What is Multicollinearity? Causes and Solutions

What is multicollinearity?

Imagine trying to predict a company’s sales using data on advertising, product quality, and customer reviews. But suddenly, your model struggles, and you realize that the advertising and product quality variables are strongly related. This is when multicollinearity becomes a factor.

In data analysis, multicollinearity occurs when several independent variables show a high degree of correlation. This situation complicates the model, making it challenging to determine the true effect of each variable individually.

In 2023, a KPMG survey revealed that 60% of companies rely heavily on data for decision-making. Given this heavy dependence on data, grasping the concept of multicollinearity is essential for making precise forecasts. Without addressing it, the risk of misinterpreting results increases significantly. For example, inflated standard errors can lead to incorrect conclusions about which factors truly drive outcomes.

The problem doesn’t stop there. Multicollinearity may compromise the trustworthiness of your coefficients, resulting in suboptimal decision-making.

What exactly is multicollinearity, and why does it matter? Understanding how to detect and manage multicollinearity is essential for ensuring your models deliver the valuable insights necessary for sound decision-making. Whether you analyze your business trends, healthcare data, or economic factors, this issue can make or break your analysis.

Let’s explore multicollinearity further.

Table of Contents:

1. What is Multicollinearity?
2. Why Does Multicollinearity Cause Problems?
3. What are the Effects of Multicollinearity?
4. What are the Reasons for Multicollinearity?
5. How Many Types of Multicollinearity?
6. How to Detect Multicollinearity?
7. How to Fix Multicollinearity?
8. How to Analyze Multicollinearity in Excel?
9. Wrap Up

First…

What is Multicollinearity?

Definition: Multicollinearity arises when several independent variables in a regression model show a high degree of correlation. This close association makes it difficult to identify which variable has a significant impact on the dependent variable. Consequently, it can lead to larger standard errors, reducing the reliability of the statistical analysis.

Detecting multicollinearity is crucial for accurate data analysis. If left unchecked, it can lead to misleading conclusions, affecting decisions in fields like business, healthcare, and economics. Addressing multicollinearity enhances the precision and reliability of your predictions in analyses.

Why Does Multicollinearity Cause Problems?

Multicollinearity might sound technical, but its impact on your data models is real and can’t be ignored. Consider creating a regression model where certain variables are intertwined to the extent that they cloud the findings. This is what occurs with multicollinearity.

Let’s explore why this causes problems.

• Unreliable coefficient estimates: When independent variables demonstrate a high degree of correlation, the model struggles to produce precise coefficient estimates. This leads to estimates that are inconsistent and untrustworthy.
• Increased standard errors: Multicollinearity elevates standard errors, complicating the assessment of a variable’s statistical significance.
• Diminished clarity: Strong correlations among variables cloud the analysis, making it difficult to determine which factor genuinely influences the outcomes.
• Increased overfitting risk: Multicollinearity raises the chances of overfitting, causing the model to become overly customized to the training data. This reduces its effectiveness on unfamiliar data.
• Collinearity diagnostic problems: Detecting multicollinearity isn’t always straightforward. Some diagnostics might miss the problem, leading to false confidence in your model.
• Violation of assumptions: Regression models assume that independent variables aren’t too closely related. Multicollinearity violates this assumption, potentially invalidating the results.

What are the Effects of Multicollinearity?

Imagine trying to figure out which ingredient makes a dish taste great. However, the flavors are so blended that it’s impossible to pinpoint the standout. That’s the issue that arises with multicollinearity in your regression analysis. It mixes up variables and makes it hard to see which one truly matters.

Here’s a breakdown of the effects:

• Inflated standard errors: Multicollinearity elevates the standard errors, complicating the assessment of each variable’s significance.
• Unstable coefficients: When independent variables are closely related, the model finds it challenging to produce stable coefficients, resulting in unreliable predictions.
• Challenges in evaluating the impact of individual variables: Strong correlations among variables make it hard to determine which one significantly influences the dependent variable.
• Decreased transparency: Increased multicollinearity can obscure the data interpretation of your analysis, hindering the extraction of meaningful insights from the results.
• Potential for overfitting: Increased multicollinearity may lead your model to adapt excessively to the training dataset. As a result, it may perform well on past data while struggling with fresh, unseen datasets.
• Collinearity diagnostic issues: Identifying multicollinearity isn’t always easy, and some diagnostic tools may miss it, leading to flawed conclusions.
• Violation of assumptions: Regression models assume that independent variables are not overly related. Multicollinearity breaks this rule, potentially invalidating your model’s results.

