# Dummy Variable Trap In Regression Models: Everything in 5 Simple Points

## Introduction

A Dummy Variable is a statistics concept used in qualitative data analysis, time series analysis, etc. This article will review the concept of a Dummy Variable Trap and help you get a foundational understanding of the Dummy Variable Trap model. The concept is also referred to as Dummy Variables in the regression model.

## 1. Dummy Variables and the Dummy Variable Trap

Dummy Variables in the regression model represent the analysis and study of sample sub-groups. A ‘Dummy Variable’ is a numerical value that characterizes categorical data set viz., gender, age, height, weight, etc. These Dummy Variables in the regression model are dichotomous and quantitative; small discrete values that are either 0 or 1. They demonstrate the absence or presence in a categorical data set where 0 represents ‘absence’ and 1 means ‘presence.’

First, let’s understand the meaning of the Dummy Variable Trap. It is a situation where the attributes are correlated (multicollinear). In this given scenario, a variable predicts the value of other variables. If one hot encoding is used for handling a categorical data set, then a single Dummy Variable attribute can be predicted with the aid of remaining Dummy Variables. Therefore, the situation is called a Dummy Variable Trap when all Dummy Variables are used for regression models.

This is a typical problem faced when working on simple linear regression. Generally, a dependent variable is assumed to be continuous. On the other hand, the independent variables can assume continuous and categorical nature values.

The next step is to review and differentiate between the interpretation of Dummy Variables in regression analysis from continuous variables in a linear model.

## 2. Interpretation of Dummy Variables in Regression Analysis

Dummy Variables in regression analysis are known as alternate indicator variables that assume discrete values as either 0 or 1. The value of 1 indicates presence, while the value of 0 denotes the absence of a category. By default, we can use only the variables of numeric nature in a regression model. Consequently, the variables of character types need to be transformed into a quantitative variable. However, a mere transformation cannot be a Dummy Variable. It can be a dummy only if it’s created as an indicator variable.

##### Let’s look at the Dummy Variable example, which would simplify understanding the Dummy Variable Trap example.

Let’s consider a marketing case study on the impact of cost on the popularity of Mahindra Thar SUV in various Indian cities. The city location is one of the parameters of a probable influence on the cost of Mahindra Thar. Now, let’s pick four cities for the analysis – Gurgaon, Delhi, Lucknow, and Chandigarh. In this example, the city is considered as the variable name. First of all, create four variables, i.e., one each for Gurgaon, Delhi, Lucknow, and Chandigarh.

The second step would be to add them separately in the model category, rather than adding the four cities together. Only three are used because the fourth city acts as a base indicator and will not reveal any incremental information to the model category.

Now, we will need to figure out which variable is meant to be dropped – any variable can be dropped. For a continuous independent variable, Y = alpha+beta*X. Interpreting the beta coefficient as a unit change in independent variable X will result in beta times change of dependent variable Y.

Next, let us look at how we interpret the categorical independent variable. The right approach analyzes the coefficient to the baseline dummy that did not get added to the model category.

In this example of price and city location of Mahindra Thar SUV, let’s assume that Gurgaon city is dropped from the model category. If we put control for city category locations viz., Delhi, Lucknow, Chandigarh – and, if Delhi does not feature in the category or is null, then, Lucknow would receive a positive and Chandigarh would get a negative coefficient.

What the positive coefficient for Lucknow means is that when compared to Gurgaon, consumers would prefer Lucknow. With a negative coefficient, Chandigarh would indicate that it has less preference over Gurgaon, and is insignificant as compared to Delhi.

Coefficient means that consumers are unbiased in their preferences. All city locations are treated equally.

If all city locations are considered in the category model, the resultant output would be an error, and the final output could be erroneous. However, accounting is considered for all information or even if all the cities add up; yet, no incremental information is provided to the model category.

## 3. Essential Aspects of Dummy Variables in Regression Analysis

1. Dummy Variables are represented by categorical values and do not have a quantitative meaning
2. Dummy Variables are multicollinear, i.e., they are highly correlated

## 4. Linear Regression Dummy Variables

Linear Regression is the method to explain the causal relationship between dependent variables and explanatory variables using a straight line. This was the first model of regression that was studied in great rigor. Understanding this concept helps in the interpretation of Dummy Variables in the regression. Linear regression is quite useful where it can be accommodated to fit a predictive model in observed values. This can be very useful when data is forecasted.

##### Depicted below is a picture example of linear regression Dummy Variables.

Image source: https://simple.wikipedia.org/wiki/Linear_regression

The blue points denote samples. With linear regression, all the blue points can be connected using a single line marked in the color red. The example shows a relationship to highlight the fact that the distance between the line and the point can be minimized.

## 5. Terms and Terminology Used

One Hot Encoding: It is a process that enables the conversion of categorical variables into a form that could be input into ML Algorithms for better job prediction.

ML Algorithm: It is an automatic method to provide systems the ability to learn and improvise from experience without being programmed. Examples of such algorithms include deep learning, linear regression, and convolutional neural networks.

Regression Analysis: Regression analysis is to research the relationship between two or more variables and forecast a variable based on the others. In other words, there is one dependent variable and several independent variables. The dependent variable is the main factor that has to be figured out; whereas, the independent variables are the probable causes that impact the dependent variable.

## Conclusion

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