KANDA DATA

Introduction

When we conduct regression analysis, it does not always produce positive estimated coefficients. In regression analysis, we often find estimated coefficients that are negative. Not infrequently, this makes us wonder: is this safe for my research?

This is especially true for beginner researchers who have just started learning data analysis. Many ask: Is the result I obtained wrong? Or was there an error in the data collection or in the model that had been previously specified and constructed?

However, one important thing to understand is that regression estimated coefficients do not always have to be positive. In some research cases, we may also encounter regression estimated coefficients that are negative.

In this article, Kanda Data will discuss and review this topic for you. I will take one example from the field of economics analyzed using linear regression analysis: how price affects consumer demand for a good X.

This article will discuss in detail, from my perspective, how to understand and interpret negative regression coefficients. After reading this article, I hope all of you will gain a better understanding of this topic.

The Function of Estimated Coefficients in Regression Analysis

Estimated coefficients in regression analysis play an important and crucial role. If you revisit your statistics materials, the general formula of a regression equation is: Y = bo+b1X1+b2X2+…+bnXn+e.
Where bo, b1, and bn are regression estimated coefficients.

The number of estimated coefficients depends on the number of independent variables used in our research. These regression estimated coefficients can take positive and/or negative values. They indicate the magnitude of change in the dependent variable (Y) resulting from changes in the independent variable(s) (X).

From this, we can learn that the sign of a coefficient is not merely a number, but carries substantive meaning that is important to interpret in our research findings.

Negative Regression Estimated Coefficients: Is It Allowed?

If we ask this question, the answer is absolutely yes. In fact, in certain types of research, negative estimated coefficients are often theoretically expected.

Let us take a case study from economic research. In economic theory, there is the law of demand which states that “when the price of a good increases, the quantity demanded will decrease, assuming ceteris paribus.”

We have known this concept since our school days. Thus, theoretically, should the expected regression coefficient be positive? Of course not.
If in a regression we find that the price coefficient is negative and statistically significant, this actually indicates that the empirical results of our research are consistent with theory.

A negative coefficient becomes problematic only if it contradicts existing theory, even though the data collection and analysis techniques have been properly conducted in accordance with scientific principles.

A Case Study in Economic Research

To better understand, let me provide a case study example. Suppose a researcher conducts a study aiming to examine the effect of rice prices on household demand. From this example, we know that rice price is the independent variable, and household demand is the dependent variable.

After conducting the analysis, the following regression equation is obtained: Y = 120-0.05X. The variable X, representing rice price, has a negative coefficient of –0.05. This means that for every increase of IDR 1,000 in price, household demand decreases by 50 grams of rice per month.

If we relate this to economic theory, it is fully consistent with the theory indicating a negative relationship. Therefore, we can conclude from the research results that consumers reduce rice consumption when prices increase.

However, an important point to note is that the coefficient must be statistically significant. Only then can we conclude that price has a negative and significant effect on demand.

Conclusion

At the end of this article, I would like to conclude that a negative regression estimated coefficient is not an error. We need to look at the research context and determine whether, according to theory, the relationship is expected to be negative or positive.
In the context of the effect of price on demand, a negative coefficient indicates an inverse relationship and is consistent with the law of demand.

This is the article I can share on this occasion. I hope this article written by Kanda Data provides benefits to all of you. Stay tuned for the next article update from Kanda Data.