What are the Reasons for Multicollinearity?

Multicollinearity can sneak into your regression models without warning, making your analysis far less reliable. Ever wonder why it happens? Here are the most common causes:

• High correlation among independent variables: When independent variables exhibit robust connections, the likelihood of multicollinearity becomes nearly unavoidable.
• Inclusion of polynomial terms: Adding polynomial terms to capture non-linear relationships can introduce multicollinearity, especially if the original variables are already correlated.
• Dummy variables: Including multiple dummy variables can increase collinearity, particularly when they overlap or represent similar categories.
• Data collection issues: Poor sampling techniques or limited data can lead to multicollinearity if the independent variables aren’t varied enough.
• Overfitting the model: When a model excessively adapts to the data, it frequently leads to multicollinearity issues. Why does this happen? The variables become overly specific to the dataset.
• Variable interactions: When interaction terms are utilized to evaluate the combined effect of variables, multicollinearity can occur if the initial variables show a high degree of correlation.
• Redundant features: Including variables that essentially measure the same thing introduces redundancy, contributing to multicollinearity.

How Many Types of Multicollinearity?

Multicollinearity appears in several forms, each influencing your regression model differently. So, what are the different types of multicollinearity? Generally, it falls into two categories: perfect and imperfect.

Let’s delve into these types to understand their impact on your data evaluation better.

1. Perfect Multicollinearity: This situation occurs when one predictor variable is an exact linear derivative of the remaining variables. Essentially, it allows for precise prediction of one variable using another. Regression models cannot calculate coefficients in such cases, rendering the analysis ineffective.
2. Imperfect Multicollinearity: This type is commonly found in real-world scenarios. Imperfect multicollinearity arises when independent variables exhibit a strong correlation but are not perfectly correlated. While the model can still run, the results may be less reliable, with inflated standard errors and unstable coefficients.

How to Detect Multicollinearity?

Detecting multicollinearity is crucial to ensure your model is reliable and provides meaningful insights. But how can you spot it? Here are the methods that help reveal the hidden relationships between variables.

1. Correlation Matrix: This is one of the simplest ways to detect multicollinearity. It shows the relationships between your independent variables. High correlations (above 0.8 or 0.9) are a red flag for multicollinearity.
2. Variance Inflation Factor (VIF): VIF quantifies how much a variable’s variance is inflated due to multicollinearity. A VIF value over 10 suggests a high degree of multicollinearity that may need attention.
3. Condition Index: The condition index helps detect multicollinearity by examining the eigenvalues of the variable matrix. A high condition index (over 30) indicates potential multicollinearity.
4. Tolerance: Tolerance is the reciprocal of VIF. A low tolerance value (less than 0.1) indicates multicollinearity. It shows how much variance in one independent variable is not explained by the others.
5. Eigenvalues: Examining eigenvalues can also highlight multicollinearity. Two or more variables are highly correlated when eigenvalues are close to zero.

How to Fix Multicollinearity?

Once you detect multicollinearity, the next step is fixing it to make your model more robust. Here are some effective strategies.

1. Remove variables: If two or more variables are highly correlated, removing one can solve the issue. This simplifies the model and reduces redundancy.
2. Combine variables: When variables are too similar, combining them into a single variable can help reduce multicollinearity while retaining the information.
3. Increase sample size: If the problem stems from a small sample, increasing the number of data points can reduce multicollinearity, making the model more stable.
4. Centering variables: Subtracting the mean from the variables can reduce multicollinearity. This technique helps, especially when polynomial terms are involved.
5. Regularization techniques: Methods like Ridge and Lasso regression apply penalties to reduce the impact of multicollinearity. This makes the model coefficients more stable and reliable.

How to Analyze Multicollinearity in Excel?

