Linear regression is one of the most commonly used statistical analysis techniques to understand the impact of independent variables on a dependent variable. In regression analysis, the estimated coefficients indicate the extent to which each independent variable affects the dependent variable.

However, we often find negative estimated coefficients. What does this negative coefficient mean, and what should we do if we encounter it in our analysis? In this article, Kanda Data will discuss several steps that can be taken when we encounter a negative regression coefficient.

**Understanding the Meaning of a Negative Coefficient**

A negative estimated coefficient indicates an inverse relationship between the independent variable and the dependent variable. This means that when the value of the independent variable increases, the value of the dependent variable tends to decrease, and vice versa.

For example, if we analyze the effect of selling price on the quantity of product sales and find a negative coefficient, this could mean that the higher the selling price, the lower the estimated quantity of product sales.

**Evaluating the Significance of Statistical Test Results**

The first step is to evaluate the statistical significance of the negative coefficient. Check the p-value for the estimated coefficient.

If the p-value is less than the established significance level (e.g., we use 0.05), then the coefficient is statistically significant. This means that the negative estimated coefficient is not a result of chance, and there is sufficient evidence to support the inverse relationship in the observed variables.

**Checking the Logic and Theoretical Basis**

It is important to consider the logic and theoretical basis of the results obtained. Evaluate whether the negative relationship makes sense based on previous research and existing theories.

For example, if we find that an increase in selling price is associated with a decrease in the quantity of product sales, this may make economic sense. However, if we find that an increase in education leads to a decrease in income, this may not be logical and requires further examination.

**Identifying Potential Multicollinearity, Heteroscedasticity, and Other Assumption Tests**

Multicollinearity occurs when independent variables in the regression model are correlated with each other. This can lead to unstable coefficient estimates and coefficients that do not match expectations.

To check for multicollinearity, we can use the Variance Inflation Factor (VIF). If the VIF for any of the independent variables is high (typically above 10), this may indicate multicollinearity that needs to be addressed.

In addition, we also need to ensure that other required assumption tests are met. This is done to obtain the Best Linear Unbiased Estimator (BLUE).

**Evaluating Model Specification**

Sometimes, a negative coefficient can be a sign that our regression model is not appropriate or that important variables have been omitted. Consider reevaluating the model and adding other variables that may influence the dependent variable.

A negative regression coefficient is not always a bad thing. It can indicate an important inverse relationship between the independent and dependent variables. However, it is important to conduct a thorough evaluation of statistical significance, logical context, potential multicollinearity, and model validity.

With these steps, we can ensure that our regression results are accurate and reliable for decision-making and further interpretation. This concludes the article from Kanda Data, and we hope it is beneficial for everyone. Stay tuned for the next educational article update.