.
• Step 3: Remove or Combine Collinear Variables
  Once you identify the collinear variables, decide how to handle them. You can either remove one of the correlated variables or combine them into a single predictor. For example, combining square footage and the number of rooms into a new variable—such as "size"—can eliminate the correlation between the two.
• Step 4: Refitting the Model
  After removing or combining variables, refit the regression model. This will help you assess the impact of these changes on the model’s accuracy and stability. The multicollinearity issue should now be resolved.
• Step 5: Validate the Model
  Finally, validate the model by checking the new VIF values and ensuring that the multicollinearity has been addressed. You can also examine the coefficient estimates to ensure they are now stable and meaningful.

Addressing structural multicollinearity in regression analysis not only improves model accuracy but also ensures reliable interpretations of the results. With these steps, you can effectively tackle multicollinearity and enhance the predictive power of your model.

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Reference(s):
https://www.manufacturingtodayindia.com/data-driven-decisions-lead-the-way-for-78-of-indian-business-leaders
https://www.trade.gov/market-intelligence/india-artificial-intelligence