Data analysis can feel like finding a needle in a haystack. Multicollinearity only makes it trickier.

Data visualization is key to unraveling these tangled relationships, but Excel’s basic charts fall flat.

This is where ChartExpo steps in to save the day. It turns complex data into clear, insightful visuals, making it easier to decode and visualize.

Let’s learn how to install ChartExpo in Excel.

1. Open your Excel application.
2. Open the worksheet and click the “Insert” menu.
3. You’ll see the “My Apps” option.
4. In the Office Add-ins window, click “Store” and search for ChartExpo on my Apps Store.
5. Click the “Add” button to install ChartExpo in your Excel.

ChartExpo charts are available both in Google Sheets and Microsoft Excel. Please use the following CTAs to install the tool of your choice and create beautiful visualizations with a few clicks in your favorite tool.

Multicollinearity Analysis Example

Let’s analyze the multicollinearity example data below in Excel using ChartExpo.

Ad Impressions	Ad Views
4310	400
4343	430
8705	855
9423	889
9679	905
10226	995
11953	1005
12118	1123
12380	1167
12983	1198
13086	1207
16106	1390
16152	1398
16481	1402
16773	1475
16890	1505
18198	1603
18650	1685
18697	1695
20576	1750
20684	1786
21582	1897
22145	1978
22842	1956
23837	2013

• To get started with ChartExpo, install ChartExpo in Excel.
• Now Click on My Apps from the INSERT menu.

• Choose ChartExpo from My Apps, then click Insert.

• Once it loads, scroll through the charts list to locate and choose the “Scatter Plot”.

• Add your data to an Excel sheet and click the Create Chart Manually button, as shown below.

• Select your column and ChartExpo and click the “Create Chart” button.

• ChartExpo will generate the visualization below for you.

• If you want to add anything to the chart, click the Edit Chart button:
• You can change the size of the circle as follows:

• You can add the trend line by clicking on the Settings button as follows:

• Click the pencil icon next to the Chart Header to change the title.
• It will open the properties dialog. Under the Text section, you can add a heading in Line 1 and enable Show.
• Give the appropriate title of your chart and click the Apply button.

• You can hide the Datapoint Label as follows:

• Click the “Save Changes” button to persist the changes made to the chart.

• Your final Scatter Plot will look like the one below.

Insights

• There is a strong correlation between ad impressions and views.
• Impressions increase consistently alongside ad views.
• The conversion rate varies, showing significant peaks at higher impression levels.
• This suggests potential for optimizing ad placements and targeting strategies.

FAQs

What is a real-life example of multicollinearity?

A real-life example of multicollinearity is in housing prices. Factors like square footage, number of bedrooms, and number of bathrooms often correlate. Larger houses tend to have more rooms, making it hard to separate their individual impact on price.

Is multicollinearity the same as correlation?

No, multicollinearity is not the same as correlation. Correlation measures the strength of the relationship between two variables. Multicollinearity occurs when two or more predictor variables in a regression model are highly correlated, affecting the model’s accuracy.

What are the main consequences of multicollinearity?

The main consequences of multicollinearity include unstable coefficient estimates, making them unreliable. It reduces the precision of predictors, leading to wider confidence intervals. It can also make it hard to determine the individual impact of each predictor on the outcome.

Wrap Up

Multicollinearity occurs when two or more independent variables in a regression model are highly correlated. This can lead to serious problems in your analysis. It confuses your model by making determining which variable has the most significant effect difficult.

When multicollinearity is present, standard errors are inflated. This can cause variables to appear insignificant when they’re actually important. It weakens the reliability of your model’s predictions.

With multicollinearity, the coefficients in your model become unstable. Small changes in the data can lead to large swings in coefficient estimates, making it hard to trust the results.

Interpreting your model also becomes more difficult. A high correlation between variables makes it unclear which factor drives the outcome.

If left unchecked, multicollinearity can lead to overfitting. This means your model might perform well on your current dataset but poorly on new, unseen data.

Detecting and addressing multicollinearity ensures your analysis remains accurate and insightful. Tools like ChartExpo can simplify the process of detecting multicollinearity in Excel.

Do not hesitate.

Install ChartExpo today and start analyzing your data with confidence.