# How to Interpret Dummy Variables in Ordinary Least Squares Linear Regression Analysis

Dummy variables, which have non-parametric measurement scales, can be used in specifying linear regression equations. The linear regression equation I’m referring to here is the ordinary least squares (OLS) method. As we already know, most variables are measured on interval and ratio scales in ordinary least squares linear regression equations.

However, nominal-scale dummy variables can also be used into ordinary least squares linear regression equations. In statistics, measurement scales can be divided into four types: nominal scale, ordinal scale, interval scale, and ratio scale.

Dummy variables commonly used in linear regression with the ordinary least squares method are measured on a nominal scale. These variables are often referred to as binary dummy variables.

## How to Use Dummy Variables in Regression Equations

In ordinary least squares linear regression equations, dummy variables can be included as independent variables. Therefore, interpreting them differs slightly from other independent variables.

Let’s say we have a regression equation consisting of 1 dependent variable and four independent variables. For example, we want to add a dummy variable to the equation based on the specification.

To include the dummy variable, you add it alongside the existing four independent variables. Thus, the regression equation will consist of 4 independent variables plus one dummy variable.

## How to Create Scores for Dummy Variables in Regression Analysis

As mentioned in the previous paragraph, dummy variables are measured using a nominal scale. Analyzing variables measured on a nominal scale needs to be quantified using scoring techniques.

Most commonly, binary dummy variables are used in statistical analysis. The categorization of binary dummy variables involves creating two categories with scores of 1 and 0.

A score of 1 is assigned to the category that aligns with our research hypothesis. For instance, when we want to determine whether household expenditures differ between regions, we can utilize dummy variables.

Regional differences are represented as a dummy variable of urban and rural areas. Based on the hypothesis and previous research findings, urban regions are expected to have higher average expenditures than rural areas.

Therefore, for scoring, urban areas are assigned a score of 1, while rural areas are given a score of 0. Subsequently, the tabulation of the scoring results can be used for quantitative analysis alongside other independent and dependent variables.

## How to Interpret Estimation Coefficients of Dummy Variables

After conducting linear regression analysis using the least squares method, you’ll obtain estimation coefficients for both regular independent and dummy variables.

There’s a slight difference in how you interpret estimation coefficients for dummy variables. To make it easier to understand, let’s use an example.

The estimated coefficient for the dummy variable representing the difference between regions on household expenditure is 2.5. Based on the scoring technique we discussed earlier, we can interpret this as household expenditure in urban areas being 2.5 times higher than in rural areas.

## Interpreting Estimation Coefficients of Negative-Valued Dummy Variables

If the analysis results show that the value of the dummy variable is negative, the interpretation principle remains the same.

For example, suppose the estimation result indicates a value of -1.1 for the regional difference variable. In that case, it can be interpreted as household expenditure in Region 1 being 1.1 units lower than household expenditure in rural areas.

Thus, the positive or negative sign of the estimation coefficient for a dummy variable indicates the magnitude and direction of its impact on the dependent variable.

## Testing Assumptions in Ordinary Least Squares Linear Regression

Even when we use dummy variables with a nominal (non-parametric) measurement scale, assumption testing is still necessary.

These assumption tests aim to obtain unbiased and consistent estimation results, often called Best Linear Unbiased Estimator (BLUE).

The assumption tests include residual normality, heteroskedasticity, multicollinearity, and linearity tests. In time series data, autocorrelation tests need to be added.

Based on what we’ve discussed in the previous paragraphs, we can conclude that nominal-scale dummy variables can be added to ordinary least squares linear regression equations.

However, the interpretation of dummy variable coefficients differs slightly from that of other independent variables. The positive or negative sign of the dummy variable coefficient determines how to interpret the results.

Alright, that’s the article I can write for now. I hope it’s beneficial and adds value to our knowledge. Stay tuned for more educational articles from Kanda Data next week. Thank you.