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How to Interpret Negative Coefficients of Linear Regression Output

Regression analysis is commonly used by researchers to analyze influence of independent variables on a dependent variable. But what if the estimated regression coefficient turns out to be negative and its influence is significant? In this article, we will explore and review the based on a case study where the estimation coefficient is negative and how to interpret it in an academic context.

A negative value of the estimated coefficient indicates a contrary direction of influence. It is essential to understand that there is no problem if the estimation results in a negative value, as regression coefficients are not always required to be positive.

In real-life situations, the relationship between variables may not always have a positive sign. Theoretical considerations may also lead to variables being expected to have a negative relationship. For instance, the influence of price on sales volume.

For illustration, let’s consider a case study where the estimation coefficient for the variable “price” is found to be negative. This negative coefficient implies that an increase in one variable will lead to a decrease in the other variable.

Based on this case study, we can conclude that the estimated influence of the “price” variable on sales volume has a negative direction. This interpretation indicates that an increase in price will result in a decrease in sales volume. Conversely, when the price decreases, it will lead to an increase in sales volume. This observation aligns with the theory that higher prices tend to reduce consumer demand, thereby decreasing the sales volume.

In summary, the presence of a negative coefficient in regression analysis does not invalidate the results. It simply indicates a reverse direction of influence between the variables involved, and its interpretation should be carefully considered within the context of the research question and theoretical framework.

Ensure that the Sign of Regression Coefficients Aligns with Theory and Previous Research Findings

As previously discussed in the above subtitle, the next step to be taken is to examine existing theories and previous research findings. If the estimated regression coefficients yield negative values, it is crucial to verify their alignment with established theories.

When conducting research, a researcher typically formulates hypotheses, which indicate whether the relationship between variables is expected to be positive or negative. If the estimated coefficient aligns with the theoretical expectation of a negative relationship, it is considered favorable as it strengthens the researcher’s hypothesis.

However, if the estimated coefficient is negative but theoretically expected to be positive, the subsequent step is to assess its statistical significance.

Statistical Decision through the p-value Alpha

To determine the significance of the influence of independent variables on the dependent variable, researchers employ hypothesis testing. The hypothesis is formulated into the null hypothesis (Ho) and the alternative hypothesis (H1).

To draw conclusions based on the analysis, the null hypothesis is tested. In regression analysis, the research hypothesis is typically formulated as the alternative hypothesis (H1).

Therefore, if based on the test results, the null hypothesis is rejected, we will accept the alternative hypothesis. Thus, it can be concluded that the influence of the independent variable on the dependent variable is significant.

In fact, regardless of whether the regression coefficient’s sign is positive or negative, it is essential to examine its significance. Criteria used for statistical hypothesis testing can involve assessing the alpha probability value or comparing the t-statistics value with the t-table value.

Using either criterion will lead to the same conclusion. When conducting analysis using statistical software, it is often more convenient to observe the alpha probability value, as it directly appears in the analysis output.

Based on the example case study above, if the test results reveal a negative estimated coefficient and p-value < 0.05, then the null hypothesis is rejected. Rejecting the null hypothesis leads us to accept the alternative hypothesis.

An important consideration to bear in mind is that if the influence is significant and the coefficient’s direction aligns with the theory, it is accordance with the researcher’s expectations. However, if the influence is significant, but the coefficient’s direction contradicts the theory, this needs attention and further investigation.


In essence, if the estimated regression coefficient is negative, there is no need for concern. What is crucial to consider is when the test results indicate a significant influence, but the direction of the influence contradicts the theoretical expectations.

This concludes the article I can write at this time, and I hope it proves beneficial to all readers. Please feel free to periodically check the Kanda Data website for the latest articles. Thank you.



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