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Understanding the Essence of Assumption Testing in Linear Regression Analysis: Prominent Differences between Cross-Sectional Data and Time Series Data

Linear regression analysis has become one of the primary tools for researchers to explore the influence of independent variables on dependent variables. The Ordinary Least Squares (OLS) method has been a mainstay in conducting this linear regression analysis.

When deciding to use OLS, it is important to undergo a series of Gauss-Markov assumption test. The objective of Gauss-Markov assumption is to ensures the consistency and unbiasedness of our estimations, known as the Best Linear Unbiased Estimator (BLUE).

Cross-Sectional Data and Time Series Data: Significant Differences

Before delving further, we must understand the difference between cross-sectional data and time series data. Cross-sectional data encompass observations of various objects at one point in time. Conversely, time series data depict observations of one object periodically over a certain period of time.

A simple example of cross-sectional data is gathering information from farmers in a specific region at a particular point in time, while time series data could consist of observations of household consumption in a specific region from year to year.

Assumption Testing for Both Types of Data

Although they differ in collection structure, assumption testing for linear regression remains necessary. However, there are some differences in how assumption tests are applied to both types of data.

Normality Test

Normality testing is crucial to ensure that residual values are normally distributed. This applies to both types of data. However, in linear regression analysis, special attention is given to residual values that require normality testing. Normality testing can use the Shapiro-Wilk test or the Kolmogorov-Smirnov test.

Heteroskedasticity Test

Heteroskedasticity testing is performed to ensure that residual variances remain constant. This also applies to both types of data. However, testing techniques may vary depending on the type of data used. To test heteroskedasticity in linear regression analysis using the least squares method, we can use the Breusch-Pagan test or the White test.

Multicollinearity Test

This test aims to ensure that there is no strong correlation between independent variables in the regression model. This is important for both types of data, and the techniques used are the same for both. Detecting multicollinearity can involve calculating the Variance Inflation Factor (VIF).

Autocorrelation Test (Specific to Time Series Data)

Autocorrelation testing is particularly necessary for time series data. It evaluates the correlation between values in the time series with previous or subsequent values. Understanding autocorrelation is important because it can affect the independence assumption of residuals.


Assumption testing in linear regression is a crucial step in ensuring the reliability of analysis results, both for cross-sectional and time series data. Understanding the differences in assumption testing between these two types of data is important to ensure accurate and reliable analysis. By considering these differences, researchers can choose and apply assumption tests appropriate to the type of data they are using.

Based on the explanations provided in this article, we can conclude that both cross-sectional and time series data require normality testing, heteroskedasticity testing, and multicollinearity testing. However, if using time series data, an additional test, autocorrelation testing, is needed.

This article discusses the essence of assumption testing in linear regression analysis and the important differences in applying it to cross-sectional data and time series data. Hopefully, this article provides valuable insights and is useful for readers interested in delving into linear regression analysis. Feel free to discover more educational content on our various social media platforms at “KANDA DATA”. See you in our next educational article!



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