## Multicollinearity Definition

Multicollinearity refers to the statistical phenomenon where two or more independent variables are strongly correlated. It marks the almost perfect or exact relationship between the predictors. This strong correlation between the exploratory variables is one of the major problems in linear regression analysis.

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In linear regression analysis, no two variables or predictors can share an exact relationship in any manner. Thus, when multicollinearity occurs, it negatively affects the regression analysis model, and the researchers obtain unreliable results. Therefore, detecting such a phenomenon beforehand saves researchers time and effort.

##### Table of contents

### Key Takeaways

- Multicollinearity refers to the statistical instance that arises when two or more independent variables highly correlate with each other.
- The collinearity signifies that one variable is sufficient to explain or influence the other variable/variables being used in the linear regression analysis.
- As per the regression analysis assumption, collinearity is a major concern for researchers as one variable’s influence on another might make the regression model doubtful.
- It finds relevance in various niches, including stock market investment, data science, and business analytics program.

### Multicollinearity Explained

**Multicollinearity in regression** is used in observational studies rather than experimental ones. The main reason behind this is the assumption that the emergence of any collinearity instance is likely to affect the regression analysisRegression AnalysisRegression analysis depicts how dependent variables will change when one or more independent variables change due to factors, and it is used to analyze the relationship between dependent and independent variables. Y = a + bX + E is the formula.read more and its results. Thus, when two or more variables correlate highly, and multicollinearity occurs, it becomes a major concern for researchers or statisticians.

Firstly, when variable correlation causes this phenomenon, the fluctuation in the values of the coefficients accompanying the independent variablesIndependent VariablesIndependent variable is an object or a time period or a input value, changes to which are used to assess the impact on an output value (i.e. the end objective) that is measured in mathematical or statistical or financial modeling.read more is quite likely. In short, even the minutest changes in the model influence the coefficients. Secondly, the collinearity affects the accuracy of the coefficients to a great extent. As a result, the statistical power of the linear regressionLinear RegressionLinear regression represents the relationship between one dependent variable and one or more independent variable. Examples of linear regression are relationship between monthly sales and expenditure, IQ level and test score, monthly temperatures and AC sales, population and mobile sales.read more model becomes doubtful as the individual strength or effort of the variables remains unidentified.

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### Causes

Conducting a **multicollinearity test** helps in the easy detection of such a phenomenon. Some of the reasons that cause collinearity include:

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#### Selections made

The first thing to keep in mind is to select appropriate questions to detect the instance of collinearity in a model. Secondly, selecting dependent variables is crucial as they might be unfit for the present scenario. The chosen dataset also has a great role in determining collinearity. Therefore, researchers must select properly designed experiments with improved observational data, hard to manipulate.

#### Variable usage

Another cause of such a phenomenon is the improper usage of variables. Therefore, researchers must remain careful about the exclusion or inclusion of the variables involved to avoid collinearity instances. Plus, researchers must avoid the repetition of variables in the model.

If users include the same variables named differently or a variable that combines two other variables in the model, it is an incorrect variable usage. For example, when total investment income includes two variables â€“ income generated via stocks and bondsBondsBonds refer to the debt instruments issued by governments or corporations to acquire investorsâ€™ funds for a certain period.read more and savings interest income â€“ presenting the total income investment as a variable might disturb the entire model.

#### Correlation degree

A strong correlation between variables is the major cause. This signifies that one variable significantly influences another in a regression model. As a result, the entire model might turn into a failure in offering reliable results. The degree of multicollinearity is determined with respect to a standard of tolerance, which is a percentage of the variance inflation factor (VIF).

If the **multicollinearity variance inflation factor** is 4, indicating the tolerance of 0.25 or lower, the phenomenon may occur. On the other hand, if it’s 10 and 0.1 or lower, respectively, multicollinearity surely exists.

### Types of Multicollinearity

Multicollinearity exists in four types:

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**High Multicollinearity**: It signifies a high or strong correlation between two or more independent variables, but not a perfect one.**Perfect Multicollinearity**: This degree of collinearity indicates an exact linear relationshipLinear RelationshipA linear relationship describes the relation between two distinct variables - x and y - in the form of a straight line on a graph. When presenting a linear relationship through an equation, the value of y is derived through the value of x, reflecting their correlation.read more between two or more independent variables.**Data-based Multicollinearity**: The possibility of collinearity, in this case, arises out of the selected dataset.**Structural Multicollinearity**: This issue arises when researchers have a poorly designed framework for the regression analysis.

### Examples

Let us consider the following **multicollinearity examples** to understand the applicability of the concept:

#### Example 1

A pharmaceutical company hires ABC Ltd, a KPO, to provide research services and statistical analysis on diseases in India. The latter has selected age, weight, profession, height, and health as the prima facie parameters.

There is a collinearity situation in the above example since the independent variables directly correlate with the results. Hence, it is advisable to adjust the variables first before starting any project since they are likely to impact the results directly.

#### Example 2

The concept is significant in the stock market, where market analysts use technical analysis tools to determine the expected fluctuation in asset prices. They avoid any indicator or variable that seems to establish collinearity. This is because the analysts aim at figuring out the influence of each factor on the market in different ways from different aspects.

### Remedies

The detection of multicollinearity changes the entire framework and arrangement prepared for conducting the observational research. In short, researchers have to start everything from scratch. Therefore, here is a list of a few ways of fixing the issue:

- As insufficient data may cause the collinearity issue, it is useful to collect more data.
- It is better to remove the predictors from the set for the variables that are less likely to represent the situation being studied.
- If there is a possibility of ignoring the degree of collinearity, given its lower value, one must not disturb the arrangement and continue with the same.
- Though multicollinearity affects the coefficients, it does not influence the predictions. Thus, if the researchers aim at making predictions only, they do not need to focus on variable correlation much.

### Frequently Asked Questions (FAQs)

**What is multicollinearity?**

It is a statistical phenomenon that occurs when two or more independent variables used in a regression analysis highly or strongly correlate. This technique is used in observational studies rather than experimental ones, given its influence on the overall regression model. It finds significance in stock market investment, data science, business analytics program, etc.

**Why is multicollinearity a problem?**

It is considered one of the major issues in the linear regression analysis as the strong correlation between the variables influences their value and changes the same as and when the value of the other variable changes. This, in turn, affects the complete arrangement prepared for the analysis by researchers. Thus, it is recommended to detect any possibilities of collinearity before conducting the regression analysis.

**How can multicollinearity be detected?**

The best way to detect collinearity in the linear regression model is the multicollinearity variance inflation factor (VIF), calculated to figure out the standard of tolerance and assess the degree of collinearity. For example, if the VIF is 4, indicating a tolerance of 0.25 or lower, there is a possibility that the phenomenon will occur. On the other hand, if it’s 10 and 0.1 or lower, respectively, multicollinearity will surely exist.

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